2012/05/21 by Kevin D. Dayaratna, Steven J. Miller, Dayaratna, Kevin D. +1
Mathematics · #Applications (stat.AP) #FOS: Computer and information sciences #stat.AP
paper · pdf · doi:10.48550/arxiv.1205.4750
7 pages, 1 Table, Appendix with Alternative Proof; By the Numbers 21, 2012
arxiv created 2012/05/21 · arxiv updated 2012/05/23
We mathematically prove that an existing linear predictor of baseball teams' winning percentages (Jones and Tappin 2005) is simply just a first-order approximation to Bill James' Pythagorean Won-Loss formula and can thus be written in terms of the formula's well-known exponent. We estimate the linear model on twenty seasons of Major League Baseball data and are able to verify that the resulting coefficient estimate, with 95% confidence, is virtually identical to the empirically accepted value of 1.82. Our work thus helps explain why this simple and elegant model is such a strong linear predictor.