from Amazon
Wednesday, September 06, 2006
What are the chances of a certain player winning a batting title?
Rob Neyer likes to say something like, “So-and so will win a batting title in the next 5 years,” usually referring to some excellent-hitting young player or prospect. The last time I read one of those comments was in a chat a few days ago, when he was referring to Howie Kendrick of the Angels, the 23-year old first/second baseman who has posted some excellent numbers in the minors, at least BA-wise, and is hitting .296 so far in 196 AB for the Angels.
I was curious as to how often a good hitter actually wins a batting title, given the competition and given that one standard deviation of BA due to luck alone is more than 40 points in a full season worth of AB.
I ran a sim of 10,000 seasons, 550 AB per season per player, assuming a mean (and median) BA of .270, 85 qualifying players, and one standard deviation of BA talent = 27 points (courtesy of Tango, based on an off-the-cuff estimate I think). Here is my distribution of players and their true BA:
2 .335
3 .315
9 .303
11 .288
16 .275
3 .270
16 .265
11 .238
9 .225
3 .212
2 .205
So, how often does one of the 2 best players in each league, with a true BA of .335, win a batting title? 30.26%. In 5 seasons, the chances of such a player winning at least one title is thus 83.5%.
If a certain player is one of the 5 best hitters in the league, then his chances of winning a title is 15.9%, which is 58% in 5 years.
For someone like Kendrick who is young and has a good MLE BA, I am going to guesstimate that the best we can do is put him in the first 3 categories above, or one of the best 14 hitters in the league, of all qualifying batters. His chances, then, of winning a title, would be 6.9%, which would give him a 30% chance of winning a title, assuming he qualifies in each season, over a 5-year span.
Interestingly, a true .265 player won a title 6 times in 10,000 seasons, and a true .275 hitter won a title in 4 seasons, so, around 1 out of every 500 seasons, we can expect a hitter who is around league-average in BA to win a title in one of the leagues. I thought that was interesting.