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.