Pythagorean Expectation Calculator & Formula
In baseball, one way to predict a team's expected number of wins and losses is with a simple formula called the Pythagorean Expectation, invented by the sabermetrician Bill James.
The Pythagorean win/loss formula uses the number of runs scored (RS), number of runs allowed (RA), and number of games (G) to predict how many games a team should have won. The original formula for win percent (W%) and total wins was
W% = RS2/(RS2 + RA2) and
Wins = (G)(W%)
The presence of the sum of squares in the denominator is what prompted James to call this the Pythagorean formula. James later revised the equation for W% to
W% = RS1.83/(RS1.83 + RA1.83).
He noted that an exponent of 1.83 predicted the actual number of wins more closely than an exponent of 2. This has led other sabermetric analysts to find an exponent x such that the equation
RSx/(RSx + RAx)
predicts the percentage of wins as accurately as possible. To date, one of the most widely used values of x is
x = [(RS + RA)/G]0.285
which was developed by David Smyth. This value of x is not a fixed constant but rather a function of RS, RA, and G. Either x = 1.83 or [(RS + RA)/G]0.285 will provide a good prediction for the actual number of games won. The following table shows win/loss stats for arbitrarily selected teams and years:
|Team and Year||RS||RA||G||Actual Wins||Pythag. Exp. *||Pythag. Exp. **|
|Chicago Cubs, 1992||593||624||162||78||77||77|
|Detroit Tigers, 2005||723||787||162||71||75||75|
|Florida Marlins, 1997||740||669||162||92||88||89|
|Florida Marlins, 2009||772||766||162||87||82||82|
|New York Mets, 2003||642||754||161||66||69||69|
|Texas Rangers, 1977||767||657||162||94||92||92|
* x = 1.83 ** x = [(RS+RA)/G]0.285When a team's actual number of wins is above the Pythagorean wins, the team is said to have been lucky that year. Conversely, when a team has fewer wins than the Pythagorean predicted number of wins, the team is said to have been unlucky.
© Had2Know 2010