Thursday, August 02, 2007

A month ago, I conducted runs-test statistical analyses of Alex Rodriguez's alleged tendency to hit homers in bunches. I concluded that there was "very modest evidence" of A-Rod's "being a streaky home-run hitter..."

In the short time since that write-up, Rodriguez has unveiled a new batting stretch -- this time of the cold variety -- to further his credentials as a streaky hitter.

As reported in the article on this afternoon's Yankees loss to the White Sox, A-Rod “ended a career-high hitless streak at 22 at-bats when he singled in the second” (the grey summary box above the article refers to an “0-21 skid,” but I believe 22 is the correct number of at-bats).

His pre-slump batting average was .312 (116/372). This translates into a pre-slump failure rate = 1 - .312 = .688. Raising the latter figure to the 22nd power (for 22 straight at-bats) yields a probability of .0003 (3-in-10,000) of A-Rod having such a drought.

In a bizarre coincidence, the statistical figures of Rodriguez's cold stretch almost exactly parallel those of a 2005 slump by Ichiro Suzuki. As I previously reported:

Seattle’s Ichiro Suzuki, who in 2004 set the single-season record for most hits, suffered through a 0-for-22 slump (longest of his career) in early August 2005. The mid-season Sports Weekly listed him as batting .311 (a failure rate of .689), so the probability of Ichiro’s going hitless in 22 straight official at-bats is .689^22 = .0003.

For the Ichiro analysis, I didn't have his batting average at the exact moment before his slump; I therefore used his average at (roughly) the halfway point of the 2005 season, which would have been a few weeks before his cold spell.

Going back to today's Yankee-White Sox game, another numerical oddity was that, after a scoreless first inning, Chicago scored eight runs in the top of the second, only to have New York put up eight of its own to tie the game. The Yankees clearly would have seemed to have the momentum, but in fact, the White Sox dominated the rest of the way, winning 13-9 (see above-linked article).


Isabel said...

"The Yankees clearly would have seemed to have the momentum..."

Is there evidence that "momentum" actually exists? People talk about it all the time -- but, for example, is a team which scores in inning N of a baseball game more likely than average to score in inning N+1?

alan said...

I'm skeptical of whether actual (as opposed to perceived) momentum exists. One also, of course, needs to look at more than just one game to draw conclusions.

Still, this really did look like the kind of situation where, having scored eight runs to tie the game, the Yankees would be propelled to victory and, conversely, the White Sox would be likely to fold.

In the links column on the right, in the subsection entitled "Other Streakiness-Related Analyses and References," there are a couple of empirical tests for momentum, if anyone is interested.