Striking Out Pythagoras

Diamondbacks Defy Logic With an Unusual Winning Formula

Washington Post Staff Writer
Wednesday, September 26, 2007; Page E01

PITTSBURGH, Sept. 25 -- So, there's this guy, name of Pythagoras, who's been going around bad-mouthing the Arizona Diamondbacks. Says they're a fluke, that they should have a losing record -- that, matter of fact, they should be scratching and clawing just to stay out of last place, instead of preparing to clinch the National League West title. Well, word has gotten back to the Diamondbacks about this character, and let's just say if they came across him, they'd be liable to punch him in the hypotenuse.

"Pythagoras?" said rookie center fielder Chris Young, when apprised of the verbal potshots. At age 23, Young is not that far removed from 10th-grade algebra. "You mean like the Pythagorean Theorem?"

Diamondbacks Manager Bob Melvin, greeting Tony Clark after he had scored a run, has done a masterful job handling his bullpen.
Diamondbacks Manager Bob Melvin, greeting Tony Clark after he had scored a run, has done a masterful job handling his bullpen. (Paul Connors - AP Photo)

Precisely. That's the guy.

Now, if you're getting confused as to what Pythagoras, a sixth-century B.C. Greek philosopher best known for inventing the theorem showing the relationship between the lengths of the sides of a triangle, has to do with the Diamondbacks, follow along closely:

Several years ago, Bill James, the noted statistician and founder of the modern sabermetric movement, developed a formula showing the correlation between a team's winning percentage and its ratio of runs scored to runs allowed. Because it involved math similar to that of Pythagoras's formula, he dubbed the product the "Pythagorean winning percentage" -- which, in a nutshell, equals a team's runs squared divided by the square of its runs plus the square of its runs allowed.

And because the Diamondbacks, despite being 20 games above .500 (88-68) entering Tuesday night's game against the Pittsburgh Pirates, actually have been outscored by their opponents by 14 runs this season -- for reasons we will attempt to explain later -- their Pythagorean winning percentage (.487) and their actual winning percentage (.564) are at odds with each other in a way rarely seen in history.

"It just shows," Young said, "you can't put this game into a math equation."

Other Diamondbacks players are well aware of how little Pythagoras thinks of them -- how, if you took the NL West standings, where the Diamondbacks held a three-game lead over the San Diego Padres entering Tuesday, and recalibrated them using Pythagorean winning percentages, they would actually be in fourth place, nine games behind San Diego, and only one game ahead of last-place San Francisco.

"I enjoy proving all the stats guys wrong," said rookie third baseman Mark Reynolds. "It's fun to read about how we should be a last-place team. I guess even Pythagoras can be wrong sometimes."

Thing is, Pythagoras is almost never wrong. Before this year, there were only three teams to make the playoffs while being outscored by their opponents -- the 1987 Minnesota Twins, 1997 San Francisco Giants and 2005 Padres. And according to, only the 1905 Detroit Tigers outperformed their Pythagorean winning percentage by a greater margin than the Diamondbacks have this year.

The Diamondbacks, in fact, may be one of the strangest playoff teams in recent history. Out of 16 NL teams, they rank 15th in batting average (.250), 14th in runs scored (690) and 16th in on-base percentage (.320). They have six rookie position players and one rookie starting pitcher seeing significant playing time. Their leadoff hitter, Young, carries a .298 on-base percentage. There's not a single .300 hitter or 100 RBI man on their roster. They have a bona fide ace in sinkerball specialist Brandon Webb (17-10, 3.02 ERA), but their other starting pitchers have ERAs hovering in the mid-4s.

"Baseball is a stats-oriented sport, and I understand that," said first baseman Conor Jackson. "But in the end, it doesn't matter. We find ways to win. We get big hits. We get big outs on the mound. We make big plays."

Added Young: "No matter what anyone else says, we've been playing great baseball. Not every player is having a great season, personally. But as far as a team playing the game the right way, we're doing a great job."

As for this Pythagorean thing, it's actually fairly simple: The Diamondbacks are a staggering 32-18, best in the majors, in one-run games, but have 13 losses of seven or more runs.

Although the stats crowd often argues that success in one-run games is largely a matter of luck, the truth is the Diamondbacks have one of the best bullpens in baseball -- at least at the back end -- and a manager, Bob Melvin, who knows how to deploy it. By tossing his lousy mop-up men into blowouts while saving his best relievers for high-leverage situations, he permits the Diamondbacks to absorb ugly losses while winning a greater proportion of close games.

"When we lose, it seems like we lose 15-0," Reynolds said. "But if we win the first two games of a series, then lose 15-0 in the third game, we still won the series."

In addition to his deft handling of the bullpen, Melvin, a leading candidate for NL manager of the year, has also shown a knack for lineup-juggling, often as a means of protecting his young hitters, such as 20-year-old right fielder Justin Upton, from the league's nastiest pitchers. Entering Tuesday, he had used 141 unique lineups in 156 games, most in the majors.

"Unlike other teams where there's a set lineup every day," Melvin said, "we have to be cognizant that we do have some very, very young guys here, and on a particular day, if they don't need to see a certain guy -- because of the psychology of it -- I might be apt to pull them back a little bit."

While the Diamondbacks were the envy of baseball this spring, with their dazzling collection of young, blue-chip talent, even the team's brass figured the kids needed a year to put it all together -- which meant 2008, not 2007, was the target.

How it all came together in such a short time may be a question better left to the theorists and stats geeks. They can explain everything, right? All the Diamondbacks know is, it's fun proving people wrong -- especially 2,500-year-old smack-talking philosophers.

"That's what we like to do," Jackson said. "We want to be able to hold up the World Series trophy at the end of the year and say, 'What's up now? Anybody else? Anybody else got something to say?' "

© 2007 The Washington Post Company