two weeks pass...
In Theory, Diamondbacks Are Winning Way Too Often
By DAN ROSENHECK
Mention the Pythagorean Theorem to a baseball statistician, and he will probably not even recall the grade-school equation relating the lengths of the sides of a right triangle. Instead, he’ll think of the formula derived by Bill James, the father of objective baseball analysis, which predicts a team’s record based on its runs scored and allowed.
James christened the discovery the Pythagorean Theorem because of its similarity to Pythagoras’s equation, and it is nearly as accurate: Since 1901, 95 percent of major league teams have finished with a record within eight games of the formula’s projection.
Most statisticians assume that variation from the equation’s predictions is the product of luck, and consider runs scored and allowed a truer measure of a team’s quality. But this season, that consensus is facing one of its stiffest tests, thanks to the Diamondbacks, who going into Friday’s games were 86-67 despite having given up 21 more runs than they had scored. According to the Pythagorean equation, a team with the Diamondbacks’ 671 runs scored and 692 runs allowed should win 48.6 percent of its games, while Arizona has won 56.2 percent. The 8 percent gap, representing more than 12 wins in a 162-game season, is the largest outperformance of a Pythagorean projection since 1905. Only one in 689 teams would manage to defy Pythagoras to this extent by pure luck.
Like all teams that exceed the formula’s prediction, the Diamondbacks have achieved an extraordinarily favorable distribution of runs scored and allowed from game to game. When they lose, they often lose big: in games decided by seven runs or more, Arizona is 6-13, and has been outscored by 69 runs. When they win, it is frequently in a nail-biter: in games decided by three runs or fewer, the Diamondbacks are 59-34, and have outscored opponents by 42 runs. Their record in one-run games, considered by most statisticians to be tossups, is a stunning 32-18. Has Arizona been blessed with improbable good fortune? Or does its manager, Bob Melvin, know something Pythagoras doesn’t?
The answer appears to be a bit of both. Arizona has certainly benefited from timely hitting: The team’s combined on-base and slugging percentages are 5 percent higher when the game is tied or within one run than when at least two runs separate them from their opponents. The lineup has been particularly effective in the final three innings of games in which they are ahead by one, are tied, or have the tying run at least on deck: Its combined on-base and slugging percentages are 7 percent better than the league’s average in those situations. Over all, according to David Appelman of the Fangraphs.com Web site, Arizona batters have created four extra wins for the team through advantageous timing of their hits, the highest mark in the National League.
That aspect of their outperformance is almost certainly luck. Researchers have never found a significant, repeatable “clutch” ability to time hits. Arizona’s clutch performance has come from a variety of unlikely sources, most surprisingly the backup outfielder Jeff Salazar. He has been terrible over all, but won back-to-back games almost by himself with a double and a home run as a pinch-hitter on Sept. 9 and 10. Melvin can’t count on Salazar for such hits in the postseason.
But Arizona also boasts one of baseball’s best bullpens, and Melvin has deployed his relievers expertly. Fangraphs.com publishes a statistic called Leverage Index, which reflects the relative importance of a particular plate appearance on the outcome of a game. If a pitcher has a Leverage Index of 2, that means that he was used in situations that affected his team’s wins and losses twice as much as average — most likely the late innings of tied or one-run games. Arizona’s three best relievers (the closer José Valverde and the setup men Brandon Lyon and Tony Peña) have combined for an impressive 1.70 L.I., while its worst (Brandon Medders, Edgar González, and Dustin Nippert) have an 0.47 L.I.
This accounts for part of the team’s outperformance: Once the outcome of a game is all but settled, Melvin gives his bullpen aces a rest and brings in the mop-up men, resulting in some blowout losses. By contrast, when the result is in doubt, he uses his best relievers. Of course, all teams pursue this strategy, but Melvin has done so more effectively. The Braves, by contrast, handed 44 innings at an L.I. above 2 to the ineffective Bob Wickman before releasing him, while their best reliever, Rafael Soriano, has an L.I. of 1.17. Unsurprisingly, they have won four fewer games than their Pythagorean projection.
So the Diamondbacks are clearly not as good as their record, but they’re not as bad as Pythagoras would have you think. Melvin deserves a raise for his handling of the bullpen, but the lineup will need to produce more hits — regardless of the inning — if Arizona is to advance in the postseason.
Dan Rosenheck writes for The Economist.
Copyright 2007 The New York Times Company
― Dr Morbius, Monday, 24 September 2007 20:03 (eighteen years ago)