Nate Silver at Baseball Prospectus posts an interesting article on Chipper Jones’s probability of hitting .400 this year. Silver correctly notes that the proper question isn’t whether or not it’s likely that he will hit .400–of course, it’s unlikely, it was unlikely for even Ted Williams to do it. If some of Chipper’s excellent hitting this year is a product of improved talent–hitting over .400 is more than good luck for a career .310 hitter–there is a realistic chance that he may do it.
At this point, however, we have significantly more information about Chipper than we did at the start of the season. Information like the fact that Chipper really, really knows how to hit a baseball. So the idea is to come up with a new estimate of Jones’s talent that incorporates what we’ve learned about him this year.
The process for doing this is a little involved, and requires the use of something called Bayes’ Theorem, but the basic intuition is as follows: sure, it seemed unlikely at the start of the season that Jones was a .360 hitter. But we also know that it’s much, much likelier for a .360 hitter to sustain a .420 batting average over the first ten weeks of the season than it is for a .310 or a .290 hitter. What Bayes’ Theorem gives us is a way to balance these two pieces of information. (I’ve used this process before to evaluate hot and cold starts, and it’s proven to have pretty good predictive power.)
Sparing everyone some math, our solution from Bayes’ Theorem is that Jones is really and truly about a .350 hitter—specifically, our estimate is that he should hit about .348 the rest of the way out. There is some uncertainty around this estimate, because it’s plausible that Jones has become a .360 or a .370 hitter who has gotten a little lucky, and it’s also very plausible that he’s still more like a .320 or .330 hitter who has gotten a lot lucky. What we can say almost for certain is that Jones isn’t really a .400 hitter, but that he’s also almost certainly better than the .310-.320 range we pegged him at before the season began.
I think it is interesting that Silver’s estimate of Chipper’s 2008 hitting is nearly identical to his predicted estimate according to PrOPS;, which estimates his , based on the way he is hitting the ball this season.
So, if Chipper is a .350 hitter this year, what is the probability that he will break .400?
Overall, out of our 1000 simulations, Jones hit .400 or better and had enough plate appearances to qualify for the batting title 125 times. So this is your answer: I estimate that Jones has about a 12-13 percent chance of finishing with a .400 average.
Good luck, Chipper!
Addendum: Here are a few things that Chipper is doing differently this season. These don’t necessarily mean anything, I am just pointing them out.
P/PA %Strikes put in play Career 3.68 35% 2008 3.48 41%
Bleg: Pre tags don’t seem to be working since I have upgraded to WP 2.5.1. Any suggestions?