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Tuesday, January 27, 2004

Pythagorean Records To Be Taken With A Grain Of Salt 

Hypothetical situation to illustrate the caution necessary when looking at Pythagorean (sometimes called Expected) Won-Loss Records:

160 games into the 2004 season, the Angels have locked up the A.L. West crown with a 93-67 record. They've scored 760 runs and allowed 649, giving a Pythagorean record of 93-67.

The second-place Mariners, 90-70, are out of wild card contention. They've scored 753 runs and allowed 660, giving a Pythagorean prediction of 90-70.

As you can see, both teams are performing exactly as predicted by the Bill James' Pythagorean Postulate (it's not a theorem; a theorem is proven mathematically) of Baseball.
(the formula is Winning Percentage = Runs squared / (Runs squared + Runs Allowed squared)

The Angels and Mariners play the last two meaningless games of the season against each other. In the first game, Jamie Moyer goes for his 20th victory versus John Johnson, a AA pitcher called up for September roster expansion by the Angels. Moyer pitches well and Johnson is absolutely shelled, and the Mariners win, 12-1.

In the final game of the season, Freddy Garcia faces Sancho Sanchez, another Angels farmhand called up to fill the extra roster spots. Freddy pitches well, but Sanchez is brilliant in his Major League debut, and the Angels win, 2-1.

The Angels finish with a 94-68 record, scoring 763 runs while allowing 662. Their final Pythagorean record is 92-70.

The M's finish with a 91-71 record, scoring 766 runs while allowing 663. Their final Pythagorean record is 93-69.

As you can see, one blowout shifted each club's "expected" record by two games. The differences between actual W-L records and expected W-L records are often cited as a credit or discredit to the managers' abilities, but neither team was managed particularly well or poorly in the last two games of the season. It would be ridiculous to think that Mike Scioscia was four games better as a manager (his team outperformed "expectations" by two games) than Bob Melvin (his team underperformed by two games) based solely on the teams' Pythagorean Records in this example. Scioscia's team simply had the good fortune of having their asses handed to them when the race was already decided.

Pythagorean Standings are based on a pretty good hypothesis, but like any empirically-obtained formula based on a population distribution, there's random error involved. In other words, the Pythagorean Standings offer a good estimate of actual won-loss record, but whether "expected" record is, say, five games too high or five games too low is just a case of dumb luck.

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