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Noted Greek mathematician Pythagoras is credited with a formula relating the lengths of sides of a right triangle. Noted baseball mathematician Bill James devised a similar formula to predict how many games a team should win, based on how many runs it scored and how many runs it gives up.

Bill James at a 2002 Red Sox press conference (AP Photo)

The Pythagorean theorem states that the square of the length of the hypotenuse — the longest side of a right triangle — is equal to the sum of the squares of the other two sides. The calculation from Mr. James, now an advisor to the Boston Red Sox, gets the same name because it also involves sums of squares. The formula is that expected winning percentage is equal to:

(runs scored)^2 / [(runs scored)^2 + (runs allowed)^2]

For a more-concrete example, consider Mr. James’s Red Sox, who on Tuesday morning held baseball’s best record, 48-27. They had scored 378 runs and given up 297 runs. If you plug all those numbers into the formula above, you get an expected winning percentage of 61.8% — meaning you would expect them to have won 46 games instead of 48. So they’ve been a little bit lucky. (Some sites, including Major League Baseball’s official site, tweak the Pythagorean formula slightly, using an exponent of 1.82 instead of 2, or varying the exponent depending on whether a team plays in high- or low-scoring games.)

Pennants are assigned based on actual winning percentage and not the result of an obscure formula. But fans handicapping their team’s chances as midseason approaches, and general managers deciding whether to pull the trigger on a big trade, would do well to calculate the Pythagorean percentage, because it’s a better predictor of how the team will do the rest of the season. In other words, outscoring other teams over the long run is a truer reflection of team quality than a won-loss record.

Clay Davenport of the research company Baseball Prospectus (whose estimates of when Barry Bonds will break the career home-run record were the subject of a recent Numbers Guy post) demonstrated in 2004 that, if you want to estimate how a team will do during the balance of a season, the Pythagorean method generally is your best bet.

Last year on this date, the Red Sox and Chicago White Sox were doing better than they should have been, according to their Pythagorean records. Indeed, both teams ended up stumbling and missing the postseason.

Again this year, Mr. James’s number-crunching may spell trouble for his team. The Yankees trail the Red Sox by 11 games, but may be poised for a rally: According to their Pythagorean standing, they should only be down by just three games. The Chicago Cubs, meanwhile, should be 40-35 instead of 36-39.

Further reading: Last month on Hardball Times, David Gassko examined some factors that may explain why certain teams over- and under-perform their Pythagorean records.