1The 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.
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 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)′.
Questia, a part of Gale, Cengage Learning. www.questia.com
Book title: Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football.
Contributors: Wayne Winston - Author.
Publisher: Princeton University Press.
Place of publication: Princeton, NJ.
Publication year: 2009.
Page number: 3.
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