On Position Scarcity… Again
Over the years, I have written a lot about the concept of position scarcity. In fact, a quick Google search yields four such articles just on the front page (I wonder how many, if any, are hiding on page 2 and beyond!):
The Position Scarcity Post To End All Position Scarcity Posts, March 2011 (oops, guess this article didn’t actually end all position scarcity posts!)
What is Position Scarcity, Really?, January 2012
What is Position Scarcity, Continued, January 2012
On Best Player Available vs. Position Scarcity, January 2015
This time I’ll take a different avenue to discuss the concept. My inspiration was an article posted last week by our friend Rudy Gamble over at Razzball.com. It was titled Debunking Position Scarcity In Mixed League Fantasy Baseball, and in it, Rudy shared his reasons why he believed that position scarcity was essentially a myth in mixed leagues.
Rudy and I have discussed position scarcity a lot over the years and the wonderful thing is that although it appears that we disagree, we both use math and data to support our positions. So it’s a constructive back and forth that allows both us and our readers to learn. After all, we still don’t have a 100% perfect valuation system, so we don’t know for sure who’s even right!
What follows will be a FireJoeMorgan.com-style response to Rudy’s article, but without the snark and mean spirit the FJM guys were lovingly known for. Rudy has graciously approved my request to skewer him, and I’ll do so as politely as possible!
Before diving in, I want to make it clear that there seems to be several definitions of position scarcity you may be familiar with, but the only one that directly affects player valuation is this one:
In the simplest terms, position scarcity exists when there are not enough positively valued players at a position to fill up every active roster. In a standard 12-team league with 14 hitters (including two catchers), a total of 168 hitters will be drafted as starters and each must be valued and purchased at a cost of at least $1. If you projected every hitter and valued their raw stats using a $260 budget per team, there is virtually no chance that 24 catchers will make your top 168. There is also a possibility that there won’t be the required minimum of 36 middle infielders as well.
Let’s assume for a moment that this is a great year for middle infielders, so only catchers are short in your top 168. We would therefore say that the catcher position is scarce. Since we must pay $1 for the 24th best catcher, every catcher would get a bump in value to force 24 of them into your top 168. This has the side effect of causing a catcher to be valued quite a bit more than a player at a different position with the exact same raw stats.
The gap in values within a position, such as a position being “top heavy” or “deep”, is irrelevant and not related to this definition. It also has no effect on dollar value, but rather in-draft strategy. This is not what we’re talking about here.
Alright, enough of the background, let’s get on with the show (all quotes are from the Razzball article)…
To start, here is a hypothetical question. Let’s say a player is projected at 80/20/80/5/.280. Should he more expensive in a draft as a 2B or a 3B? Catcher or SS? 1B or OF?
I believe that his value does not change (except a bit with a catcher in 2 catcher leagues). Perhaps add a dollar if he has useful multi-position eligibility and remove a dollar or two for a DH. But the difference most people think exists is largely a false perception like how one might feel a ton of feathers would be lighter than a ton of lead.
Let’s answer Rudy’s question. The answer here is…that we do not have enough information. It’s not what Rudy was looking for, but it’s the truth. If you use my definition of position scarcity above, it would require you to project every player, run your valuations ignoring position, and then answering the question. But all we’re given is a raw stat line with no context, so it’s impossible to answer accurately. In a two catcher league, I would be fairly certain that the catcher eligibility should yield the highest dollar value, but that’s never a guarantee.
Rudy does not believe the player’s value would change, which is certainly possible. But then makes the acknowledgement that it might in a two catcher league. That little acknowledgement signals to me that wait, position scarcity is actually a real thing?! The only way a player’s value would change given catcher eligibility is if position scarcity existed, which is precisely what Rudy is arguing does not.
I think the belief in ‘position scarcity’ is rooted in thinking one or both of the following is true:
-Certain positions have lower floors/replacement values than others (e.g., the last drafted OF is greater than the last drafted SS) thus a player from a position with lower replacement value has more marginal value.
-Certain positions have fewer ‘stars’ and thus one gains a relative advantage vs competitors by having a rare positional star (e.g. Posey as your catcher)
The first bullet point is precisely describing the concept of position scarcity. A position with lower replacement values is more likely to not be a top 168 hitter, and therefore needs the value boost to get enough of those guys in there.
The second bullet point describes what I mentioned earlier, the gaps in talent within the position, rather than the stats available from the replacement pool. This is not position scarcity. Or call it that if you want, but it’s not what should boost a player’s value. The limited number of star catchers doesn’t increase the value of Posey.
Do certain positions have lower floors/replacement values than others and, if so, how should we handle it?
Below is a dollar value distribution by position that I took from my ESPN 12 team mixed projections (C/1B/2B/SS/3B/5 OF/CI/MI/UTIL). I broke up OF into OF1 through OF5 to fit the grid on the page.
Positions for multi-position eligible hitters are assigned in the following order of most to least valuable: C/SS/2B/3B/OF/1B/DH. The only position adjustment made was an approximate $1.60 boost to all catchers so that the last catcher is worth $1. I will revisit that decision at the end of this section. The dollars are calculated by my own methodology that’s a variant of Standings Gain Points (SGP) where I focus on a player’s contributions versus the average rostered hitter vs a ‘replacement’ hitter. (I’m overdue to update my FAQs on this after some notable changes last year.)
To me, this seems like an argument for position scarcity, not against it. Rudy admits to bumping catcher values by $1.60 so the last one is worth $1. Furthermore, the last shortstop, the one highlighted in orange in column 16 is worth -0.7. He’s crying out for a position scarcity adjustment himself! If that were to be made, suddenly shortstops would be boosted by $1.70 themselves, and all that extra money would have to be removed from other positions. We can then say that both catcher and shortstop are scarce.
Let’s take a look at the two catcher league table Rudy shares based on NFBC rosters:
Here is the same distribution for the standard NFBC roster format (15 teams, C/C/1B/2B/SS/3B/5 OF/CI/MI/UTIL). The boost to catchers to ensure the 15th catcher is at $1 is only $0.70.
Now 2nd catcher, that gets ugly. The last catcher is at negative $9 (and that’s with a 70 cent boost!). This is not surprising when you consider that: 1) You are drafting a catcher per MLB team whereas other positions are only drafting about 0.75 per team, 2) catchers average less playing time than position players, 2) catchers are typically defense-first players, and 4) catchers are more likely to do a 50/50 share (vs standard righty/lefty platoon). So how should we handle it?
Woah nelly! Check out the C2 line, which represents a team’s second catcher. The last draftable player is valued at -9 with no positional adjustment! Clearly, a team drafting this player won’t be given $9, he’ll have to spend at least $1 (or the dollar equivalent of a pick in a snake draft) to acquire him, so something needs to be done. Rudy then asks how this issue should be handled:
The traditional approach would be to add $10 to all catchers so the last catcher is worth $1 (-9+10). This would mean that drafters would divert $300 of its pre-draft hitter dollars across the 30 catchers. To give some perspective, if we assign 67% of $260 for hitter dollars and then multiply by 15 teams, it equals about $2600. So this redistribution represents over 10% of all hitter dollars. (For snake drafters, this is the equivalent of moving all but the very top catchers up several rounds).
Depending on your valuation system of choice, it won’t necessarily mean adding exactly $10 to every single catcher, but the idea is that catcher values are boosted by a high enough percentage to ensure the last one is worth $1. I subscribe to this philosophy as the math supports making this adjustment.
I can think of two instances where one could justify adding a premium to a good’s true worth (where there is no true scarcity in supply, time, etc.):
-Insurance – You reduce the risk/exposure of a worst case outcome (car crash, home damage, death, etc.) with insurance. You are paying more than it’s true value since there has to be something in it for the insurance company to offer the downside protection.
-Inflation – The market inflates the price of a required good so you have no choice to pay the premium – e.g., concessions at a movie theater.The $10 premium on all catchers does not make sense from an Insurance point of view because the WORST CASE scenario is you are paying a $10 premium per catcher by getting the two worst catchers for $1 leading to a net loss of $20. With that floor in place, you should look to buy catchers for less than a $10 premium.
Rudy and I agree on this — yes, of course you should look to buy catchers for less than a $10 premium. I look to buy every hitter at a discount to their worth. This is not specific to catcher and has nothing to do with position scarcity.
The premium one puts on these 16 catchers is largely insurance – saving you from drafting one of the below minimum bid players. The threat of being stuck with a below min bid catcher increases the more catchers taken – e.g., when you take Buster Posey as the first catcher, there is only a 14/29th chance that you were going to get a below average pick. But that last $1 catcher is your final chance to potentially buy at ‘face value’ so the odds are now 100%.
I disagree with this. The premium one puts on catchers, or any position deemed “scarce”, is a result of the quality of the replacement pool at that position. We’re not bidding a higher amount on Posey than his raw stat line is worth to ensure we’re not “stuck” with a -9 catcher. We’re bidding a higher amount because of how much better his stats are than a replacement level catcher compared to a similarly valued hitter (unadjusted for position) at a different position versus his replacement.
The formula I used for the ‘Rudy’s Premium’ column for $1+ players is:
(ABS(AVERAGE(Negative Val Catchers)+Min Bid)*COUNT(Negative Val Catchers)/29
So the premium for Buster Posey (the $22.3 catcher) is calculated as (4.4+1) * 14/29 = 2.60 with the average of the under $1 catchers equaling -4.4 (converted to absolute value of 4.4) and adding in an extra $1 for min bid to reflect that the average premium you are paying for that whole group is $5.4.
This premium increases steadily up to the 16th catcher where one could warrant the full $5.40 premium. For the below $1 players, the formula changes to:
(ABS(AVERAGE(Remaining Negative Val Catchers))+Catcher Value)
So the premium on the 29th catcher is worth (8.85)+-8.6=$0.25 with 8.85 being the absolute average of -8.6 and -9.1. In essence, your premium in this case is half the difference of the two.
Here is a grid with these calculated premiums alongside the old school method:
Rudy Gamble’s Catcher Premiums
Rank Value Rudy’s Premium Adjusted Value Old-School Premium Adjusted Value 1 22.3 2.6 24.9 10.1 32.4 2 20.7 2.7 23.4 10.1 30.8 3 11.4 2.8 14.2 10.1 21.5 4 8.5 2.9 11.4 10.1 18.6 5 6.7 3.02 9.72 10.1 16.8 6 6.4 3.15 9.55 10.1 16.5 7 5.3 3.28 8.58 10.1 15.4 8 4.7 3.43 8.13 10.1 14.8 9 3.2 3.6 6.8 10.1 13.3 10 2.5 3.78 6.28 10.1 12.6 11 2.5 3.97 6.47 10.1 12.6 12 2.1 4.19 6.29 10.1 12.2 13 2 4.44 6.44 10.1 12.1 14 1.2 4.72 5.92 10.1 11.3 15 1 5.03 6.03 10.1 11.1 16 1 5.39 6.39 10.1 11.1 17 0.8 5.19 5.99 10.1 10.9 18 -0.5 4.29 3.79 10.1 9.6 19 -1.2 3.95 2.75 10.1 8.9 20 -2.6 2.91 0.31 10.1 7.5 21 -3.5 2.3 -1.2 10.1 6.6 22 -4 2.06 -1.94 10.1 6.1 23 -4.1 2.21 -1.89 10.1 6 24 -4.1 2.53 -1.57 10.1 6 25 -4.4 2.65 -1.75 10.1 5.7 26 -6.3 1.28 -5.02 10.1 3.8 27 -6.7 1.2 -5.5 10.1 3.4 28 -7.2 1.1 -6.1 10.1 2.9 29 -8.6 0.25 -8.35 10.1 1.5 30 -9.1 0 -9.1 10.1 1 Total 40 90.9 130.9 303 343 SOURCE: http://razzball.com/debunking-position-scarcity/
First off, I have a hard time understanding the logic behind a varying premium depending on the ranking of the catcher. I believe it should either be a flat value boost ($10 in Rudy’s example) or a flat percentage boost, which is high enough to get that last catcher to a buck.
If you move over to the Adjusted Value column, you see what happens when you add varied premiums. Suddenly the ranking order has changed! The 11th best catcher is now the 10th best catcher and the 13th is now the 11th. If you look further down, you find that the former 16th ranked catcher becomes the 12th best catcher. Rudy didn’t comment on this peculiar activity in his post, so I’m eager to hear what he has to say about it.
The final sum of ‘premium’ dollars for catchers is $90.9 or $3 a catcher with the $1+ catchers at an average premium of $3.70 and the negative catchers at $2.28 (with the last catcher warranting no premium). I could see spreading these averages across all the catchers versus a dynamic premium which would be very difficult to maintain during a draft.
That is FAR less than the $300 combined premium ($10 per catcher) proposed by the traditional method.
Yes, it is certainly far less, but does that make it correct?
One additional advantage for the thrifty catcher buyer is that at least a handful of snake drafters wait until the absolute end to draft their 2nd catcher (or leave $1 in auctions). Just timing your 2nd catcher buy makes it quite easy to avoid the full $10 penalty. In LABR, I drafted Dioner Navarro in the 28th of 29 rounds after I had already taken 5 reserve picks but before 4 other teams took their 2nd catcher.
Woah, hold your horses Rudy! We’re talking about a completely different issue now with waiting on catchers and avoiding the premium. Are we interested in a catcher’s true worth or attaching a value that a thrifty catcher buyer will like and make him feel okay about going cheap at the position? How drafters behave is irrelevant as we’re only concerned with the true worth of a catcher (and whether position scarcity exists), not how easy it is to scoop them up cheaply and avoid the premium.
So my suggestions for 2 catcher premiums in mixed leagues are as such:
-Catcher Haters/Gamblers – I am in this camp. I do not want to invest a lot of money in catchers for various subjective reasons (injury prone, less reliable). I suggest no premium on catchers.
-Slightly Averse to Crappy Catchers – I would follow the ‘insurance’ model where you would add about $3-4 (or 30-40% of the traditional method). You might jump a little quicker to get a catcher near face value.
-Really Averse to Crappy Catchers – I would follow the ‘inflation’ model and add about $6-$7 to catchers. This likely leads to picking two catchers in the first 2/3 of the draft. I do not recommend this but if this the market inflation rate on catchers, it is not unreasonable.
It seems this post has taken a turn toward discussing in-draft catcher strategy, rather than properly valuing catchers and accounting for position scarcity, if it exists. Why are three groups described with different levels of premiums advised? I care only about what a player is worth and that should be a definitive answer based on the valuation method chosen. I do not believe it should be up to the drafter to decide how much a catcher’s value should be boosted.
When Buster Posey was chosen in the 2nd round of LABR by Howard Bender, he was forgoing the option of choosing a more valuable player (using position-neutral values). Let’s say he chose Edwin Encarnacion or Chris Davis to solidify 1B. Assuming he drafts Trumbo again in the 10th round, we then swap out the choice of Mitch Moreland in the 18th round for Yadier Molina. I have Encarnacion/Davis a few bucks more valuable than Posey and Moreland a few bucks more than Molina.
In this case, there is no advantage or disadvantage because all 4 picks in this example (Bender’s actual two, my substituted two) are reasonably valuable picks at those draft slots. I am not arguing that taking Posey there was a bad decision, it’s just that whatever advantage he gained in having a much better catcher than the rest of us was negated by having Mitch Moreland vs a better 1B/3B. This is why I typically view most misguided ‘scarcity’ plays to be benign (and bristle when I hear/read scarcity used to gush over a pick).
I think that this example supports the idea of position scarcity. There’s no reason to think that Bender gained an advantage by drafting Posey in the second round. And when mythically paired with Moreland, the duo should be about equal in position-neutral values to the Encarnacion/Davis and Molina pair. But that’s the point. Posey’s value was boosted due to his catcher eligibility and that pushed him into the second round. Based on his raw stats, he’s obviously not a second rounder. But doesn’t the combo of Posey/Moreland being worth the same as Encarnacion/Davis and Molina prove that the second round actually is Posey’s true value and the “premium” is justified?
‘Position scarcity’ in mixed league fantasy baseball drafts is largely an illusion except for 2 catcher leagues. In 1 catcher mixed leagues with typical roster formats, you should not even worry about positional adjustments and treat every hitter position-neutral (possibly adjusting up for multi-position and down for DH). In 2 catchers leagues, some adjustment could be made to catchers but it should be much less dramatic than the traditional method of ‘worst catcher value’ * -1 + 1 (e.g., worst catcher worth -$7 means a premium of -$7 * – 1 + 1 = $8). Based on my analysis, I’d put it at 30% of that figure.
Yes, it means you’ll have some draft-worthy players valued at less than $1 (particularly in 2 catcher leagues). But the alternative (significantly goosing up the values of all players at the position) distorts your rankings/values and could lead to making sub-optimal draft decisions (i.e., drafting catchers early – or paying more in auctions – thinking you are getting a discount when you should be diligently shopping for the best possible bargain).
How can you have draftable players worth less than $1? Proper values require every hitter to be worth at least $1 to fill all active roster slots. If everyone drafted perfectly based on those values with the last catcher worth -9, all the money is going to be spent and that last catcherless owner isn’t going to have the dollar to spend on a catcher since $10 extra was spent somewhere else that shouldn’t have been!
I’m not sure how boosting the values distorts rankings/values. To me, that’s what’s necessary to first get to accurate values. That process makes the values accurate to begin with. What makes drafting a catcher early sub-optimal? As long as you don’t overpay versus the player’s position-adjusted value, it’s perfectly fine. Overpaying for a player at any position is always sub-optimal.
—
Phew!
Your valuation method of choice should help you determine the best “premium” to add to a scarce position. The system I use does it automatically and I only know about how much is added when I change the player’s position and see how the dollar value changes. You should never arbitrarily boost a player’s value without doing the math to determine how much, if any, boost is required. You also shouldn’t calculate a player’s position adjusted value and then take that player earlier than your value suggests during your snake draft “because he plays a scarce position”. Your dollar value should already account for position, so by giving him that additional boost during the draft, you would be overvaluing the position factor.
Mike Podhorzer is the founder of ProjectingX IQ, an advanced fantasy baseball analytics platform that transforms projection data and in-season performance signals into actionable intelligence. He is the 2015 Fantasy Sports Writers Association Baseball Writer of the Year and three-time Tout Wars champion. He is the author of the eBook Projecting X 2.0: How to Forecast Baseball Player Performance, which teaches you how to project players yourself. Follow Mike on X@MikePodhorzer and contact him via email.
i didn’t read most of this, but so much effort has been put into what is essentially a pointless argument.
The dollar values you sit down with before a draft become marginally more irrelevant with each player picked. For fun, try removing all of this years first round players from your player pool, and look at the impact on the dollar values of the remaining players (this is irrespective of whether you use SGP or z score).
Further, the dollar values don’t account for how you’re constructing your team. One argument against Billy Hamilton is the negative value he creates in certain categories. But if you’ve built up a strong batting avg (say miguel cabrera betts 1st 2 rounds), your team is better equipped to absorb his weak average than another team that doesnt have as strong of a batting average base. This isn’t reflected in the $ values either.
Achieving perfection may be unrealistic, or at the least, it’ll suck alot of the fun out of draft day (by maintaining the real time changes in player value as players are picked).
Point is to not get wrapped up in how much “value” your accumulating. The value of a certain player is different to every team drafting at every point in the draft. Focus on category management.
I’m not positive I’m understanding, but if you take the first round players from the player pool, don’t you also have to take the money spent on those players out of the money pool? Which, if the players are being bought at a fair price, then it shouldn’t have an impact on the rest of your values. Paying attention to inflation as the draft goes on is more important.
I do agree completely about focusing on filling categories and players being worth more or less to different owners.
If no one agreed on filling categories, or that the category from which a player’s value arises matters, would there even be incentive for trades in-season?
No, its a hypothetical. Just imagine the 12-15 guys currently being drafted in the first round were not playing this year. The dollar values would be different for the remaining players. The cluster of the stats would be even tighter without the outliers of the first round (the top performers).
This happens after every single pick. As players and stats come out of the pool, the value of what’s left changes. The value of what’s left is also impacted by how you and your opponents are drafting. You could say a 40 save closer is worth $xx; but those 40 saves are worth a different amount to someone with 3 closers than someone with no closers.
While true, players still contribute to all categories and $values, SGP values, standard deviation points etc. all reflect that value. As the draft moves forward the differences get smaller and smaller and you’re looking for certain stats and positions instead of the marginal value differences. That’s all that changes really. The point of assigning a $value is always to try to leave the draft with as balanced of a team as possible while maintaining as much excess value as you can.
No one suggests always take the highest $value at all points of the draft because a) you won’t fill out a well rounded roster (i.e. You probably just tanked something) and b) you will almost definitely leave a 2 Catcher league with your first 10 rounds being 8 pitchers and 2 catchers if you adjust catchers upward. While possible to win that way, it’s really not recommended at all.
Nate – trades are an added wildcard to the value. I happen to play in mostly non-trade leagues. But my closer argument is a bit different if you can spin that closer off via trade.
You’re absolutely right about how values change during the draft. You’re also right about how each team’s particular roster construction affects value.
However, I disagree about pursuit of optimal dollar distribution “suck[ing] a lot of the fun out of draft day.” I do in fact track real-time changes in player value during auction drafts. And that’s the part of the draft that I enjoy most.
I hear ya; if you have a solid excel model its a bit easier too. I do so in the money leagues, but with my friends etc, it’s more about the social aspect for me.
Billy Hamilton is a great example.
In standard ESPN auction leagues, using the Depth Charts projections from Fangraphs, I have him as the third or fourth most valuable player overall. However, if I already had Dee Gordon and Jose Altuve on my team, Hamilton wouldn’t have any value for me. On the other hand, he’d be tremendously valuable to a team low on steals.
The draft manager apps that I’ve seen have a long way to go in real-time roster optimization. I use an open source solver.
With all due respect, your valuation model is broken. You are either crediting too much value to his SBs or not enough penalty to the opportunity cost of his HR/RBI.
If Hamilton 2016 was really the #3 player, he went at a massive discount in 2015 and, thus, one would surmise that their teams would dominate. Billy Hamilton had an ADP in the 101 Razzball Commenter Leagues (12 team mixed) and his teams averaged 68.7. That’s not bad (average is 65) but not enough to suggest he was a top 3 player.
These were the top 10. The only speedsters are Dee Gordon and AJ Pollock and I’d argue their appearance is more b/c they overachieved in several categories (Gordon – AVG, Pollock – across the board)
name count avg adp pts
Jake Arrieta 101 82.5 78.8
Bryce Harper 101 21.2 75.7
Josh Donaldson 101 18.5 75.1
Eric Hosmer 101 135.4 75.0
Dee Gordon 101 66.6 74.5
Michael Pineda 101 179.9 74.4
Albert Pujols 101 38.0 74.4
Gerrit Cole 101 75.7 74.3
A.J. Pollock 101 142.4 74.0
Matt Harvey 101 66.0 73.3
Rudy
Value always depends on context.
The context for my leagues:
1. 10 teams
2. 13 offensive starters (c/1b/2b/3b/ss/ci/mi/of/of/of/of/of/util)
3. unlimited transactions and unlimited starts for offensive players
4. standard roto categories
Each MLB team plays 162 games, but there are ~178 days of baseball. I can do extremely well in the counting categories by fielding a full lineup every day. Doing so last year, I did very well in R, HR, and RBI. With SB, I was only middle of the pack.
For example, using only waiver-wire players, I led six out of ten leagues in HR, but I typically finished in the bottom half in SB.
It’s easier to pick up HR off the waiver wire than steals in an extreme streaming strategy. Scott Van Slyke against a LHP at Coors has a relatively high probability of hitting a HR. That’s a lot easier to predict than forecasting the days on which Jarrod Dyson will get a steal.
I’d play in a RCL if you did auctions instead of snakes, by the way.
The Buster Posey example closes the case. Since projections are relativity close and people have different value systems it is easy to pick situations where position scarcity appears not to exist.
It seems that draft strategy is getting mixed up with actual value. For example, in a 10 team 1 catcher league I like the later catcher options so I won’t pay full price from Posey.
You could say that for every single position. That’s one reason why 10 man leagues have lower projected prices.
To Mike’s comments, you’re not necessarily wrong, but you should still understand the range of potential values for each player based on your valuations. In an ideal scenario, we’d have something that could live update for us as the draft goes on, but I know I don’t have time to build that.
As far as Rudy’s argument goes, I think at best he argues in favor of positional adjustments, and at worst ignores simple supply vs demand. The fact that explicitly different roster spots exist necessitate that their values be determined by their eligible draft pool and replacement level. If we just had all Utility positions then of course it’s a different story, but we don’t, so you can’t ignore the necessary adjustments.
My ‘inflation’ argument is supply and demand 🙂
It’s clear that, in the two catcher example, that both the average drafted catcher is weaker than the average at other positions and that pretty much every C2 would not be drafted if they were eligible at any other position.
So then the question is “How much should you adjust?” and I think I provided two alternatives that are rooted in the real world (Insurance and Inflation) versus a cockamamie truism that ‘every draftable player has to be worth $1’.
I read Rudy’s piece last week (and argued with some of it). I think a lot of the difference in these two articles comes from differing goals (feel free to correct me if I’m wrong):
Mike is striving for the most accurate valuation method. He’s looking to perfectly translate a projected stat line into a dollar value, taking into account roster size & position requirements. How this dollar value impacts the draft strategy is left unexamined here.
Rudy is primarily trying to come up with an actionable plan for drafting catchers, i.e. combining valuation & draft strategy. IMHO, the strength of Rudy’s argument isn’t the math, but rather the high-level concept of maximizing the value drafted across all roster spots.
I’m somewhat torn… on a purely math basis, Mike’s method holds up. But of course we’re not just looking to have the most accurate valuation method, but the best team (I’m sure no argument from Mike there).
The other challenging point is that being a stickler for $ values places too much confidence in a system of predicting the future. We can feel confident that our method accurately values a given stat line… but the stat line itself is almost certainly going to be inaccurate on the individual level. As a whole, projections do a much better job than almost any of us can hope to do, but on individual players, they’re all over the place.
So if we know ahead of time that our $ values are almost certainly going to be wrong, I think it’s perfectly defensible to allow bottom-tier catchers to come in at less than $0. We’re dealing with imprecision all over the place; it’s more important to have an actionable draft plan than mathematically sound values.
Having catchers come in <$1 is fine for a snake draft, not for an auction.
The reason you out give pre determined $ values on imperfect projections is that it actually gives you something to follow for what you actually believe will happen ahead of the auction or snake draft. It makes it so you don't have to blind guess how much relative value a 20/20/80/80/.280 line actually gives you.
The article is about position scarcity and every indication is that it's really only catchers that are scarce, even in 1 catcher leagues. If you're not doing an auction you don't ever need to assign $ values which means less math to adjust but you can make fine tune adjustments based on the value in whatever system you have on the last guys per position which is way smaller than people think (it's mostly a tie breaker). Whatever method you use though, catcher should be the only position that loves more than 2-3 spots in overall ranking most of the time.
I build my own valuations from projections (Z-scores) and translate to dollars. I know how to convert a 20/20/80/80 line into $$. This is not about a willingness to do the math, but rather an acknowledgement that even after doing the best math possible, the accuracy of the output is NOT high at the individual player level. Hell, if every player was within +/- 10% ($) at year’s end, my guess is that projection system would dominate any accuracy rankings.
That doesn’t mean we shouldn’t try to do the best projections and valuations possible. But valuation doesn’t get you a team. With a set of valuations that we KNOW will be wrong, I think it’s reasonable to say “screw the math, I’m letting a few catchers drop below $0 on my spreadsheet” if you think it helps build a better roster.
Hey TinDoor –
Nice point/counterpoint…except for one thing. I would argue that Mike’s valuation method is less accurate because there is no mathematical justification for making every catcher worth $1. It is accepted as a truism. It is not. The last catcher in my example is worth -$9. Just because I have to draft a catcher doesn’t magically require he be worth $1. It’s a matter of reading the market and one’s draft philosophies to determine the right way to minimize the downside of having to draft a position with insufficient depth.
Rudy
I argued against you on your blog – I can’t figure out where I’m at on this. 🙂 Trying to figure it out by asking tough questions from a couple of smart guys.
So here’s a question. It seems you both agree that, on raw-stats alone, the last catcher in a 2C league is “worth” some negative dollar amount (let’s use -$9 from Rudy’s chart above).
Using replacement value, that player is now valued as a positive contributor to your team ($1), because he’s better than the alternative (a catcher worth -$10, etc).
Rudy’s method would just call a spade a spade, and say his worth is -$9.
In both cases, the acquisition cost is just $1. The impact on your team in both cases is identical – the player’s stat line.
So two questions if a guy is dragging your team down by $9, would you just be better off with a blank roster spot? I think not – the contributions to the 4 counting categories offset any negative impact to batting average. He’s not actually worth -$9 to your roster, because if so, you would just leave the roster spot blank. Rudy, any comment on this point?
I think you’re conflating the ideas of value and cost . The last catcher drafted may earn (or have a “value” of) ($9) but if he is drafted in an auction he will cost $1.
These are being thrown around interchangeably, I think, but are not at all the same thing. Clearly not every catcher is worth $1. But every catcher drafted will cost $1.
Since it’s obvious that even a bad catcher is better than nothing (which would be valued at some astronomically negative dollar amount), any ‘premium’ one places is driven by their draft philosophy. I think on catcher, Mike and I are similar in that we are looking for the best value. I might look at his Schwarber (pre-Fowler) and say he got him at ‘true value’ and he says he was at a $10 discount!
Where it gets dangerous is let’s say one makes the $10 adjustment on all catchers and Schwarber’s going for a $2 discount (or, in my eyes, $8 premium). They really like Schwarber and think “$2 discount and less chance I have to worry about end game catchers, sweet!” Mike might be disciplined enough to avoid that but others won’t.
So, everything equal, not adding the premium is less likely for the average user to make a bad judgement because, even with no adjustments, you are more likely to grab some 3rd tier catcher at a value approaching fair value (b/c of differences in catcher values) vs paying an $8 premium.
OK. So I don’t hear you arguing with the point of the 24th catcher actually EARNING $1 (i.e. $1 more than the next actual alternative, the 25th catcher). Your comments here are back to draft strategy. You’re talking about looking at the catcher pool and identifying places where the draft cost is cheapest relative to their value.
As Mike notes, that’s the goal regardless of valuation methods. At every position, you’re trying to accumulate the most value relative to cost.
So even if you put a full $10 premium on catchers, you should still look for weak spots pre-draft and build a strategy to target players with excess value. That’s frequently at the lower end of the pool (where I tend to shop as well).
LOL, I unequivocably believe that forcing the last drafted catcher to be worth $1 is unfounded. If you have not gleaned that yet from my post or the other comments on this page, I don’t know what to tell you. I say he’s worth -$9 and that any justified adjustment using actually real-world mathematical theories like inflation and insurance, suggest a premium 30-70% of $10.
“It is accepted as a truism. It is not. The last catcher in my example is worth -$9. Just because I have to draft a catcher doesn’t magically require he be worth $1.”
This is exactly correct. I think Mike Podhorzer is a very smart person and a great writer and I love reading his work, but the method he describes makes no sense logically. Why would you have to value everyone at least $1?
Ha. I don’t know man. In theory, I agree with Mike’s valuation method. In practice, I tend to draft like you, wait it out and grab a guy cheap/late.
Sorry Rudy, but you must have a completely different definition of value than I do. I’m thinking of some kind of measure of willingness to pay.
To say that a player has -$9 value means that the player is worth $10 less than a hypothetical player who you would be willing to pay $1 for in an auction.
Presumably you want to own a catcher. If you do, then you are going to be in trouble, since you will try to pay $1 for a catcher who is better than replacement level. And any catcher after that you have valued at less than $1, presumably meaning you would not pay anything for them.
It is just supply and demand. Supply of C is low relative to 1B. If demand is the same for C and 1B, the lower supply pushes up the price.
Seems simple to me.
Here is my biggest issue with the scarcity argument:
Projections are already educated guesses as-is and we know 30-40% of drafted players “bust” or “breakout” and finish +/- 100 spots of projected value.
Now we are going to add an across the board positional fudge factor to this already approximated projection and this positional fudge factor is calculated assuming that the projections will reflect reality….. The potential compounding of errors right there turns me off positional adjustments.
It is very hard to tell where your fudge factors plus the error bars inherent in the projections end and where any actual signal amidst all that noise begins.
I think it is important to recognize that there is less skill available at certain positions and to let that reality be a tie-breaker between equivalent projected lines coming from a SS vs 1B but getting too granular with scarcity based value adjustments is overfitting.
But that’s done for you already by positional requirements and picking the best guys to fill all required positions.
I’ll give you an idea of the values for the last spots and the positions they fill in a 2C/1B/2B/SS/3B/CI/MI/5OF/U league before $value
C: 103 (C) C 24
1B: 177 (Util) 1B 24
2B: 178 (Util) 2B 20
SS: 179 (MI) SS 17
3B: 181 (Util) 3B 16
OF: 177 (Util) OF 61
DH: 196 (Util) DH 6
By my valuations everyone is relatively close for the bottom draft able guy except catcher. In 1 catcher leagues the bottom guy is still at 140. The differences between the other positions come from the next guy down being below a 177 value going into it.
The values are imprecise but what else are you going to use? Gut feel? Trying to look smart at the draft with trendy picks? These values come from somewhere, and that’s from your own thoughts on what you believe the player will do and what those stats translate to for a value. The reason to adjust a catcher up is because in my example above the worst top 12 catcher is worth as much as the worst draft able 1B because you can’t put the 1B in the catcher position.
Was this meant to be a reply to my post? All I am saying is that there is a certain degree of uncertainty in any projection as well as a certain degree of uncertainty in any method used to arrive at a positional adjustment. Furthermore the data used to calculate the adjustment uses the projection data so you are compounding the error inherent in the projections.
Put it another way: Can we trust projections to accurately peg the talent level demonstrated by a pool of players at a given position in the pre-season? Individual projections are tricky enough but pegging exactly what the 12th, 20th best SS or Catcher line is likely to be in the pre-season seems a fools errand.
I used to go through this exercise and try to make positionally adjusted values for my various leagues each year: depending on personal judgments like how many shortstops will actually get rostered or whether I am pro-rating skills vs raw projected totals replacement levels could fluctuate wildly. I found the exercise meaningless as I’d always end up making an arbitrary decision along these lines which impacted the replacement level calculations.
I guess the question I have is, where does a -$9 value come from? What is that measured against? Having what you believe is a must draft player have a negative value seems like it makes no sense, like replacement level is set too high. The last guy has to be worth $1 because his stat line (or SGP or whatever value system you use) is replacement level.
The positional adjustment for catchers comes from 2 things: a) you have to have 12/24 catchers drafted and b) their value is much lower than the last OF or 2B (who are generally comparable).
Most valuation methods put the last catcher and last non-catcher each at $1 because that’s what you can pay for them. Catchers are adjusted up for the SGP (or whatever method you use) and they have to be rostered (in your own opinion). The $1 catcher cannot be worth -$9 precisely because he is the baseline for catcher and baseline is worth $1. Comparing him to the baseline non-catcher doesn’t make any sense, in mixed leagues something like 2/3 of catchers in 2C leagues likely fall below your replacement level but again, have to be drafted. That’s precisely why the positional adjustment is made. Every other position is close enough that it changes on the order of cents for most players in most non-yahoo roto leagues.
I think his reasoning makes sense if you have the negative valuation, but having the negative $ value is what’s wrong. It makes no sense that a player you think will have to be drafted is a negative value
Scotsman sorry I didn’t mean to repost to you (twice now) I don’t know how that happened except to say that I’m posting from my phone
Projection error and player variance is a key issue for me too. In most leagues, there are only about 100 players who are likely to offer positive value even if they underperform by a bit. Everyone else is split between a)a personal choice about whether they will outperform the projections or b)’so what?’
Me? I spend my time identifying those 100 – and the people I think will outperform – and I don’t draft anyone from outside that pool until it is empty. I have often found myself near the end of the draft either ‘needing’ to fill a scarce position that the draft software forces you into taking – or walking away from the draft with the position unfilled.
If I have to fill it cuz the software says I have to – well OK that’ll be my last choice. But avoiding ‘scarcity’ has never really created a problem for me. Because I never do have scarcity in what matters. I always have trade chips to acquire what I need to. And even if a trade doesn’t happen, I will almost inevitably see those ‘better’ marginal C’s and SS’s dropping into the waiver pool soon after the season starts – and I’ve got the worst of that group anyway so I can act even faster to pick up the typical undrafted guy who now gets playing time cuz of injury.
Leaving a player slot empty is also not an earthshaking tragedy either. Most of those marginal players actively harm your ratios (so empty is better) and their counting stats are easily offset by having valuable players on your bench for awhile or having platoon options or somesuch. Better to have a player like that on your bench than in the player pool (and soon on someone else’s team). This works even better with relievers. While everyone else is getting ERA/WHIP hammered trying to get that one extra save from closers who everyone knows suck, I’ve got middle relievers pushing my ratios (and K’s – and more often than you think vulturing wins too) to unbeatable very early on
Mike –
Thanks for the thoughtful review.
Two clarifications/rebuttals:
1) The vast majority of mixed league players are in 1 catcher leagues and, in my eyes, use the illusion of position scarcity to pay premiums on C/2B/SS that I think the charts show should not exist.
2) Our fundamental difference is in this quote: “Depending on your valuation system of choice, it won’t necessarily mean adding exactly $10 to every single catcher, but the idea is that catcher values are boosted by a high enough percentage to ensure the last one is worth $1. I subscribe to this philosophy as the math supports making this adjustment.”
That is just wrong. There is no mathematical or economic imperative that requires every player to be worth $1. Doing that through the traditional method (I can’t speak for yours but the FG calculator mirrors it) means that you are distorting every catcher’s value up to the absolute worst case situation.
The insurance and inflation model show that this is too high of an adjustment. The same would be the case in, say, a Yahoo! 12 team format if 11 Shortstops are $1+ and the 12th is -$0.70. If everyone else pays a $1.70 premium, then I can take the 12th for $1 at no market penalty (because I got players at $0 premium where everyone else reached for their shortstop).
Rudy
Aren’t you paying the $1.70 premium for the last shortstop by spending $1 on a -$0.70 player? Everyone would be taking the same net loss if they add that premium and every player then goes at fair value.
Right, why should everyone who doesn’t draft the last SS pay the same penalty?
If you were forced to choose 1 of 12 envelopes where 11 had $100 bills and the 12th had an invoice for $1,000 OR you can pay a bribe and get tipped off so you’re ensured a $100 bill, would you bribe and, if so, how much?
The expected value of choosing an envelope in the first example would be $8.33. So the bribe would be at max an amount that would yield at least an $8.33 expected value. So $91.67 is the maximum bribe I’d pay.
Mike –
Exactly. I totally agree. Expected value of $8.33 (11*100 – 1000)=100/12=$8.33. $100 – $8.33 = $91.67.
You could even justify a little more if you like for ‘insurance’.
While catcher values are not this extreme, I’m arguing for the same logic.
The $1,000 invoice is worth -$1000. Just because we have to pick an envelope and that may be one of them, it doesn’t magically make it worth $0. We just have to think about all net-positive selections and revalue them based on the potential for net-negative selections. In this case, we put a $91.67 premium on a $0 pick solely to fray the negative outcome.
BUT $91.67 is a looooot less than a $1,000 premium which represents the worst case outcome.
Hence, my insurance model looked at the s***show at C2 and says that the ‘premium’ to avoid negative outcomes is about $3-$4 instead of the absolute $10-$11. How’s that different?
If you are required to fill your roster and pay at least $1 per player then the best available player is worth at least $1.
Ok, so what if we played in a 3 catcher league? Last catcher still a $1?
What if I made some crazy rule that said, “The last team without a catcher gets zero stats in that position and it’ll cost them $1”? Is that still worth a $1?
Alex–
Again, this is incorrect. The last player rostered will cost $1. Many players will not earn $1.
Ok I think I see where you’re going wrong. Positional adjustment is not so much about what that last guy is worth. It’s about how much more the better guys are worth. So in your 30 catcher league, you say the last guy is worth $1, then you adjust everyone else so that they are worth whatever they should be above that guy.
In your crazy rule league, you should value the 2nd last and better spots at some huge multiple based on how much better the 2nd last catcher is over having an empty spot.
What a player actually earns is a whole different question than what they are worth in an auction. Mike Trout may not earn $1 this year.
Not sure what you’re saying there. Based on the requirement that the last draft-worthy player HAS to be worth $1, I’m testing your theory. So what is the value of Ryan Hanigan in a 12-team standard format except 5 catcher sports versus one? If he’s -$20, should I increase all catchers by $21?
Provide a real world example where this truism that everything you purchase must have a net positive-to-neutral value (i.e., since you are paying $1, it must be worth $1).
> should I increase all catchers by $21?
Not quite, what you do is set Hanigan’s value to $1, then recalculate everyone else’s value as multiples of Hanigans. So if Posey is 20x better than Hanigan then he is valued at $20.
Last year, I participated in ten 10-team standard ESPN auction drafts. I only bid on pitchers; I didn’t spend more than $1 on any position player. I didn’t use any bench spots for position players.
Using Razzball’s Hittertron (which I believe is Rudy’s work), I fielded a full lineup of hitters everyday. I dropped any hitters whose teams had off days. I usually did not place waiver claims, so all my hitters came from the daily free agent pool after all the other managers had a chance to pick through.
My average catcher line: 78/23/91/2/.274
Average 1B: 80/27/88/4/.265
Average 2B: 97/20/88/11/.285
Average 3B: 87/30/106/6/.276
Average SS: 83/17/72/12/.274
Average CI: 79/22/84/4/.254
Average MI: 85/15/68/8/.264
Average OF: 97/24/81/13/.284
Average Util: 83/22/80/7/.267
In a league with unlimited transactions, I definitely would not spend more than $1 on a catcher. Last year I got Posey-level production from the waiver wire.
However, based on the Depth Chart projections, I would spend for Carlos Correa or a top-tier 1B. Mike Trout is projected to be most valuable in my leagues, but (using an optimization algorithm) Paul Goldschmidt is worth slightly more because of the relative scarcity of waiver-wire 1B.
yes, you have to be clear on whether you mean projected auction price or projected end of season value. Every player who will be rostered has a minimum price of course, but the projected benefit to your team could be substantially below $1. I can see Rudy wriggle admirably, but the very fact that a projected price for a set of players will be substanially higher than their projected value demonstrates position scarcity. There may very well be no position scarcity in ESPN 10-team mixed leagues, but there just as certainly is scarcity at catcher in NFBC 15-team two catcher leagues.
Several comments have been written in the time it took to post this, but I’m doing it anyway.
I’ve spent a couple days thinking about Rudy’s article and replicating his points method (with the limited info I have). I’m with you on scarcity.
Regarding your comment about varied premiums, “If you move over to the Adjusted Value column, you see what happens when you add varied premiums. Suddenly the ranking order has changed! The 11th best catcher is now the 10th best catcher and the 13th is now the 11th. If you look further down, you find that the former 16th ranked catcher becomes the 12th best catcher. Rudy didn’t comment on this peculiar activity in his post, so I’m eager to hear what he has to say about it.”, I believe this is dynamic.
You don’t pre-draft make the 11th best catch the 10th best catcher. The $3.97 premium applies to the 11th positive value catcher sold in auction (whether he’s ranked #1 or #16, so long as he’s positive). A player’s projections don’t change during the draft – should his dollar value?
If you don’t use an application to update values during the draft, I actually like the idea of using a premium to estimate it (and estimating inflation).
However, I also like the idea of making draftable players worth negative values. Why do draftable players have to be worth >$1? Just because you must bid a dollar doesn’t mean the player is worth it.
I posted above, but thinking about this last point specifically. If a player is worth -$9, that’s saying the player is literally hurting your team. You’d be better off with an empty roster spot than a -$9 player, right?
But of course this isn’t true. You’d lose 40 R, 40 RBI, 10 HR, and 2SB, even from the 24th catcher out there. You’d rather have those stats on your team (even with a .220 avg) than an empty roster spot.
So it’s not ‘real’ to say the player is worth -$9. He’s $1 better than the best actual alternative you have (the 25th ranked catcher), so he’s worth $1.
Well, that depends. How free is free agency?
If you can pick up a catcher after the draft, you’d be better with the empty roster spot. I do this in fantasy football all the time, drafting a high risk/reward RB instead of my kicker.
If you account for ratio categories, it absolutely is possible for players to have negative value.
A low strikeout pitcher who doesn’t get wins, for example. If he has a bad WHIP and ERA, you might be better off leaving the pitcher slot empty.
I know it’s possible to have a negatively valued player. But catchers are not that situation. 4/5th of hitting categories are just raw number accumulation. So ANY R/RBI/HR/SB is better than any empty C2 spot, and if the average is truly abysmal (like .150), that catcher won’t be the 24th ranked and you’ll have someone else.
Why can’t no catcher = -$50? Just because you have to take a catcher at $1 does not mean he is worth $1. That would mean you got him at value when, in my example, you are paying a $10 premium. If anything, you use the inflation example I provided of about $6 and, at least, it shows he’s a -$4 vs market average premium player.
Certainly a catcher could be worth -$50. In this hypothetical, what does the rest of the catcher pool look like?
If the rest of the pool is normal, you just wouldn’t draft that player (24 other catchers would be better, obviously).
If the rest of the catcher pool is similarly skewed so that this guy is one of the top 24, you’d have to calculate whether or not an empty roster spot is a better choice. Considering that 4/5ths of the categories are counting, even the worst player is likely better than 0 stats.
So at that point, this player is HELPING YOUR TEAM because they are adding counting stats, and better than all available alternatives for the roster spot. Isn’t that the definition of a positively valued player?
What I’m starting to question isn’t “does the -$9 catcher that I buy for $1 help my team”, but rather “would it be a better strategy to ensure I don’t draft negative value players”? Maybe I can spread the premiums in a way that’s more optimal. Maybe the full position scarcity adjustment (+$10 to all CA) is the best method. It’s league dependent, and I want to test it more rather than just assume.
This is the fallacy of ‘replacement player’ valuation. The assumption that every player’s contribution in non-ratio categories MUST be positive value.
If you have 12 envelopes that each cost $1. You have to buy one. 11 have a $1 in it. The other has a dime. It’s positive value so it’s better to take that 12th envelope than just donate your $1.
Is that envelope worth -$.90, $0.10 or $1?
The envelope analogy isn’t valid, because there’s a known, true/fixed value ($.10), as opposed to our problem of converting varied stats in fixed roster spots into $$.
Let me try it this way. How do you set the bar at $1 for the ENTIRE player pool? Let’s say 12-team league, 14 roster spots, 168 players. You convert individual categories into a total number, and then convert to auction $$. Or you convert each category contribution into a number, and then into $$.
Either way, you’re benchmarking an individual player’s contribution to a category against the alternatives . When you’re dealing with the full player pool, those alternatives are everyone ranked 169 and lower. We know we can get player 168 for $1, and he is worth more than player 169.
This is exactly what we’re talking about with Catchers. We’re valuing an individual player’s contribution against the alternatives, which in this case is all the catchers ranked 25 and lower. We know we can get catcher 24 for $1, and he is worth more than catcher 25.
The envelope analogy is valid. That’s $0.10 vs $0. It has positive value!!! What if it was $0.50 instead of $1? That purchase still has a net negative value even though it is better than nothing. That’s what I consider catcher purchases to be at the lowest levels.
If you are using dynamic premiums, it will inevitably lead to a situation where one player’s value jumps over someone who is better. You couldn’t apply a dynamic premium before the draft because you don’t know what order the players are drafted.
That is why I suggested just taking the average premium if applying it before a draft.
But if someone has to pay $1 for a player whose value is -9, that premium on price — not value, but price — is the result of excess demand or insufficent supply, which is to say scarcity.
Yeah, it’s pretty easy to see that Rudy is unequivocally wrong in stating that position scarcity is a myth, but kudos for pointing out that he applies it even while denying its existence. If Rudy had argued that position scarcity is often misapplied or overstated then I would agree with him, but denying it entirely is easily proven false.
In an extreme hypothetical two team points league that uses only a catcher and an outfielder, you have four players to choose from. Catcher A is projected to accrue 10 points, Catcher B is projected to accrue 50, Outfielder C is projected to accrue 60, and Outfielder D is projected to accrue 70. A person who did not consider positions would take Outfielder D with the first selection of a snake draft and they would obviously lose, as D+A = 80 points while B+C = 110. A player’s actual value is determined by how they compare to the worst alternative at his position that has to be used by some team. Obviously in real leagues the difference won’t be anywhere near as dramatic as in this extreme hypothetical, but the effect clearly exists.
Where in my post does it say it’s a ‘myth’? The title says ‘Debunking’. The conclusion is “‘Position scarcity’ in mixed league fantasy baseball drafts is largely an illusion except for 2 catcher leagues.” Could I have used a slighter word than debunking, maybe. But that was Mike’s misinterpretation of my POV or your misinterpretation of his interpretation – not my words.
Sorry but those simplistic hypotheticals are worthless. Here’s a more realistic one that summarizes my POV. If you are in a 12-team Yahoo league where 11 shortstops are valued at $1+ (without adjustments) and the 12th SS is at -$2, then we know that the last person to take a SS is taking a $3 hit in value. WHY WHY WHY would one convert that -$2 to $1 and then, to make sure everything’s even, add $3 to the other 11 shortstops only to ensure that EVERYONE has to pay the $3 premium that only the 12th guys is forced to accept.
In your example, wouldn’t it make sense to pay $2 more for the 11th SS to avoid paying $3 extra on the 12th?
If the 11th SS is worth $1 and the 12th SS is worth -$1, then one could justify paying up to $4 for that 11th SS. That’s the math in the dynamic insurance premium I provided. But that same $3 extra doesn’t apply to the first catcher drafted b/c there are 10 other chances at paying face value.
The part where you wrote: “the concept of ‘position scarcity’ (aka boosting up the values of certain positions like C/2B/SS) in mixed leagues is false.”
While it is an understandable reaction to be dismissive of something that proved you wrong, it undermines your credibility in future discussions because it illustrates that you prioritize the appearance of being correct, or at least the ability to pretend as much, over the genuine pursuit of knowledge and understanding. I acknowledged right from the start that my hypothetical was an extreme case, but I employ those kinds of extremes precisely because they allow us to test the underlying principles of the subject. That extreme, unrealistic hypothetical definitively showed that just picking points values without regard to positions is a mistake.
Because that’s what the actual value is due to positional requirements. Why do we calculate replacement value at all? Why don’t we just use raw totals with no consideration of baselines? We calculate from replacement because value is relative. Maybe you would be better able to understand this if you also had a background in fantasy football, as some people struggle to understand why quarterbacks aren’t inherently the most valuable players even though almost all points systems have them posting the highest raw points values.
In theory, since you have a 1 in 12 shot of ending up with the worst SS, wouldn’t a $.25 premium on the 1st SS taken be the break even point?
Secondly, is it worth it to pay a premium for a player that will be in the starting lineup for a team as opposed to the bench? Say the 13th 1st baseman(only can start 12 in the league) is worth $3, and the 11th SS is worth $2 and the 12th is worth $1.
You’re right in that I should’ve qualified that ‘false’ like I did in other sections of the post. But I think a full read would’ve made it clear that my focus there is standard mixed leagues are not two catcher (at least amongst razzball readers). The misadjusting of 2B/SS early in drafts because of perceived position scarcity is what bothers me the most.
I do not employ position adjustments (aside from the noted nominal catcher adjustments in the post). I am basing player $ based on SGPs against the average drafted hitter based on the modeled universe (so a composite of all positions) and then creating a general replacement level and then a $/SGP multiplier.
So based on my calculations, I’m saying that 11 of the 12 SS are worth $1 or more. If that’s the case, and the 12th is worth -$1, how much premium do you put on each of the 11 shortstops knowing that, if you wait until the end, you get a -$2 return on your money?
I fully understand the strengths and weaknesses of replacement-level valuation. I can’t speak for football player valuation but my clear preference is for average-level valuation. For MLB players, there is WAR and WAA. WAR is way more popular and I think that’s because there are so many AAAA players in free agency or on major/minor league rosters. Okay bat, awful glove. Vice versa. Plenty of them.
But in fantasy baseball, I think it leads to the misvaluing of players. I subscribe to the theory that one should not make adjustments (particularly dynamic calculations) unless sure they do more good than harm. Basing the premium on all players at the position on the value of the ‘replacement’ level where natural volatility could cause a range of several dollars is the epitome (for me) of why one should rethink beliefs like “I should adjust based on replacement level” and “I need to make every draft-worthy hitter worth $1 and, thus, boost every other player at the position”.
The 12-team example above – and my alternate theories around insurance and inflation – do just that. So, if you could please answer that question…
OutOfTheBox – Yes, that’s what I argued in the dynamic insurance model where you are paying a premium to insure you don’t get the negative value.
The principles don’t change. I agree that positional scarcity is generally less pronounced in shallow mixed leagues because the baselines tend to be more similar and don’t have that massive drop that you see at catcher in two catcher leagues, but it’s important for you to recognize that positional scarcity still exists in every league even if the positional adjustments you need to make are negligible. Again, I would have agreed with you wholeheartedly if you had written that many people overestimate the positional adjustment (usually because they guesstimate it rather than calculate it), as I have preached that myself. But in any game where players are assigned particular positions and teams are required to select players from those positions, positional scarcity will exist.
You’re still confused. All of them are actually worth the extra money because their value is relative to the baseline for that position. If you can get one of them for less than their actual worth, that’s awesome, but it doesn’t change what their actual worth is.
Back in the late ’90s when I began writing about fantasy baseball and doing my own valuations I too started by calculating from the average. John Mosey quite successfully berated me into using the replacement level by illustrating how calculating from the average tends to distort the results, particularly at each extreme.
I did answer it, but you want to believe what you want to believe regardless of what anyone else tells you.
Okay, we agree that most people overestimate position adjustments in shallow leagues. And, agreed, that’s because they guesstimate or perceive it being large.
Regarding average vs. replacement, note that I’m using the composite of all rostered hitters – NOT the average at the position. So two catcher 15-team league, that’s 210 hitters. Everyone against that composite and that difference in the stat category is then valued against SGPs. No comparisons vs the other positions. My POV being that, after accounting for all CI/MI/UTIL selections, it is best to do nothing unless there are significant differences at the bottom of a position.
Please correct me if I’m wrong but the replacement level you are talking about is based on one player. So you are saying that if the 12th SS is -$1, each SS is worth $2 more. If the 12th SS is worth $2, each SS is worth $1 less.
How is a method using one (or even the last couple) hitter’s value at a position less extreme or distortive than my method using the whole rostered player pool to determine a baseline?
Does it not strike you as counter-intuitive to (in effect) add a $2 premium to all players at the position and accept the same value penalty (-$2) than the poor schmuck stuck with the last SS is forced to accept?
Incorrect. It is based on a grouping of players around that level.
Correct, because in any game where positions are fixed and required for lineups, value becomes relative. Learning more about fantasy football and why quarterbacks aren’t all first round picks despite being worth far more in total points than other players would presumably help you understand this.
Mosey could explain this better than I, but it’s where you draw from that creates the distortion. When you’re measuring from the middle of the pool it causes both ends to be distorted, particularly for ratio categories.
No, because that’s the actual value. You continue to get hung up on the raw value as is there were no positional requirements. How much more is the eleventh shortstop worth than the twelfth? $3, correct? And how much more is the tenth worth than the eleventh? How about the ninth more than the tenth? In your scenario you’re demanding that the value differences magically disappear at some point.
I’m just going to agree to disagree with you on this as neither of us is convincing the other. I do appreciate the time and effort you put in to state your side. I apologize that I wasted your time with what you consider a position being without merit.
To summarize why position scarcity only counts for catchers in two-catcher leagues:
Non-catcher hitter values range from ~$40 to $1. The replacement level hitter value for ALL HITTING POSITIONS BUT CATCHER will be a little less than $1.
Catcher values are typically between $25 to -$9. The replacement level value for replacement catchers is thus < -$9.
The premium placed on catchers is the alternative to being forced into taking a -$9 catcher that you have to pay a buck for.
You do not need to do this at any other position.
You generally don’t need to make significant adjustments for other positions because their replacement levels tend to be similar, but that’s not always the case and you can illustrate that quite easily by fiddling with roster settings. Take a conventional fourteen position player league with two catchers, then replace two of the outfielder spots with a duplicate CI and MI. Do the values of outfielders stay the same or would they change? Obviously the outfielder values would scale downward.
I position scarcity does exist, but I would argue against using a positional adjustment to capture it. The method I prefer is to basically calculate the value-over-replacement for each category at each position, and then create values based on that pool off numbers. For example, if Buster Posey projects for 80 runs scored, and the last catcher drafted projects for 30 runs scored, then Posey will account for 50 runs over-replacement. Now let’s say that Andrew McCutchen projects to score 100 runs, but the replacement level OF will only score 50 runs. McCutchen would ALSO be worth 50 runs over-replacement, meaning that he and Posey have the exact same value in runs scored for your team: 50. Since every team should expect the minimum stats from a position, creating values based on over-replacement stats gives a better sense of the true value of a player to a team, and it builds positional scarcity into the value!
Ding ding ding. This is precisely what the valuation method I use does! No need to arbitrarily boost a position for scarcity. Doing the calculations for stats over replacement at the position already reflects any scarcity, if it exists.
Does the distribution matter?
For example in a 5 team league shouldn’t a distribution of
80,80,80,80,30 yield different values for Posey from 80,30,30,30,30?
Yes, because value is calculated based on the player’s share of the pool above replacement. So in the former the category dollar value would be divided among 200 runs above replacement whereas in the latter it would be divided among only 50 runs above replacement.
If you do this then you have to be careful to make your replacement baselines from a grouping of players around that level rather than a single one, otherwise you run the risk of your “worst player taken” (or “best player not taken” if you prefer) baseline being misleading. For instance, if the last catcher drafted projects for 30 runs scored but has a .280 average then you’re going to wrongly devalue batting average for the catchers above the replacement level by calculating from that point rather than a more representative baseline.
You are correct JD, good point. I take a sampling of players for the replacement group, generally about 10% of the number of starters we have to draft.
I’ve been thinking about position scarcity a lot recently because I’ve been rolling my own rankings for the first time (NB: it’s easy and hard at the same time, which means, THANK you for your hard work, men and women of fantasy websites everywhere!). Most of my leagues are Yahoo! H2H category leagues with snake drafts. These are 10 team leagues with a mere 9 or 10 hitter spots and deep benches (6 or 7). Most of the advice on position scarcity comes from 1 or 2 catcher leagues, leagues where have to play 5 OF, and leagues with a CI and an MI slot and from roto leagues, which just isn’t true of these Yahoo! weekly leagues. It’s nice that you have cumulative totals as a proxy of player value, but it’s not the whole story in a weekly league with a shallow player pool. For example, according to my admittedly noobtastic math, there are only 5 catchers that are worth a damn (based on zScores and an average of multiple sets of projections), which lead me to conclude: if half the league has a crappy catcher, there is little comparative advantage in having a good one, let alone paying a premium at that position, especially if it costs me an everyday player with legitimately better stats (or likelihood of having a good week). Only ten catchers have to be drafted anyway, so it’s not like they are all that scarce given that 30 major league teams really do have to put a catcher behind the plate every game. Basically, I’m saying that Rudy’s reasoning on this makes sense to me, but I often play in the shallow end of the pool. In other words, do y’all think that the size of the positional scarcity adjustment could actually be a function of the size of the player pool? Is there a tipping point in the player pool where position scarcity begins to matter more or a threshold beneath which positional scarcity has a negligible impact on player value? So, like Mike and Rudy are both right, some of the time?
Another question that keeps coming up for me is how do you deal with negative player valuations in the context of the snake draft. It seems necessary to adjust negative dollar values to positive ones in the context of an auction where you have actual costs, but I am using the calculated dollar values as a measure of relative value. In other words, the 6th catcher and beyond are below average players, regardless of what I pay for them in terms of draft pick. There’s no need in a snake draft to adjust negative dollar values because the ADP/round information is what matters, right? Or rather, as a positive question: how do you create clear and meaningful rankings for a snake draft? I’m using dollars because it’s easier to differentiate pennies than rounds and I sort of get what the dollar value means, whereas the zScore is just a number. Like I said, I’m new to this.
I promise to play in harder leagues as well and even take part in an auction draft. But bros before strangers in a random public league, am I right?
First off, position scarcity adjustments are going to be very dependent on league settings. So yes, in your shallower format, adjustments likely will be different.
However, being that half the league is going to have a negative catcher doesn’t change the concept. The point of the position scarcity boost is that pairing Buster Posey with the worst first baseman is going to better for your stat line than a first baseman with the same position neutral value as Posey and the worst catcher. Once we boost Posey’s value with a position adjustment, he’s suddenly going to have the same position adjusted value as someone like Encarnacion, for example. Now, the Posey/worst first baseman and Encarnacion/worst catcher should be valued the same. That’s why Posey deserves to be paid more. If he’s not given that premium boost, whoever drafts him will be at a significant advantage since his production is so much better than the worst catcher.
I don’t really understand the notion that you don’t need accurate values for a snake draft. You still need to rank all your players in the correct order, mixing in all the positions.
I see. The Posey/worst 1B vs Encarnacion/worst C example makes a lot of sense to me. Thanks for that.
Sorry for the lack of clarity on dollar values. I guess what I am asking is how do you create accurate values for a snake draft? It makes sense to adjust the replacement player’s dollar value to $1 in order to get the correct value and ranking because in an auction, you have to play at least $1 for the player. That’s a practical fact. But in a snake draft, isn’t relative value still captured if you make a VORP adjustment, even if that happens to be a negative number? Or does the fact that VORP is negative indicate a need to refine my VORP values?
Sorry for the down vote. I am new here!
The same way you create accurate values for an auction. It’s the same thing, regardless of which method you use to acquire your players. You still have to boost the catcher to make the playing field level across all positions.
there is no such thing as a hard or easy league based on just settings. You still have to beat all the other teams under the same rules.
I am looking forward to a time when this topic changes to one of Opportunity Cost, not “positional scarcity”.
For a simplified example, let’s say you have to $10 left and 1B and C left to fill — let’s say you pay $9 for a 1B that will earn you $10 (nice buy!) but that forces you to pay $1 for a C that is projected to earn -$9 (ouch!)… then those $10 you spent will earn you a total of $1 (OUCH!).
Let’s say the alternative scenario you could have spent $5 on a 1B that will earn you $4 (ouch!), but that allows you to buy a catcher for $6 that will earn you $0 (ouch!). This second scenario allows you to end up with a more value 1B/C combo ($4 total value), even though you didn’t get a good “value” for either player.
The opportunity cost for buying that nice shiny 1B with an apparent $1 profit actually ended up costing your team because in the end you got stuck with crap for catcher. So in the end, even if you don’t want to pay $6 for a catcher that will earn $1, be wary that in the end you might get stuck with a worse value later (like spending $1 on a -$9 catcher).
One thing worth noting that I mentioned in my post is that 2nd Catcher gets so bad that those picks happen in the quasi-reserve rounds of drafts – not where you’d be taking, say, a $1 pitcher.
I love this debate. Reading Mike and Rudy argue over this is like listening to Edison and Tesla debate electricity.
I’m more in the Mike camp (for the opportunity cost reason that chadkay offered), but one “real world” complication that enters works in Rudy’s favor. The actual pool of stats available is not the same as the projections. We don’t know what the pool of stats will look like during the year, and the true replacement level for each position is largely determined by the stats of the free agent scrubs and minor-league call-ups who go undrafted. Plus, the effect of the Utility position is to spread those players to replace the worse position players. Just because your model shows that the 12th SS in projected stats is worth -$5, that is not the true replacement level due to the uncertainty in stat projections and all of the undrafted players. (And if someone can model that, I want to see it.)
The impact of that all is that player scarcity as a concept is real, but might only practically matter in extreme cases like 2C leagues (or perhaps if we played back in the 70’s when MI couldn’t hit a lick.)
You’re giving Rudy far too much credit by comparing him to Tesla, as his argument really has no merit whatsoever. He’s presenting a lot of verbiage that sounds valid, but when you break it down as Mike did and examine the actual calculations, the claims no longer make any sense.
That’s not Rudy’s argument at all, but you are correct that the baseline is sometimes different from what we initially project, and you’re definitely correct that some deemed below replacement level will end up being above it (while some above will end up below). That uncertainty doesn’t change the mechanics of the calculation, however, because we know that’s the correct way to calculate values that are known and we have no way of accurately predicting how off our values will ultimately be. The only way this uncertainty would help Rudy’s argument was if catchers routinely have a higher eventual replacement level than the projected replacement level, but that isn’t the case.
This is a great point. The utility slot absolutely does function as a smoother of baselines to bring the replacement level of multiple positions closer together. I keep going back to football because it’s easier to demonstrate there with fewer positions and raw points totals, but this is exactly what “Flex” slots are designed to accomplish. The Utility slot is why we generally don’t see that much differentiation between non-catching baselines. Without it, you would see more of a difference. That’s something you’ll notice if you calculate your own values.
Put me squarely in the pro scarcity camp. It seems pretty intuitive to me that the distribution of projected “value” (i.e. end of year earning) at a given position group SHOULD affect your strategy for acquiring players/stats/value in an auction/draft. Take a simple (albeit extreme) example comparing two position groups in a basic 10-team leagues:
Position Group A (Projected EOY value, not auction cost)
Player 1: $15
Players 2-10: $5
Position Group B
Players 1-9: $30
Player 10: $21
Which player should be drafted first (i.e. Who has the highest value)? Taking the projections at face-value, I would argue its pretty clear that Player A1 is the most valuable player, even though he generates a significantly worse “line” than everyone in Position Group B. The manager who acquires Player A1 has banked a $10 lead over everyone else in the league since each team must play 1 player from Position Group A. That manager will give back $9 of that lead because he is stuck with the worst player (B10) in Position Group B but on aggregate he’s ahead $1. If you buy that then its pretty easy to extrapolate that argument out to a league with more than 2 positions. This line of thinking ties in directly to the concept of tiering- you always want to acquire the last player in a given value tier.
That’s the easy question, though. The harder question is when looking at a real-world distribution of projected values in a given position group and taking into account he “average player” and the “replacement player”, how do you formulate a player acquisition strategy.
But “scarcity”, at least as I define it, is definitely real. If Rizzo gains Catcher eligibility tomorrow, of course his draft slot/auction value goes up, even though his projected line doesn’t change, because he’s now being measured against an objectively weaker pool of ownable/draftable players.
I’ve always wanted to conduct an experiment where a bunch of smart people did a mock draft/auction of fixed stat lines, rather than players. If every manager knew exactly what every player in the pool would do over a 162 game season, how would that draft/auction play out.
Wow, can’t believe I had to scroll so far down just to reach the comment box. Who knew the controversy this would brew!
Turns out that there is an answer to this question, it varies by format, and is dynamically changing as the draft goes on. I’m reticent to give away the milk for free here, but the temptation to drop knowledge bombs is so strong… I’d be glad to write up a game theory post, Mike, and share my Excel programming I use in every draft, but only after draft season is over and my classes at medical school are out for the Summer. If you’re intrigued, leave a comment and a way to contact you long form/privately (or send me an e-mail through the site if such things are possible) and I’ll send over some results. Since this is the last year I’ll have the free time to pay for my student loans with “gambling” (read, headfirst Scrooge McDuck money-dives) perhaps it’s time to share what I know with the SABR community at large on the subject at hand.
As to DylanJH directly above me, the question you’re asking (that I know how to answer) is the start of it all. 🙂
I spent way too much time reading this article and the majority of the comments and one thing stands out to me.
If we accept the notion that some level of inflation/adjustment/insurance is required to acquire players at position with an average below league average, why does it make sense to do it after we have calculated the values? Why wouldn’t we just calculate the initial values using the mean and stdev at each position?
I think you’re in the majority here and I’m in the minority. I don’t like comparing players to solely the mean/stdev at their position. I feel there’s more sample-driven volatility in that method versus comparing everyone to the average results of all rostered hitters.
I also don’t like STDEVs for this as it tends to get erections lasting more than 4 hours for SBs.
But, if done right, the reality is there isn’t much difference b/w either method.
Given the majority of people who’ve read this thread seem so locked in that one ‘must value players by others in their position’ and that ‘you can’t value guys at less than $1’, i’d like to open the thought exercise I did for Mike above.
If you were forced to choose 1 of 12 envelopes where 11 had $100 bills and the 12th had an invoice for $1,000 OR you can pay a bribe and get tipped off so you’re ensured a $100 bill, would you bribe and, if so, how much?
The parallels here are that:
1) You have to pick one (effective bid $0).
2) We know the values.
3) As per my position-neutral valuation method, the values within each envelope is unadjusted
4) We are balancing positive and negative outcomes (does anyone want to argue that a 2nd catcher is a ‘negative’ hitter when compared to the average hitter? That Carlos Perez isn’t getting drafted with 1B eligiblity?)
Wouldn’t paying about $92 be the break even point?
Choosing 2nd would be about $100?
Choosing 3rd would be $110?
Yes. You could even justify a little more if you like for ‘insurance’ to avoid the big payoff (that’s why we have an insurance industry).
While catcher values are not this extreme, I’m arguing for the same logic.
The $1,000 invoice is worth -$1000. Just because we have to pick an envelope and that may be one of them, it doesn’t magically make it worth $0. We just have to think about all net-positive selections and revalue them based on the potential for net-negative selections. In this case, we put a ~$92 premium on a $0 pick solely to fray the negative outcome.
BUT $91.67 is a looooot less than a $1,000 premium which represents the worst case outcome.
Hence, my insurance model looks at C2 and concluded that the ‘premium’ to avoid the negative outcomes of drafting a catcher who is not roster-worthy from a position-neutral perspective is about $3-$4 instead of the absolute $10-$11 (to boost something like -$9 to $10).
If one is too hung up on “It has to be positive value because a dumpy catcher is better than nothing”, change the example to 11 envelopes of $100 and the 12th is $1. All the envelopes have positive value (so you want to take one). The justified premium is about an $8 bribe to ensure you get $100 since expected value is 1101/12=$91.75.
I agree with the idea here that I’m willing to pay something as “insurance” in order to be guaranteed to not have to pay $1000.
I think where I fail to see the alignment of this with the scenario of the Catcher is that all positive value catchers are not worth the same amount, so the “bribe” would be incrementally more depending on the value above the alternatives that the envelope is worth. Not drafting a catcher at all is more equivalent to the ($1000) scenario – I can choose to do nothing, and live with ‘free’ ultimately forcing me to take the $1000 invoice. But realistically the ($9) catcher is not a $100 bill or a $1000 invoice. It is somewhere in between there and absolutely has a positive value associated with it due to the alternative being ($1000).
When no envelopes are chosen the break even is $92.
When 1 envelope is chosen the break even is $100.
When 2 envelopes are chosen the break even is $110.
Isn’t it worth it to pay more for the 1st envelope to avoid having the paying the higher premium for the 2nd one?
Yes OOTB, you are correct. After the first one is taken, you’d pay a little more insurance. The worst part of this comparison being that, in my hypothetical, the first envelope could’ve been the invoice.
That said, you are using my ‘insurance’ argument to protect yourself against a bad outcome. That is what I’m considering negative value catchers. The fact that the premium you are paying is way lower than the penalty holds true if we reduce the ‘invoice’ to $10 (the premium would be $0.92, $1, $1.10), etc.
I’m surmising the argument that just adding $10 so that the last envelope is worth $0 isn’t mathematically imperative.
mZimm – Copying from a different reply:
“If one is too hung up on “It has to be positive value because a dumpy catcher is better than nothing”, change the example to 11 envelopes of $100 and the 12th is $1. All the envelopes have positive value (so you want to take one). The justified premium is about an $9 bribe to ensure you get $100 since expected value is 1101/12=$91.75.”
If you want the distribution to look different, picture the 11 varying increments with an average of $100 (e.g.,150,140,130,120,110,100,90,80,70,60,50).
You could consider getting the $1 better than nothing but it is significantly worse than the average expected outcome of $91.75.
So the worst case is a net loss vs expected of $90.75 or we can say picking the wrong envelope will cost you $99.
To avoid the worst case outcome, you pay $9.25. You don’t pay $90.75 or $99.
Now if it was just two envelopes (say $50 and $1), you’re up to a $25.50 premium. That seems CRAZY….except when you realize that the traditional baseball model would suggest everyone pay $90.75 as a premium because that’s the worst outcome (replacement level = worst outcome).
Rudy,
What should the value of the 1st two catchers be in this scenario be?
value + .92 + insurance?
value + 1.10 + insurance?
Insurance implies that I am overpaying(in terms of expected value) to avoid the worst case scenario. Shouldn’t the price be (value + .92 + X + insurance)?
In the above case I would pay an extra amount (X) to get the 1st player at the same premium as the 2nd player. (I don’t know how to calculate (X) as the premium propagates down the ranks.)
You’re right. Insurance implies overpaying above expected value. I did the exercise across all 30 catchers in my post (http://razzball.com/debunking-position-scarcity/) but what I was calling ‘insurance’ really is doing expected value calculations.
Completely subjective what one pays for insurance. I would think the ceiling should be the effective market inflation rate (what they pay vs your values) which, in my study, turned a $3-$4 premium into a ceiling of $6-7.
So there is no magical formula lol.
Assuming the top 2 players are valued at $10 + premium.
Player 1 is brought for $10+ premium.
Now Player 2’s value becomes $10 + higher premium.
Player 1 will always be cheaper than Player 2. So if you get a player at value + premium you will have an advantage the earlier you select a player at a premium position.
If you have to choose between the following case:
Player A $12 + 0 premium
Player B $10 + 2 premium
Player B will always be the better buy because you will save yourself from paying a higher premium at Player B’s position later on? Insurance must always be greater than 0?
Is the major difference between you and Pod that if the 12th SS value is -$9, he wants to add $10 to all other SS and you are saying the value added to SS should be Premium + insurance where the Premium + insurance is way less than $10?
I’d say yes, the major difference b/w myself and Mike on $ valuation is that he adheres to the ‘replacement-level adjustment’ method where you force every ‘draft-worthy’ player to $1 and adjust every player in that position up by (1-replacement level – e.g., 1 minus -9 = $10, if the replacement was +4, you’d take everyone down by -$3).
I stated in my post that having a varying premium is kind of nuts and that using the average of all those premiums is easier. That came out to about 30% of the ‘replacement-level adjustment’. I’d expect similar if I was to run it on a SS instance where the replacement was -$1. In that case, I’m looking at $2 * 0.3 = $0.60 which I’d find silly to do since replacement-level (based on one or a couple of players) has so much volatility in it and the difference between the $1 and -$1 is not statistically significant enough IMO to adjust other players by it.
My post from last year (http://razzball.com/position-adjustments/) does a good job at putting this all in perspective. The impact of these position adjustments is felt in the distribution of $ per position (see Average $ Per Position Indexed Against Average Hitter $ chart). Given Mike and I’s projections aren’t that different, I concluded that position adjustments forced an odd depression in 3B pricing and distributed it to C/2B/SS compared to mine, NFBC ADP, and our commenter leagues. If I recall correctly, it was because the system he uses gives 1B/3B the same replacement value. In my eyes, it just underscores why one should question every single adjustment they make on batters since each one is an opportunity to f*** something up.
Thanks for all the replies. It is a different perspective.
I am still on the fence. lol It seems the position adjustment for Pod is too high and yours too low.
Rudy must be a libertarian. The ability to argue endlessly with seemingly logical points while never accepting any counter arguments is entirely in line with the libertarians I’ve met.
There is absolutely zero doubt that Mike is correct here. jdbolick is doing a great job, but can we also point out that Mike is valuing players exactly like we do in real life, I.e relative to replacement value?
are you crazy? jdbolick is reading everything out of context or too narrowly.
Rudy is saying that positional scarcity is overrated except for C2. He never said it was a myth, despire jdbolick’s attempt to put those words in his mouth.
Nope. I’m just a masochist that feels a desperate need to get people to rethink/question orthodox positions just because they seem unimpeachable.
re-reading the article, it looks like Pod made the same errors as JDBolick. “hey, this part isn’t about valuation…”. Yes, because Rudy already laid out the valuation, and described how he captured surplus value at the draft, relative to other people.
Both made the same error: not defining their terms. This has produced a ton of confusion in this comment thread.
I understand Mike’s arguments because his definitions of terms are very similar to mine.
I have no idea what Rudy is talking about. Who is willing to pay $1 for a player worth -$9? That is insane. But I don’t think this is what he actually means. However, I do not know what he actually means.
well someone has to pay $1 for someone worth -$9.
Key points in nutshell from my original article and subsequent comments:
1) ‘Position scarcity’ either does not exist or its impact is highly exaggerated in 1 catcher mixed leagues
2) Putting aside general valuation differences, I think the traditional method of significantly boosting the values of all players at a position because their last rostered player/replacement player/blend of replacement players are different than at other positions is misguided. I provided two alternatives with real-world perspective (insurance and inflation) that show (evidently only in my eyes) these adjustments are extreme. These can be best stated as “If we all have to draft 1 SS and the last SS really stinks, we should pay a little bit more for SS to avoid the stinky one but not the WHOLE amount that player stinks vs a $1 replacement player.”
Rudy – I think you’re the victim here of a poor headline. As Mike points out in this article, you basically agree that some adjustment is warranted (maybe not required) for insurance or inflation, which can be considered nothing other than an adjustment for the position.
I think most people are agreeing that the position adjustment should not be 100% of the absolute value of the negative value that the last “starting” player at a position is projected to be worth. The adjustments for all players above him at his position would undoubtedly be a percentage of that.
I do appreciate that you are sticking to the premise of your argument here in order to entertain this conversation.
As noted before, the vast majority of mixed league players are in 1 catcher leagues. Maybe could’ve done a better job making sure this was crystal clear in my title and opening paragraphs.
You’re wrong in that the general argument here is that Mike/others are suggesting one should pay the full premium on players when ‘replacement-level’ is below average and I’m suggesting a lower percentage (or ‘split the difference’ as Jeff Erickson said when I discussed w/ him just now on SiriusXM).
So we’re on the same page mZimm. Yay!
Now that we’re on the same page here and solved this problem for the world, I’m going to stray off topic.
You mentioned that you don’t like using STDEV because it inflates SB. I just finished building my calculation for values using my 5×5+K/bb+OPS lg and was running through final values from 2015 as a sanity check. Dee Gordon and Mookie Betts came in at 27th overall and 40th overall. Billy H 459th. I feel like this is just about right,
I mostly use STDEV over SPG because I don’t like the assumption that what was good enough in past years will be good enough this year, though I can see where it may be easier to calculate and understand. Z-scores are tedious, especially with rate stats.
I agree – those values seem in line. Hard for me to say how much Hamilton should be dinged when adding K/BB and OPS but I certainly would expect his value to decrease b/c he’s bad at both. Betts is an all-around player vs what we call SAGNOF (steals ain’t got not face). Gordon’s value seems about right.
I find myself thinking about this far too much today.
Isn’t the argument against adjusting based on position similar to argument against adjusting for inflation? If you have $50 in value off of the board with only $10 spent, then you better adjust the auction “values” up for the remaining players. Not because you expect them to earn more, or actually be more “valuable”, but they are worth more to add to your team than the alternatives remaining.
Fun reading. My day job is about applied mathematics so I have always liked doing this stuff. I have been doing my own valuation tools and draft programs for 10 years but I have not read about what others do.
I am surprised that anyone would doubt anything that Mike has written in his article:
Given a set of projections (or actual stats it does not matter), given a league budget and given that you must fill the roster, your mathematical process is going to add the $10 to each catcher is the replacement value for this position is at -$8 [or to any position if needed]. It is pure mathematics. Actually, in top of that, there is no need to artificially set a Pitchers/Hitters split, the calculation does it for you based of the quantity of each available commodity.
Rudy, if you do not want to follow the valuation process, you are doing yourself a disservice. You are not going to “see” because we deal with projections anyways so the error you commit tweaking these $ values won’t be seen easily .
Maybe the confusion is that the $ valuation is actually a context neutral evaluation of all players. When we draft, we need to add context (our roster, our needs) and then comes the strategy and the $ value is not the unique parameter.
To help me, I have done a draft tool in Python:
– pre-draft, it starts with a $ evaluation, similar to what Fangraph auction tool does.
– after each pick, I run again the $ valuation (it takes a couple of seconds). the new parameters for this valuation is that I subtract the $ value of the drafted player, I subtract one to the pool of players needed to be drafted (if the first catcher is drafter, I go from 24 to 23 Catchers evaluated with at least $1).
– after each pick, I compile the standing to see where each player stands.
– In addition to the $ evaluation, I do another valuation with is entirely based on context. This one is based on roster needs (how many catchers I need, etc), points needs (am I behind in RBI or Saves). The highest value will be attributed to the player that will bump me the most.
So at any point in the draft I can choose between players ranked by value or by need.
On this screen capture,
http://reho.st/self/c563843fb1536e3647fbf179b95aa91c5b55b784.jpg
the program tells me Jordan Zimmermann has highest value but Christian Yelish would help me the most for the ranking (it is round 4 and I am testing random things int his draft, don’t pay attention to actual numbers)
Using both valuation methods during my draft, I have always managed to balance what the theory says (pure $ values) and what my team needs.
I’m a bit burned out on this subject but definitely think it’s cool someone with an applied mathematics background chimed in on the subject.
I do think a lot of the disconnect comes from my belief that
positional replacement value is not necessary to produce proper fantasy player values. I’m not saying it doesn’t work. I’m just finding that its acolytes in the comments section (and it’s original poster) are quite closed-minded that it’s the ONLY method.
So here’s my question.
If we had a position-neutral valuation system that identifies the last player at all non-catcher positions to be roughly $1 but the last catcher is -$9. (Note all other catchers are positive value so it’s obvious that the last guy is going to get stuck with a $10 “penalty”.) Why would ever other drafter add this $10 premium to their catchers and basically accept the same penalty? Why wouldn’t you use applied mathematics determine a premium lower than this $10 penalty since that’s the absolute worst case one could have?
It becomes even more painfully apparent to me when you layer in game theory. Because so many people wait until the final round to draft a C2 (or save $1 for it in auction), just by going 1-2 rounds earlier (or adding an extra $1), you can bypass a number of the worst catchers and significantly reduce your ‘worst outcome’. I did this both in this year’s mixed LABR and Tout.
Look forward to your reply!
> If we had a position-neutral valuation system that >identifies the last player at all non-catcher positions to >be roughly $1 but the last catcher is -$9
I think you still don’t understand valuation. You can’t have a negative value for a player. What you refer as a “position-neutral valuation” system would be a valuation for a Util only league.
Let’s take a simple example so that I can explain it better:
Consider 15 drafters in a HR league only. the roster is 1 C, 1 OF, 1 3B. It is so simple that the $ value is actually proportional to the number of HR.
45 players will be drafted. Look at the picture here:
http://reho.st/view/self/26cc061348bdcafb3e2165aad092669851e2700f.jpg
There are several columns:
HR column is obvious
val vs ALL: I subtract 19 to the HR total. [19 is HR total of the 45th best HR hitter of the groups of OF, 3B and C in baseball … ]
val vs OF: I subtract the HR total of the 15th best HR hitter of the OF category.
When we look at the column val vs ALL, it is a proxy of the dollar value without consideration for the roster. It would be the player value if the game was to draft the best HR hitters among OF,3B, C but with 3 Util positions. It is NOT his value in the league we are playing in because we must fill C, 3B, OF.
When we look at the column val vs OF/C/3B, it is a proxy of the value of the player relative to its peers.
The ‘true’ value of Wilson Ramos as a *baseball hitter* player is -4 (league with only Util) but since you must draft him, its real value as a *baseball player* is actually 4
He is as valuable as Evan Longoria so he will have same $ value in this league configuration.
$ values are relative to the contribution of each player among his peers, there are not relative to the contribution of that particular player to the total points of the league.
In order words, adding 1 HR as a catcher is more difficult than to add 1 HR as an OF, so the value of 1 HR varies depending on the player type.
So even if the contribution of the last catcher drafted in your league seems so little, its value is REALLY $1 for you, you do not take a -$10 penalty
Hope this helps …
Paulll – I totally understand valuation. I totally understand the concept of replacement-level valuation. That said, I appreciate the effort involved in the example.
Here are the reasons I choose not to use this model:
1) Volatility in Replacement-Level Calculation – I imagine you’ve seen what I’ve seen when doing these types of calculations where the removal or addition of one person to the player pool has fairly noteworthy changes to the calculation of a hitter’s 5×5 $ value. In a two catcher, 15 team league, how one calculates the replacement (1 player, average of bottom 3, etc.) could easily lead to swings of $2. Adding $60 to catchers is redistributing 2.2% of all hitter dollars (assuming 67/33 split) based on the values of a couple hitters with error bars way higher than $1-$2.
2) Differences in Player Valuation in Draft Room – So for two catchers, let’s say you value 33 catchers and use any combination of 31st catcher, 31st-33rd, etc. to calculate ‘replacement value’. The reality is that there is enough divergence that one’s ‘replacement player’ is not actually the worst case outcome. It could be that the 25th catcher is the worst outcome. That could be swings of $5 in my example or $150 distributed away from other hitter positions.
Even in snake drafts, any redistributions of $ are important because it changes the rankings between hitters and pitchers. So even if an OF is the 50th hitter, taking away $1-$2 could affect his rankings enough that a drafter chooses someone else.
My alternative:
1) Create a ‘modeled player universe’ reflecting players from all the various positions
2) Determine stats for the average rostered hitter
3) Credit SGPs (I call them Point Shares on Razzball) for all hitters against this roster (I model the SGPs based on the stats of the hitter universe)
4) Determine a net SGP sum as your replacement-level (it will be negative since you start with the average). Add that to everyone’s total.
5) Determine the price per SGP/Point Share based on (Hitter $ Pool – Number of Rostered Hitters) / (Sum of SGPs)
6) Calc as 1 + SGP * $ value of SGP
I then go through an iteration to ensure my modeled hitter universe has been allotted all the hitter $.
That is how I create position-neutral values. I did add code last year that forced the nth catcher to be worth $1 with n=# of teams. I COULD do this for other positions but choose not to because I feel the results are so close to expected distribution for the final players that further fiddling is unnecessary.
It’s through that prism that I can say the 30th catcher is worth -$9 and I can reason that adding $10 to each catcher does not make sense because, in effect, you are forcing worst-case penalties onto each catcher. It also means that I have to accept that it is better to roster a negative valued player than to not roster anyone at all. This seems hard for people to accept. But would an MLB team be better served starting a negative WAR guy like Jeff Francoeur in RF or leaving it open and forfeiting the lineup spot?
I’d be interested to see how your hitter $ distribute across position and compares with my distribution. From the exercise w/ Mike last year, it was interesting to see that 3B had as dramatic a difference in $ allotment as Catcher.
If interested, e-mail me at rudy@razzball.com and we can compare notes.
I think positional scarcity is shown as a real thing with a simple example. Imagine a three team, three position league. The following players are available:
Catcher A: 200 points
Catcher B: 100 points
Catcher C: 100 points
Outfielder A: 300 points
Outfielder B: 250 points
Outfielder C: 250 points
Pitcher A: 400 points
Pitcher B: 350 points
Pitcher C: 350 points
With the first pick of this snake draft, you clearly must take Catcher A, even though his stats are worse than all outfielders or pitchers. In this simple example, the first pick will win the league by 50 points, because the relative value of Catcher A is greater than any other player.
This is over simplified but applies in general. Even if you believe the scarcity above does not exist, you have to set up your valuation system under the assumption it does, and get some kind of value on it.
I think everyone in the comments agrees that in certain instances (notably 2C), one needs to consider a position adjustment.
The debate is how much of an adjustment and, at what point, does making minor adjustments based on volatility/noise in replacement values make sense.
I’m intrigued to hear what Rudy thinks about fantasy football quarterbacks, as jdbolick mentioned above.
It’s kind of the opposite scenario, where QBs (in a 1-QB league) cannot be started anywhere else, so in a 12-team league you essentially have replacement level QBs scoring dozens if not hundreds more points than starting RBs and TEs. You need to factor in the position or else you’d take a QB #1 overall and secure your backup QB in round 2.
RBs are generally ranked so highly, despite today’s passing-focused game (or because of it?), not because they score the most points, but because the production trails off rapidly when you take the 30 or so needed in starting lineups out of the pool.
Suffice it to say, I’m not sure if you can compete in a football league if you don’t believe in position scarcity (and its inverse). Sure, the roster structure of a fantasy football league is quite different than a baseball league, but I think if the principle is obvious in one, it can at least occasionally manifest in the other.
(Basketball, for what it’s worth, presents very little scarcity effect due to the increase in “positionless” styles of play leading to near-ubiquitous multi-position eligibility.)
I really haven’t dug into football but, given the significant differences in value by position, I’m sure positional adjustments are required.
Rudy,
The thesis of your article was:
“Let’s say a player is projected at 80/20/80/5/.280. Should he more expensive in a draft as a 2B or a 3B? Catcher or SS? 1B or OF? I believe that his value does not change (except a bit with a catcher in 2 catcher leagues).”
Which, as Paulll, GVeers, myself and others have clearly proven, is absolutely false. Your hypothetical player’s value is 100% tied to what position he plays. You’re right that for any given season, format, position that difference may be small, and the average fantasy player may overrate its importance, but it still exists and should be accounted for in player acquisition strategy. And the fact that projections are subject to error doesn’t change that fact.
Personally, I think the term “scarcity” is a misnomer. What we’re really talking about is contextual value adjustments based on positional constraints.
If you believe it is clearly proven, hurrah for you. It’s not for me.
I am not arguing the imperfection in projections is the driver. I’m saying that whatever method all of you are using to make position adjustments is based on noise vs signal. If you think it’s 51+% signal/, maybe it’s a net positive. I think it’s way below it.
Do you believe that 2B should be given a boost or kept about the same in NFBC this year? FanGraphs auction calculator actually concludes that 2B should receive a smaller positional value than 1B/OF (http://www.fangraphs.com/auctiontool.aspx?type=bat&proj=steamer&pos=2,1,1,1,5,1,1,1,0,1,6,3,0,10&dollars=260&teams=15&mp=20&msp=5&mrp=5&mb=1&split=67&points=c|0,1,2,3,4|0,1,2,3,4&lg=MLB&rep=0&drp=0&players=). How much of that is signal vs noise? How much of that is wonkiness in trying to come up with a replacement value calculation?
If you think adjusting Shortstops by +$1.7 and Outfielders by -$0.7 or whatever your results are, that’s fine. It’s not having major impact. If you think adjusting all catchers up $10 from their position-neutral value makes sense (FG calculator is at +$14), fine. It’s ill-advised based on my arguments but, if you’re savvy enough in a snake draft, you’ll hopefully get max market value on your catchers. And in an auction, hopefully that extra $1 you took from the other hitters doesn’t burn you.
Here’s another expert (Tristan Cockcroft) saying the same thing as me except still stuck in the belief that you have to raise all players to $1. Not exactly sure what he’s doing here but his experience is also telling him that making massive adjustments to all players based on the ‘tail’ at the position is counter-intuitive: https://t.co/sRqXVGDFd9.
(Note: If you want to see neutral-position value, you can see it in FanGraphs calculator by choosing 10 UTIL and something like 1 1B, 1 3B, 2 OF).
Look at NFBC and expert drafts and you’ll see catcher values are lower than the replacement model suggests. Why should this be if one has account for less playing time and injury chances in the projections?
The difference b/w the author + many of the commenters and myself is that I have perspective from both sides. After actively questioning each part of the replacement-level process, I concluded that it has flaws in practice and adjusted my values to better reflect what I think is optimal drafting values. I still have to adjust in the draft room but I’ve found it forces patience on 2B/SS/C which leads to better values at those positions. Just as I’ve invested time to ensure my category values are in line with both true value (and, even, the average draft room) so I don’t sit there wondering why 4 catchers are at the top of the queue or why speedsters aren’t going for more.
I’m not a huge fan of positional scarcity valuation. Not because I disagree with the system proposed by Mike, but because the inherent randomness and unpredictability of fantasy makes it low on the priority list.
Who knows what players will get injured, who will outperform, who will available in free agency one month in. As a result, I’d rather go with the BPA for a non filled position than potentially draft an inferior player because they play at a weak position.
Positional scarcity adjustment is nice in theory, but I’m skeptical of just how much value it adds in practice.