__JamesÕ ÒPythagorean TheoremÓ__

__ __

In the mid-1990Õs, 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 JamesÕ ÒPythagorean 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.**