The Interaction of Keeper Value and Inflation
This is a topic I probably should have brought up earlier in the draft season when more owners could use the concepts to select their keepers. I’ve decided there’s still a reason to talk about keeper value and inflation as it could inform your trade talks or how you think about the game in general.
A couple of my auction keeper leagues included hefty inflation this year. We’re talking prices over $10 above retail. As I’ve said in previous posts, the best way to handle the craze is to join the fray for a few big names then position yourself to be the king of dollar days. But let’s take a further step back. How should we prepare for rampant inflation before the draft even begins?
There are parts of my thought process we can (and should) debate. I see inflation as a non-linear entity. The supply of -$3 to $3 players greatly outstrips the demand for such assets. For example, not long ago, I picked up Jake Lamb and Danny Valencia after a 350 player draft. It’s possible nobody even thought about drafting them. They’re free fantasy replacement level guys with some upside. They could be core performers, or I may end up cutting them in April.
On the top end of the scale, everybody wants the Mookie Betts and Starling Marte’s of the world. These top players are inflated substantially more than lower quality players. Thus you might get a graph that looks like this:
Expected value is listed on the x-axis with prices to be paid on the y-axis. Note, this is a representation of what happens. The numbers are not meant to be precise. The point is that the gap grows larger for particularly good players. We even see this happen in redraft leagues when multiple owners assume they’re better at finding viable scrubs than their rivals.
The implication for keepers is pretty obvious. Be more willing to “overpay” for top talents than run of the mill players. If you have Chris Sale at his expected, pre-inflation price, it’s an easy keep. If you have Josh Reddick at cost, then you can keep or cut based on your whims.
I semi-tested this concept in one draft where I released Adam Eaton, DJ LeMahieu, Joe Panik, and Devon Travis at their inflation adjusted price. Eaton went for $12 – the exact amount I could have kept him at. Panik and Travis were $6, a $2 discount from the keeper price (I re-selected Panik). LeMahieu was $5, a $3 discount. Based on my best estimates, Eaton should have been $10 while the second basemen were valued appropriately.
We should take these so-called findings with a grain of salt. Really, this is just an anecdote from one non-representative league. It supports a theory that smells reasonable and has general acceptance in the industry. It’s not proof of anything.
If we assume non-linear inflation is a real thing, how can we use it to our benefit in trades? Again, this comes out as rather obvious, bundle low cost players for high cost players. That $25-to-keep Puig is more likely to be a value in 2017 than a $7-to-keep Addison Russell. Let’s say those wind up as their expected values in 2017. Russell would be drafted for about $7 while Puig would run closer to the $30 to $33 range. You’d get surplus inflation value from the Cuban.
Of course, there are contradictory forces in play. Even with a breakout, Puig doesn’t stand to gain much value. He’s already a high priced, well-regarded player with his ceiling priced into his current cost. If Russell puts everything together, he could boost his value by $20. In other words, Russell could create a much larger discrepancy between his price and projected production during the 2016 campaign.
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Danny Valencia just went for $16 in our auction. Our league has tons of keepers whose price-tag is far lower than their value, so a lot of money was spent on middle-of-the-road talent with upside, especially where multi-positional players were concerned.
I’ve always been intrigued to distribute the inflation to only the top tier players, but have never found a way to do it without just guessing. Assume 15% inflation, A $1 player is still going to be a $1 player by the end of the draft when inflation is gone so why apply a 15% inflation price to him, only to have inflation come down by the time $1 players get drafted.
Wouldn’t it be smarter to take the .15 cents and apply it to the top priced players who’s prices will be affected by inflation. I was thinking of not inflating any player less than $10 and taking all that inflation money and apply it only to the top players, therefore inflating them more, allowing me to make better decisions.
For example if my league has $300 in hitter savings, apply that extra $300 to only batters valued at $10 or higher. Therefore raising their inflated prices more than if I evenly distributed across all draft-able hitters.
Again I just don’t know where to “cut off” from inflating without just blindly guessing.
See my comment below – the valuation in a normal inflation period should reflect what you’re talking about (top hitters get much higher bumps). I could see taking all the money that is “rounded” out of values for the $1-$2-$3 guys and pushing it to the top… I probably wouldn’t try to build it into my values sheet, just be aware that there’s a few extra dollars in the pool and be willing to go +$1 if needed to get a stud.
Only-leagues are a different beast, but in 12-team mixers, there are ALWAYS guys I’m happy to take in the $1-$5 pool. Buy the stars, even if it takes an extra $1.
I implemented exactly this last year, and found that it allowed me to redistribute about $230 from the $1,$2, and $3 players into the rest of the remaining players for this year.
That’s pretty huge (about 7% of sum of budgets), but divided by the number of players remaining, it’s not a big swing per player. So you’re probably right to ignore it. I don’t regret doing it, but probably don’t need to spend any more time thinking about it.
It looks like an exponential so use an exponential model. Maybe try something like expected value above replacement ($1 player) as the x-axis. Then a replacement player will be $1. Not sure what constant you would use though without fitting. Or a power law with a constant of $1 added.
A well-formulated inflation valuation will reflect this. Let’s assume a 20% inflation rate (just for an example).
A $1 player gets bumped to $1.20. Still won’t go to $2, so no change.
A $10 player gets bumped to $12. So now you’re willing to go +$1.
A $25 player gets bumped to $30. Now we’re talking real differences; $5 should be the difference between bidding and dropping out.
A $40 stud is now worth $48. Huge difference at the top.
So I don’t think your graph is “hypothetical”, but really just the natural result of valuing correctly.
I think Brad’s point is that practically, the application of inflation is non-linear. In your example, it is still a linear function, albeit with rounding.
In keeping with roughly the same number of total dollars you mentioned in the example with those 4 players, Brad is proposing something more like $ = x^1.1:
$1 player = $1
$10 –> $12
$25 –> $31
$40 –> $52
I concede that these numbers are not that different from yours, and on draft day, it might not affect your outcome. However, I contend when you see big young (hitting) stars going for astronomical prices, perhaps a non-linear model might better predict other owner’s auction habits, and therefore still *could* be helpful even if it doesn’t change your board.
Hmmm I do like the idea of raising it by the inflation percentage instead of just multiplying, that might work.
I don’t treat my values as hard and fast anyways, I typically have to go above my inflated values in the beginning of the draft in order to ensure that I use my budget anyways. Having a “better” idea of what the true inflation value of a player is more helpful than anything else.
So what’s the goal – to predict the market, or to have a ‘true’ valuation based on the stat line?
I could see including the non-linear prices in a second column, similar to how I might include TOUT/LABR auction prices – as a way to quickly reference what I expect the player’s pricing to be. But when I’m making my actual purchasing decisions, I want to use my “true” (non-linear) valuation as much as possible.
By comparing the inflated and non inflated, you will then be able to realize a form of surplus value in your players that is not obvious by just looking at your “by the projections” prices. I love the game theory that goes in to fantasy baseball, and I love how this gives some concrete methodology to quantifying game theory.
@Nate: Agree with the last point. I do project the cost to acquire a similarly priced asset in the draft, and use that in my keeper decision making.
I find that #1 starters, for instance, almost always go several dollars above my numbers. Because of that, I’m more likely to keep an ace at a reasonable number, even if it’s less of a savings than another player.
@TheTinDoor
I go into a draft with my actual value assigned to each player based on steamer projections and an estimated, updating inflation number. I don’t use either number as hard and fast, but generally stick pretty close to both values.
Typically because I’ve spread inflation as a [Salary*inflation] I’ve had $1 players at $1.15, etc. In general the first few players off the board go for at our around my inflated levels, but I think it could be an advantage to have the higher priced players further inflated to better represent how money will actually be spent.
I guess again, it comes down to the goal. Depending on the league, non-linear could possibly better reflect the likely draft cost of a player. That’s valuable information.
But that is NOT the goal when you’re valuing players. Your goal is to put a dollar figure on the stat line, in the context of all the other draftable stat lines. Inflation plays into this; other owners’ pricing decision (often irrational) should NOT.
This should be self-evident with an extreme example… if everyone in the league decides to pay $50 for the top-tier of closers, should you? Of course not. Let them overpay, then come in after some of the money is gone and own the values that result.
Trying to make your values match what you expect prices to be at should just NEVER be the goal. Use it as a reference point in planning, but not as a price sheet.
TTD – extreme examples aside, you do need to adjust for leaguewide bidding behavior. Failing to do so is a good way to wind up with a bunch of “bargains,” leftover cash, and a mediocre roster.
It’s one thing if Wade Davis is $30 and Jeurys Familia is $7. But if every closer is predictably overpriced, then you have to join the fray. That or you need to be very confident Tony Zych, Daniel Hudson, Brandon Maurer, etc will quickly ascend to closer status.
Yeah, that’s true. Maybe it was a bad example. I still don’t see how knowingly changing your values to be LESS accurate is a net benefit.
I DO use projected draft cost, but only as a reference to help me plan on attacking positions and spending my money wisely, not as a modifier for my values.
Brad, this is exactly how my first ever auction team turned out. I was so proud, and my team sucked so bad due to lack of top end talent. Lesson learned forever, so I love the application of this piece to strategy that extends beyond keeper value. Those marginal gains are very valuable to roster construction at the high end.
I’m noticing that in our league (5×5 11 team 12 keeper $310 cap) that all of the inflation is on the hitting side. Posey could have been kept for $37 (I’m valuing him at around that number) but I’m calculating his inflationary price at $54. On the other side of the coin, I’m seeing Bumgarner (highest rated non-keeper pitcher), who I’m valuing around $29-30 having an inflationary (in this case deflationary) price of $27-28.
An auction software will solve all these problems. I recommend RotoLab (and no I don’t work for the company.)
But thats not as fun as building your own models 🙂
Above commenters have alluded to this, but there are really 3 types of inflation calculations being discussed here:
1) Post-inflation price = Pre-inflation price + Fixed dollar amount
2) Post-inflation price = Pre-inflation price * (1 + inflation %)
3) Post-inflation price = Pre-inflation price ^ (1 + inflation %)
Brad, you seem to be arguing against #1 and therefore advocating #3, when #2 is the way pretty much everybody does it already. I don’t think we need to discuss why #1 is a bad way of calculation inflation. However, that doesn’t make #3 the best response. Essentially, you’re assuming that keeping these high-performance players is going to reduce the supply of top-tier players without reducing the demand, when that’s not true.
Pretend you’re in two different leagues. One has an auction budget of $300 and one has an auction budget of $600. If you’re willing to pay $30 for a player in the first league, then you should be willing to pay $60 for a player in the second league. The amount of money is arbitrary. Unless you’re arguing that the underlying value of a player changes (i.e. how much he incrementally helps you win over a replacement player), then formula #2 is the only one that makes sense.
Assuming the final few players are going to go for $1 in both leagues, then the $30 would be more than $60 in the $600 league. Therefore you’d need to distribute more to the top tier players than simply doubling their prices. A $1 player would most likely still go for $1 in the $600 league, not $2. That extra $1 can therefore be distributed to the higher priced player.
True, but that’s a rounding argument and not an argument for inflation being fundamentally exponential. Also, that extra $1 is more likely to go to a guy worth $1.49 dollars to bump him up to $2 rather than a $41.49 player to $42. This is because there are more players down in the few dollar range than the top tier range.
The key is that you would have to re-calculate the inflation % to fit your chosen model. The inflation percentages in 2) and 3) cannot be equal because size of the dollar pool is fixed.
I’m also interested in whether Inflation affects certain stats more than others.
If a Billy Hamilton gets kept at a good price, does that make the price of a Dee Gordon (or a Jean Segura) jump higher than other hitters?
Anecdotally, my NL-only league pays through the nose for saves. Guys speculate on middle relievers for a buck, and when they take over the closer role the pool of “saves dollars’ gets flooded and Kenley Jansen goes for $27 at auction.
I don’t think so. You could even argue that the guy who kept Billy Hamilton now has more money to spend, and he’s going to spend it on power rather than speed. Therefore, there’s more money trying to buy power.
I think what you’re seeing is a different phenomenon. If guys are speculating on middle relievers for a buck and burning roster spots, you’re basically saying that saves are valued very highly in your league (either due to league settings or overvaluation).
Looking back at my league’s recent auctions — yes, I realize small sample size (n=3), poor sampling (one set of owners) and possibly skewed expected values (only my algorithm) — I consistently find a bump in the $12-20 range of expected values, where inflation rate is much greater than for cheaper ($20) players.
Does anyone else see this behavior?
I partly attribute the effect to owners in my league (a) underestimating the effects of inflation at the beginning of the auction for high-valued players and/or (b) being risk averse, undervaluing players with already large salaries. This behavior means that even more cash is available for 2nd- and 3rd-tier players, resulting in extreme inflation caused by the synergistic effects of position scarcity and more-than-expected amount of money available.
This is very common in early keeper leagues with people who don’t use advanced models or strategies. As the league continues, owners will remember this happening and adjust. This is why I usually advocate the strategy of striking early and often while saving some money. You’ll have a long lull, but there will still be plenty of good players on the board when you’re back to having a top budget.
I see this happen pretty frequently, regardless of the “skill” of the league. The first few auctioned players dictate prices for the next few dozen players. Then, as the pool starts to dry up, budgets begin to dictate prices.
I think there’s a sort of cognitive bias that artificially caps the inflation for elite talent (whether it’s inflation caused post-keepers but pre-draft, and/or caused mid-draft) when people bid at the beginning of a draft. It gives true inflation a more parabolic shape than the multiplicative or exponential shape you’d expect to see.
I think the inverse would apply, too, if owners, for whatever reason, bid on mediocre players first and elite players last. The elite players would see much more inflation because of some preconceived notion of the value of the mediocre players.
I agree that nomination order may have a significant impact on inflation, in addition to the immediate perceived need/supply and owners’ general portfolio management strategies. (Fortunately, as you point out, nomination order is generally correlated with player value for much of the auction.) In our recent auction, someone nominated Solarte second overall — between Sale ($36) and Altuve ($34) — and he went for $8 in a 5×5 OBP league with a player universe equivalent to an 11-team league and with 40% of roster spots (13; 10) filled with pre-auction keepers. Unfortunately, Solarte doesn’t profile as a player who would’ve induced a bidding war at any time, so I’ll have to nominate pitchers like Liriano, Samardzija or Hamels early next time to see what happens.
Inflation absolutely should be calculated using an exponential function and not a multiplicative one. You can see that from a theory perspective simply by focusing on $1 players, as they should always be $1 players regardless of the amount of inflation. An exponential equation keeps their value at exactly $1 rather than $1.40 or whatever the multiplicative function would return. In terms of actual practice, obviously when dealing with human beings we usually don’t make perfectly rational decisions and therefore actual inflation might be distributed in any number of ways that deviate from the theoretical model, but my own experience does lead me to believe that value from inflation should be disproportionately applied to the elite players. For my first draft this year, I calculated inflation at (Pre-keeper value)^1.1499.
I like the theory of forcing the last player to be $1, but don’t like this method exactly. If you put all your positively valued players at (pre-keeper value)^1.1499, don’t you significantly overburn the total dollars available to spend? It boosts up everyone exponentially, PAST the point of actual dollars in the auction pool.
No, the exponent is determined by the ratio of dollars remaining versus value remaining. It’s the same total of inflation as the multiplicative calculation, only the distribution is different.
You just need to re-normalize the dollar pool based on whatever you choose for your model. Treat the exponent n as a variable, and come up with a value for n that fills the entire pool of available dollars. In my above example, I did it by hand: sum of ($)^1.08 ~ 1.2*($) ~ 90 for your 4 players.
This is a bit nitpicky, but an exponential function has the variable (in this case the $ value) as the exponent, e.g. c^x, where c is a constant term. What you are talking about is a power function, of the form x^c, where c is a constant inflation value. Both can produce the curved shape observed in the inflation data. A power function will have a rate of inflation increase proportional to the dollar value of the player. An exponential function will give a fixed proportional increase of inflation for an increase in the expected value.
Very good point. Thanks.
While inflation might manifest as an exponential function in many auctions, it is important to remember that the goal of an auction is to purchase the most value. Value, by definition, is a linear function if you’ve calculated it correctly (and if you trust your valuations). In other words, all players have a value relative to each other, and the total amount of money to be spent (which will be higher in keeper leagues) is a multiplier…not sometime which will change the inherent value of players relative to each other. Focus on buying the most value. But also have to spend your money. Here’s why….In theory, 26 $1 players would provide as more value a 1 $25 player, but you’d leave a lot of amount of money (and value) on the table if you filled a roster with 26 $1 players. So yes, you have to make sure you spend all of your money, and buying a carefully selected top dollar player is a good way to do this. I try to calculate inflation as a linear function, and overspend only as much as necessary (to spend all my money). If top dollar plays are going above linear inflated values, there will be values later. If top dollar players are going at or below inflated values…the buy up…as there may not be great values later. Nothing ruins an auction more tha overpaying for a bunch of player you don’t want after all of your targets are gone.
There are many real world scenarios in which value is clearly not linear, so I don’t understand why you would say that value in general is linear by definition. That is definitely not true.
Yes, but those values will frequently be in the $2-$5 range, and you correctly pointed out that amassing value on low dollar players is constrained by roster limitations.
JD, can you please give an example of situations where value is not linear? I’m struggling to think of one and I think seeing an example will help me out.
My thoughts are that in an auction draft scenario we’re trying to battle for a fixed amount of resources. We can call them home runs or we can call them widgets.
Each widget has the same value.
If I pay more per widget than you do, I’m going to end up with fewer widgets than you.
The one wrinkle that I can’t account for (I don’t know how to), is that we don’t know exactly how many widgets there are. It’s a mystery to us. And along the way, more widgets will appear that we hadn’t anticipated (free agents) and others will break.
If we knew the exact number of widgets in the pool, paying more per widget is a losing strategy. But if we’re unsure, maybe it is better to pay more.
Perhaps this is where the exponential piece comes in and makes sense. But I need someone to help me piece this all together.
De Beers and the diamond market is one of the most classic examples, as their stranglehold over supply allowed them to inflate the value of diamonds far beyond what it would have been without them. So the discovery of a new diamond mine would have had significantly more value to De Beers than it would to some random company not previously involved in the diamond market. Or think of a company that liquidates its assets as a result of bankruptcy. Those assets will typically have more value to a company already present in that industry than one that it is not for a variety of reasons.
To use baseball examples, FanGraphs has written many times about how a 2 WAR player has more value to teams higher on the win curve than teams toward the bottom of the win curve, primarily because teams higher on the win curve are closer to realizing goals that create additional value. You can see this same phenomenon in fantasy baseball where players being dumped by non-contenders have very little value for other non-contenders and varying degrees of value to teams in contention. Meanwhile in constrained systems you often see the opposite effect where having an abundance of something decreases the value of acquiring more, such as any particular category in rotisserie baseball. There is a set maximum of points that you can get for winning the steals category, so if you already have Billy Hamilton and Dee Gordon then Jarrod Dyson has significantly less value to you than anyone else.
In the real world, value typically isn’t linear. We often use linear approximations for convenience, but theoretical and practical value are influenced by so many different factors that they move all over the place. And note that I’m not even talking about what people will be willing to pay for something, as that’s an entirely separate discussion. I’m referring specifically to value gained from acquisition without consideration of its cost of acquisition.
I’m going to side with Charlie Hustle on this one.
When discussions like this break out, I feel as though people are talking about two different things. Some folks are interested in “modelling what prices will be in the draft” more than they are “calculating the value of player stats”.
I don’t think a home run from Mike Trout is worth exponentially more than a home run from Kevin Kiermaier.
I do think having 40 Trout home runs is better than having players A and B combine for 40 home runs. There is opportunity cost and roster spots saved by condensing stats into one player. This should make them more valuable than a linear sum of stats.
What about .280, 80, 15, 80, 5 from an outfielder versus from a catcher? Do those have the same value?
JB, to answer both you diamond analogy and your OF vs. C question:
1. In the case of the DeBeers and diamonds, I am not saying that an given diamond (player) will have the same value to every diamond company (owner). Ditto with WAR/players to contending and non-contending teams. Everyone might have a different intrinsic value for each player. But we are talking about inflation in a fantasy auction draft….a very specific situation where you must purchase a specific number of players on a specific day. If only one variable changes, the total amount of money that can be spent, the only way that you can preserve the relative intrinsic values of the players (as that are of value to you) is to increase the price for each of them proportionally. This is a linear function. Any nonlinear adjustment will change the intrinsic values of the players relative to each other.
2. A similar argument goes for outfielder and catcher. People might value them differently, but an increase in league wide money supply will affect them proportionally…all other things being equal.
Nate, you are talking about roster positions as a scarce resource. They can be depending upon the league. If you believe that getting 40 HRs from one player is worth more than 40 from 2, then you should factor that into your valuations. It is a calculation which is independent of inflation. If inflation exists, the value of all three players (40 HR guy, 25 HR guy, and 15 HR guy) will need to be recalculated to account for it.
However, in the context of what Brad is writing about, inflation in very deep keeper leagues, that last roster space is not worth much. You are filling those last roster spots with some pretty bad players, replacement level players ranked #300 in an only league. Worth something? Yes. Worth a lot? No.
In a power function only one variable is changing and the players remain exponentially proportionate. Their intrinsic value is maintained. In each case you are subjecting that intrinsic value to a modifying constant, just a different type of modifier. The problem for the percentage model is that we know it produces the wrong result for the $1 baseline.
Enjoying the conversation. I still maintain that inflation is a linear function if correctly applied. There may be other factors in play which influence valuations in some keeper leagues that aren’t linear, but they are not inflation. For example, fi you playerd in 3 NL-only non-keeper leagues with total budgets of $26, $260, and $2600, Bryce Harper might be worth $4, $40, $ 400. You would not argue that he would be worth $4, $50, and $600 because there was more money to be spent in the other leagues. This is a example of money supply impacting value in a linear fashion.
There are very likely factors in play in some keeper leagues, such as scarcity, which can legitimately cause the values of elite players to escalate disproportional to the rest of the pool, but this is not inflation. Take a such a league with 30% inflation. I believe that you could eliminate that inflation by reducing everyone’s coffers by 30% and you would still see the elite players going above pare value. So it is not the inflation which is causing it.
Finally, you can apply inflation to $1 players, but you must do so rigorous. Every player in the pool must be rounded to the smallest increment of the draft. If this is $1, then many of these players are $.60 and $1.40 players which are rounded. Some of them would be come $2 ater inflation, and many of the higher-up players would pick up an extra dollar for the same reason. Accurate rounding is necessary, no matter what valuation process and/or level of inflation that you use.
Too many typos!
No, the goal isn’t to purchase the most value. The goal is to purchase the most production.
Agree. You should your assign values based upon expected production. Then, the difference between purchasing value and production becomes moot.
They’re the same in theory, but in reality, production plays and surplus sits on the bench as your back-up middle infielder.
I use a weighted average of the last few years worth of bids based on positional ranking (e.g. 1B #1, 1B #2…. ), the numbers are pretty similar from year to year. Guys in your league are only willing to pay what they’ll pay. If you have a fairly consistent league (likely in a keeper), consider just using past values as a starting point.