James’ “Pythagorean Theorem”



         In the mid-1990’s, a man named Bill James developed a formula that predicted the percentage of games a team is to win based on the number of runs scored and runs allowed.



Win % = (runs scored)^2 / [(runs scored)^2 + (runs allowed)^2]



You can see that he used the Pythagorean Theorem in a round-about way:


(runs scored)^2 = (runs scored)^2 +(runs allowed)^2, where runs allowed =0.


Note:  This formula is not exact.  Bill James used this formula as a tool not as an exact science. 


-  For example, the 1998 Yankees scored 965 runs and allowed 650 for an estimated winning percentage of (965^2)/(965^2 + 650^2) = 931,225 / 1,353,725= .688.  So, for a 162-game season, this means the Yankees had approximately 111.5 wins. However, they actually won 114, so the formula was off by a little more than two wins.



There were some variations of James’ “Pythagorean Theorem:


A basketball analyst, Dean Oliver, applied James' Pythagorean theory to his own sport, the result was similar, except for the exponents:



Win % = (Points For)^14 / [(Points For)^14 + (Points Against)^14]



Steven J. Miller models game runs of professional sports leagues in general:



Win % = (runs scored)^a / [(runs scored)^a + (runs allowed)^a]


Where a=1.82 for baseball, 13.93 for basketball, etc.