from Amazon
Wednesday, June 11, 2008
Chipper: does not compute
Nate tells us that:
The probability of a .310 hitter getting at least 92 hits in 219 tries is 0.023 percent—that’s a one-in-4,423 chance, for those of you who like your odds Vegas style.
He also presents some more data, which presumes that Chipper is a true .348 hitter. And in there, he’s got him hitting .438 in one simulation (out of 1000 ran). If we assume that he gets a total 550 at bats, then .438 means getting 241 hits, or an extra 149 hits from now on, in 331 at bats (or a .450 batting average).
Here’s my problem: if the chance that a true .319 hitter will hit .400 or better in 219 tries is one in 4 thousand, how is it that a true .348 hitter will hit .450 (in 331 at bats no less) just one in 1 thousand? It’s not. That number is actually 20 thousand to 1.
The issue, as I see it, is that Nate gave a non-fixed true talent level (which is good) in his sim, so that, presumably, when he came out with a .438 batting average, his true batting average for that sim was say .370 or .380 or whatever. However, he did NOT give the same possibility in his original 4 thousand to 1 assertion. In that particular case, he presumed that .310 was a fixed talent level (which is bad).
It’s very possible that the chance of someone who is *probably* a .310 hitter (but could very well be anything around .280 to .340) has a one in one (not four) thousand chance of breaking .400. I don’t know the numbers. But, all Nate needs to do is re-run his sim, and keeping all his other parameters the same, except make Chipper a .310 hitter. It’s on that basis that he should say what his chances are as a .310 hitter, and not say that he has a 4 thousand to 1 shot if he’s a true .310 hitter.
By the way, I ran a quick Marcel. I’ve got him as a true .330 hitter. I don’t see how .348 is possible, unless Nate is treating his 219 at bats as if it was 500-600 at bats.