THE BOOK--Playing The Percentages In Baseball

Interesting. So perhaps the truth is that the market inefficiency I found is limited to older players whose teams let them go, perhaps explaining why it was 2- and 3-year deals that had the largest discrepancy between re-signed $/win and newly signed $/win.

My theory is actually that the old teams not signing the player know something more about the player’s aging curve, not the player’s true talent, because the 1st year of the deal’s $/win war similar for re-signed and newly signed players. What’s interesting is that it appears that the first year of the deal is already over-projected using the 0.5-WAR-from-true-talent-level method for the older players, while I found that re-signed and newly signed players both had similar $/win in their first year after signing. I guess the question becomes whether maybe teams are already cognizant of the steep aging in the first year, so maybe the difference in performance during year one after free agency is not a source of a market inefficiency, but perhaps teams are unaware of the steep aging in the 2nd and 3rd year of deals for newly signed players.

A bigger sample size would really be helpful but it’s really tough to gather all these contract details for older contracts, and using future contracts would assume that the market inefficiency will persist after it’s been discussed on the internet a good amount already.

Matt, yes, I agree, it is fascinating.  It seems odd to have for example Carl Crawford in a group with say Paul Konerko, if both their respective teams are cutting them loose.  It’s hard to imagine that “something” might apply to a 30yr old as a 35yr old.

In any case, I think you had a great idea, and it’s just a matter of establishing more parameters to consider.

But, as you said, sample size is not our friend.

Another limitation to that kind of study is that teams have unequal resources. The Rays may think Crawford isthe greatest guy in the world, and a great bet to age gracefully. But regardless, they have zero chance of keeping him. Had he come up with the Yankees, he’d be looking at a big extension right now.  It doesn’t make sense to aggregate him with, say, Andruw Jones who the Braves probably were not optimistic about his aging.

Right, #3 above.  While on the average, Matt may be right (about re-signing and letting go players), but I think there is great variability among teams with regard to that AND I think we can make some reasonable inferences regarding which teams cannot re-sign a player no matter what and which teams seem to simply let a player go and then apply that knowledge (or educated guess actually) to each player’s aging curve.

And good work Tango!  Of course if you look at my aging curves, you will clearly see a steeper curve as the player gets into his 30’s (I think).

In fact, here is my lwts per 500 (lwts rate) aging curve function:

y=.0083*x^3-.5666*x^2+7.44*x-8.1526

where x=age-20 and y is the lwts per 500 PA.

So from age 28 to age 33, a player loses 8.3 runs or 1.66 runs per year.  That is offense only and is a rate and does not include diminished playing time, base running, or defense.

From 34 to 38, the player loses 4.43 runs per year in lwts rate, quite a bit steeper!  In fact, I think Tango is STILL underestimating WAR loss in those later years as compared to the earlier ones.

Tango:  wasn’t the discrepancy in $/WAR between you and Matt much too large to be explained by the age 34+ players alone?  Maybe I’m misremembering, but I thought it was a huge difference. 

I wonder if looking only at players with 16 WAR in past 4 years is distorting things a bit.  That sets not just a performance minimum in rate terms, but also a high health/durability minimum over a long time.  If you were to use Marcels instead, and projected average PA based on age, I bet you would find that you overestimated WAR by a larger margin.  It all depends on how you forecast playing time, of course, but I’d guess that many forecasts underestimate risk of decline in playing time (whether because of injury or performance).

Well, I’ve posted various other aging curves.  I think I’ve done one-year Win Shares at all levels of performance, and I think I’ve also done the one-year WAR for pitchers at all levels of performance.

Basically, you are asking that I repeat that with WAR for nonpitchers, and show all the players in some number of buckets, so that we can see the various paths each group follows.

No, I’m not asking that you do that.  I just recall that Matt’s original findings were that FAs delivered fewer actual WAR than expected by many projection systems (not necessarily yours). If one uses a Marcel or PECOTA performance rate projection, and project a full season of performance, you will overstate production (especially for pitchers).  And if the player is in his 30s, you will overstate it a lot.  So I think the result is that players are paid $3-4 M per projected WAR—IF you assumed close to full-time play—but are paid more than that once you use actual production.

Wouldn’t older players that have averaged 5.0 WAR for a period of time be more likely to have been out-playing their true talent level than younger players at the same level? How many players in their early-to-mid thirties are truly 5 WAR (or 4.7 WAR) players? I think there’s a good chance that a lot of those players aren’t really 4.7 (or whatever) true talent players, but more like 4.3 or something that have had an exceptional season or two, masking their real decline in ability. You did notice a very sizable drop in the next season WAR for these players.

"Wouldn’t older players that have averaged 5.0 WAR for a period of time be more likely to have been out-playing their true talent level than younger players at the same level?”

You take the number of PA that the 5.0 (or whatever) represents, and you regress toward the mean for that type of player.  If all we know are age, then we regress toward the mean of players that age (and probably whether they are full time or part time players).  That gives us an estimate of that player’s true talent during that 5.0 period.

So the answer to your question depends on the length of time they have been “5.0 players” and the exact age you are talking about when you say “young” and “old” and more precisely the exact age during the 5.0 span.

For example, since players peak at around age 27, then a player who has been at 5.0 from ages 23 to 25 is more likely to have outplayed their true talent than a player who has been at 5.0 from ages 26 to 28, if their playing time over that 5.0 span were the same and we knew nothing else about the player.