from Amazon
Tuesday, August 05, 2008
Observed Performance Inferring True Talent (OPITT)
I talked about this at length in the Edgar thread, so let me reserve this thread for more generic and technical arguments and presentation.
Let’s say you have someone who has a .380(*) career wOBA in 10,400 PA (16 seasons of 650 PA). How many standard deviations (SD) is he from the league mean of .340? Answer: 8.0
(*)For those new around here, a .380 wOBA is the same thing as a .380 OBP, with a corresponding profile of SLG, something like .475 or so.
A guy with a .380 wOBA in 10,400 PA is roughly +36 wins above average (WAA) and 69 wins above replacement (WAR). This is around the discussion level of someone being a hall of famer.
Now, suppose someone has a .420 wOBA. How many seasons does he have to play in order for us to say that he is 8 standard deviations from the league mean of 8.0? Answer: 4 seasons. That gives him a WAR of 26 wins and WAA of 18 seasons.
And a wOBA of .460? A little under 2 seasons. And a wOBA of .500? Just one season, with a 11 WAR and +9 WAA. That is a Bonds-like or Pujols-like season at their best.
So, is that enough? Is it enough to say that your performance is 8 standard deviations from the league mean, in order for your Observed performance to infer great talent?
I don’t know.
Now, let’s try asking: how far away are you from a .300 wOBA level, which is right close to replacement level. Here’s how that looks:
wOBA seasons SD.300 WAR WAA
0.500 2.5 16.0 28.3 23.0
0.460 4.0 16.0 35.3 27.0
0.420 7.1 16.0 46.7 32.0
0.380 15.9 16.0 69.2 35.9
0.340 63.6 16.0 132.9 00.0
So, when comparing to the .300 wOBA level, here is how many seasons each Observed performance level requires to be 16 standard deviations from the .300 level.
Is this all we need? Do we need 4 high-end Pujols season for us to put him at the same level as the typical borderline HOF candidate?
I don’t know.
We also see that if someone could compile a league average career for 64 seasons, he’s also in the discussion. His WAR would be outstanding, but his WAA would be zero of course.
Let’s make the comparison level even lower, that of a .260 wOBA.
wOBA seasons SD.260 WAR WAA
0.500 4.0 24.0 44.3 36.0
0.460 5.7 24.0 50.8 38.8
0.420 8.9 24.0 59.1 40.4
0.380 15.9 24.0 69.2 35.9
0.340 35.8 24.0 74.8 00.0
0.300 143.1 24.0 (24.6) (323.6)
Now, we see we need 4 Bonds-like seasons, 6 Pujols-like seasons, 9 typical star-like seasons, 16 typical HOF borderline candidate seasons (and 36 league average player seasons) to all be 24 standard deviations from the mean.
And now, look at their WAA. All so very close, all around +36 to +40 wins. The WAR are still leaning heavily toward guys with longer careers. But the league average and below players provide the wrinkle.
Is this what we mean about guys having a Observed Performance Inferring the same Talent?
I don’t know. Maybe? Probably?
If we try one last comparison, and that is how far away is the performance from a .220 wOBA hitter (basically, someone who is a decent hitting pitcher), this is what you get:
wOBA seasons SD.220 WAR WAA
0.500 5.2 32.0 57.8 47.0
0.460 7.1 32.0 62.7 47.9
0.420 10.2 32.0 67.3 46.0
0.380 15.9 32.0 69.2 35.9
0.340 28.3 32.0 59.1 00.0
0.300 63.6 32.0 (10.9) (143.8)
0.260 254.4 32.0 (618.9) (1,150.4)
Now, we need 5 Bonds seasons, 7 Pujols seasons, 10 star seasons, and 16 borderline-like seasons, and 28 league-average seasons. All of these are 32 standard deviations from a true .220 wOBA player. In this case, we see the WAR are much closer, all around 59 to 69, while the WAA are in the 36 to 47 wins. In this case, the WAR for the league average player makes (in 28 seasons) its way into the discussion, but WAA precludes such a player.
So, which model are we talking about, when we talk about guys that are equivalent in their Observed Performance Inferring True Talent?