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Tuesday, November 30, 2010
Are my WAR aging numbers not aggressive enough?
Matt has noted in the past that my $ per WAR numbers are too low. And yet, I countered, my overall $ numbers are in-line with what happens. His conclusion therefore was that my WAR numbers were too high as well (i.e., I made two wrongs to make one right). After all, if WAR x $/WAR comes out correct, and the $/WAR is too low, then my WAR must be too high.
Last week, I posted the WAR aging curves for the great players. The sample was selected based on players with at least a 4 WAR per 700 PA over a 4-yr period. Those players averaged 5 WAR per season. Since we observed 5.0, this would imply a true talent of 4.7 or so. What I would then do is simply subtract 0.5 wins to get my true talent for the next year at 4.2 (to include aging).
Now, this is what I got for players entering their age 28 through age 36 seasons:
Age Next1
28 4.2
29 4.5
30 3.9
31 4.4
32 4.1
33 4.3
34 3.6
35 3.4
36 3.2
From age 28 to 33, the average was exactly 4.2. That is, for players who we’ve observed to have a 5.0 WAR over the preceding 4 seasons for each of those ages, they then performed at around 4.2. This implies that the aging function works pretty darn well.
Furthermore, here is the aging for each of the 5 seasons, for players entering their age 28 through 33 seasons:
4.2 3.7 3.2 2.7 2.2
A beautiful line of 0.5 wins drop each year.
All is not well however, as players entering their age 34 through 39 seasons following an observed 5.0 (implying 4.7 true talent in those years, and aging of 4.2) averaged only 3.4 wins in their first season. This therefore does points to not aggressive aging in the first year. And it gets worse, because for 5 years we get this:
3.5 2.6 1.8 1.1 0.7
That’s a drop of around 0.7 wins per year. So, not only did I not apply a strong enough aging for the first year, but then each subsequent year should have shown a stronger aging.
So, for players entering free agency aged 34 and older, then yes, Matt was correct: my WAR estimates were too high for both the initial year and subsequent years. For players entering free agency aged 28-33, I am correct.
Notice that I said “free agency”: Matt has a theory that signing as a free agent with another team should have a further adjustment, as the old team not signing the player might know something more about the player’s true talent. And so, I haven’t really shown that here. I am presupposing that Matt’s theory is non-existant.
If Matt is correct, then I would have to diminish the WAR estimates further.
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