BASEBALL'S PYTHAGOREAN THEOREM
|•||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 defineas 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)′.