  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.
