Sunday, November 9, 2008

Which Players Had The Most Uncharacteristically Good Seasons? (adjusted for their age)

I did this last week but did not adjust for age. The key stat I used is offensive winning percentage, so read last week's post to understand it. The idea is to find out which player had a season that deviated the most from his norm or career average. But I did not take age into account. Player performance improves, then peaks, then declines. The typical peak may be as young as 25. So a player doing 100 points better than his norm at age 25 is not the same as doing 100 points better at age 38. To find the expected performance at a given age, I found the relationship between age and average OWP at each age using all players with 15+ seasons of 400+ PAs. That relationship is

OWP = -0.0008*AGESQUARED + 0.0474*AGE - 0.0574

This comes from regression analysis which had an r-squared of .95, meaning that 95% of the variation in an age's average OWP is explained by the equation. The standard error was .008 or pretty low. But as Bill James, Phil Birnbaum and probably many others have pointed out, averaging each player's OWP at a given age to predict career trends can have many problems. One is that as we get to older ages, there are not many players to use to get an average because so many players are not good enough to even play anymore. If those retired guys had kept playing, the average OWP for ages 39, 40, etc. would be much lower. So this equation will underestimate how unusual some seasons might have been for older players.

To predict a player's OWP at a given age, the above equation is used. But an adjustment is made based on his career norm, too. The average OWP by age for the group was .588. If a player had a .550 career OWP, then at any age his predicted OWP is adjusted down by .038 (a player with a career OWP of .638 would have each predicted OWP upped by .050). Once that was done, I found the 50 top seasons in terms of OWP above the prediction. The table below shows this. For example, Tommy Tucker in 1989 had an OWP of .783 at age 25. The equation predicts that he would have an OWP of .628. But his career OWP was .495, or .093 below the norm. So his adjusted prediction is .535. Since .783 - .535 = .248, his OWP was .248 better than expected. This was the highest positive difference ever (you will need to click on the table to see a larger version).

Barry Bonds' 2004 season at age 39 is number 31. His 2002 season is 54th, his 2001 season is 163rd and his 2003 season is 172nd. There were a total of 6319 season. So the four Bonds seasons from 2001-04 (ages 36-39) are all in the top 2.7%. He is the only player in the top 3% to have 4 seasons.