I'd be remiss if I didn't point out that the statistics I presented in my last post are far from canonical, and that there is in fact a fair amount (among, you know, anyone who cares about this at all) of disagreement about how likely was Joe DiMaggio's 56 game hit streak. My methodology was extremely simplistic, essentially treating each game in DiMaggio's career as a coin flip. Here, by contrast, is a study that tries to estimate how likely a 56 game hitting streak was to occur in a season like Joe DiMaggio's 1941. In this season he hit .357, but of course a season's worth of games is far fewer than a career's worth. They conclude that by random chance, in about 16,000 seasons like 1941, Joe DiMaggio would have a 56 game streak exactly once (by comparison, I said 24 in 10000 careers, DiMaggio's career was 15 years long, so my estimation was more or less 1 streak in 6250 seasons).
You might at this point note that all of this statisticalizing pretty much flies in the face of everything I profess to believe about statistics. The fact is, DiMaggio's 56 game streak already happened, so did his 61 game minor league streak, so did his .325 lifetime batting average. As such, my statistical analysis above is just as valid as the above linked folks who figured out the odds of hitting in 56 straight games in 1941, that is to say: not. The odds of these phenomena happening are one, because they happened. In the universe in which they didn't (which I don't believe exists, but whatever), this entry is an analysis of some entirely different phenomenon from baseball or somewhere else in the world of happenstance.
The nice part of Odds-are-One-ness is that it cuts through a lot of otherwise intractable problems--for instance, a direct corollary of it is that the disagreement about the statistical odds of DiMaggio's streak exists precisely because the question has no statistical answer. The more difficult part of OaO-ness is avoiding the resulting nihilist pitfall, e.g. saying that DiMaggio's streak was meaningless. It clearly wasn't: it happened 65 years ago and statisticians and baseball fans alike still talk about it. Once you figure out that you're posing the question in such a way as to be unanswerable--"What are the odds that Joe DiMaggio will hit in 56 consecutive games?" OaO-ness doesn't really direct you other than to say, "Mr. DiMaggio has already done this. Can I interest you in rephrasing your question such that I can give you a more informative answer?"
So what is it about things that, while they have in fact occurred, somehow seem unlikely to have occurred? It's the only thing that's keeping the Creationists going at this point, for instance. It seems to point to a hole in our model of history, of how events transpire, of how we got from there to here. I'm still working on the new model. I'm sure I'll have it for you any day now.
Next: Propositions! Lemmas! Corollaries!
Tags: Meaning Of Life, History, Statistics, The Odds Are One