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Friday, October 17, 2014

San Francisco v. Kansas City: what would Pythagoras think?

Pythagoras was a Ionian Greek philosopher and  mathematician.  The Pythagorean theorem, in geometry states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of the other two sides—that is, a^2 + b^2 = c^2.

There's a baseball equation that kind of looks like that and so it uses that name.

Kapitolinischer Pythagoras adjusted.jpg

pythagorean winning percentage:


Pythagorean winning percentage is an estimate of a team's winning percentage given their runs scored and runs allowed. Developed by Bill James, it can tell you when teams were a bit lucky or unlucky. It is calculated by

               (Runs Scored)^1.83

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 (Runs Scored)^1.83 +  (Runs Allowed)^1.83
The traditional formula uses an exponent of two, but this has proven to be a little more accurate.
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I compared actual regular season wins with the number estimated by Pythagorean winning percentage.

teamWinsPythW-PWCseries 1series 2
Angels98962
Baltimore Orioles96942Bal beat Det 3-0
Detroit Tigers90864
Kansas City Royals89845KC beat OakKC beat Ang 3-0KC beat Bal 4-0
Oakland As8899-11
Washington Nationals9697-1
Los Angeles Dodgers94922
St. Louis Cardinals90837StL beat LA 3-1
Pittsburgh Pirates88871
San Francisco Giants88871SF beat PitSF beat Was 3-1SF beat StL 4-1

If the difference is truly luck, then Kansas City was lucky to have qualified for the tournament at all as it projected to only 84 Pyth wins.  In the wild card game Kansas City was MINUS 15 Pyth wins to a very unlucky Oakland team.  That was the first of multiple extra inning games that KC won in the tournament.  Even with its 8-0 record in the tournament, KC still has fewer wins than the Angels.

Baltimore was plus 8 Pyth wins over Detroit, which it swept, and plus 10 Pyth wins over KC, which swept Baltimore.

San Francisco was even with Pittsburgh, except that the Pirates had home field in their wild card game.  Washington was plus 10 Pyth wins over SF but still lost.

SF was plus four Pyth wins over St Louis, so SF winning was not really much of an upset, especially with StL literally throwing away two games.

So in addition to the obvious stuff so far in this loony tournament suggesting that Lady Luck is involved, Pythagoras weighs in to confirm our suspicions.

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