Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

1
BASEBALL'S PYTHAGOREAN THEOREM
The more runs a baseball team scores, the more games the team should win. Conversely, the fewer runs a team gives up, the more games the team should win. Bill James, probably the most celebrated advocate of applying mathematics to analysis of Major League Baseball (often called sabermetrics), studied many years of Major League Baseball (MLB) standings and found that the percentage of games won by a baseball team can be well approximated by the formulaThis formula has several desirable properties.
The predicted win percentage is always between 0 and 1.
An increase in runs scored increases predicted win percentage.
A decrease in runs allowed increases predicted win percentage.

Consider a right triangle with a hypotenuse (the longest side) of length c and two other sides of lengths a and b. Recall from high school geometry that the Pythagorean Theorem states that a triangle is a right triangle if and only if a2 + b2= c2. For example, a triangle with sides of lengths 3, 4, and 5 is a right triangle because 32 + 42= 52. The fact that equation (1) adds up the squares of two numbers led Bill James to call the relationship described in (1) Baseball's Pythagorean Theorem.

Lets define

as a teams scoring ratio. If we divide the numerator and denominator of (1) by (runs allowed)2, then the value of the fraction remains unchanged and we may rewrite (1) as equation (1)′.

-3-

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