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October 27, 2004

Lies, Damned Lies

Being on the Brink

by Nate Silver

For all intents and purposes, the World Series is over. No team has ever come back from a 3-0 deficit -

Scratch that. It was less than a week ago that David Ortiz busted about a 250-pound hole through that particular argument. But to hear the pundits talk, you'd think that the Red Sox had pulled off a one-in-a-million feat.

Cardinals fans can rest assured that their odds of pulling off a similar miracle are substantially better than that. A naïve model, which simply assigns each team 50 percent probability of winning each game, would conclude the odds of a Cardinal comeback are 15-to-1 against, or exactly the same as having a coin come up tails four times in a row. Clay Davenport's model, which is anything but naïve and takes into account relative team strength (and regards the Cardinals as the better team), puts the odds at a more palatable 12-to-1 against.

Neither of those estimates would seem to take history into account. The Red Sox, after all, were the first team ever to come back from a 3-0 deficit to go on and win the series. How amazing is that?

Actually, it's not all that amazing. The Red Sox might have been the first team to pull off the feat, but only 25 teams before them had had the opportunity. If the team leading the series and the team trailing series were of equal strength--meaning a team trailing 3-0 has a 1-in-16 chance of going on to victory--we'd expect the trailing team to have come back to win the series 1.625 tries in 26. Instead, they've come back one time out of 26. We can't draw any conclusions from that.

In fact, there's no reason to think that the teams ought to be of equal strength. That a team has won the first three games of a series provides some prima facie evidence that it is, in fact, the stronger club. For example, suppose that, if the two teams played one another an infinite number of times, Springfield would win 55% of the time, and Shelbyville would win the other 45%. Shelbyville will jump out to a 3-0 lead in a seven-game series approximately 9% of the time (figured as .55^3), while the Isotopes will manage the feat around 17% of the time, or almost twice as often.