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Pythagorean Records and Other Essentially Random Derivations

Just got an email from our new colleague Marc Normandin of Beyond the Boxscore, asking me to avail myself of the Pythagorean, or statistically expected, standings he has posted at his site.

Sure, Marc; ideas for content are always greedily snatched up. . . .

So moseying on over to Marc's site, I found that based on their current runs scored and runs allowed totals, the Astros can right now be expected to finish at .507, or with 82 wins. Put another way, based on the simplest and most fundamental way of breaking it down, and working with today instead of extrapolating, the Astros should be 14 - 14 heading into the Pettitte game Saturday night with the Braves, instead of 11 - 17.

Whoa! That's great news! Instead of being 6½ out, they should be 2½ out! And here I'd been so depressed.

Then I started thinking. Given the way the team has played, 11 - 17 kinda seemed more accurate than 14 - 14. All those innings in all those scoreless games where they couldn't punch through the single needed run, all those defensive gaffes by Lane and Taveras and Biggio and Lamb. . .no, even with pitching that has now sunk to merely better than average, 11 - 17 seemed right.

So we've got the conflict between what the Pythagorean method tells us--that the Astros are better than their record--and what considered reflection tells us--that they might even be lucky to have the 11 wins.

So what are our assumptions here? Well, the first thing that jumps up at you is that the James pythagorean theorem of baseball kind of assumes that WHEN a team scores its runs is completely random. The method treats a clutch, game-winning walk off two-run homer the same way as it does, oh, Jason Lane's two-run homer last night. The idea is that over time, the runs scored when they matter, and the runs scored when they don't, will migrate toward their own natural ratio, mirroring the team's won-lost record.

But that idea in itself makes another assumption, and that is that there are no situation-specific run-scoring skills, either for the individual or for the team; no player or no team is any better than any other player or team at scoring runs in the eighth inning, down by one, for example.

Debating the existence of clutch hitters is not only not new, it is also not likely to be solved here, so beyond saying that even James is rethinking his ideas on the subject, I'll concede the point that they don't.

But even if I'm not gonna tear down the pythagorean theorem over ideas of clutchness or situational hitting, I sill think the 2005 Astros--at least so far--are a special situation that the Pythagorean method has trouble handling. Call it the Hitless Wonder effect. Again I'll harken back to the Clemens-Ishii and the Clemens-Hudson games. I know that I was not alone in my feeling that the Astros were so handcuffed that no matter how long the games went, the Astros would never break through. This is not saying the Astros are not clutch, mind you, merely that they're freaking anemic.

Back on April 9, Jose Vizcaino hit a ninth inning double vs. the Reds that brought in Willy Taveras from first. This is to my eye, the only game-winning 8th or 9th or extra-inning hit the club has had. Now,I don't think the team is any worse in those situations, I just think that they perform about as well as expected, about as well as they do in all their other situations.

And it is my contention--again totally apart from any "clutchness" they may or may not possess--that the Astros are so anemic that they are *not* equally likely over the long haul to split their 1 - 0 games; rather, they are likely to be right about where they are at: .272. Put another way: Any sufficiently good enough pitching staff can outlast the Astros' hitters over any amount of innings.

And because the Astros' staff has to eventually give up a run sometime, if only by accident, the Astros will--at least if they don't significantly pick up the pace offensively--tend to lose more one run games than they win.

This in and of itself is enough to skew the Pythagorean record by three games, and enough to solve the disparity to my satisfaction.