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Just a friendly reminder: David Dobbs will be speaking today at 3:35 in HBB 102; pizza prior to that in Aconda 113. THE PROBABILITY OF A STATISTICAL ODDITY IN BASEBALL Professor David E. Dobbs, UT ABSTRACT We begin by comparing the batting performances of four baseball players. Tables include each player’s batting averages for the first half of the season, the second half of the season, and the entire season. It is noticed that Player A has “lost paradoxically” to Player D in the following sense: Player A had a higher batting average than Player D in both halves of the season, but Player D had a higher batting average than Player A for the entire season. The main part of the talk determines the probability that such a “paradoxical loss” could befall Player A. The analysis makes certain realistic assumptions. A theorem is proved involving a branch of a rectangular hyperbola, and we also make use of the SOLVER feature of a graphing calculator. The discussion depends only on Precalculus and Calculus II (the latter is needed only because some definite integrals arise in the calculations) and thus provides an introduction to the calculation of probability for continuous (as opposed to discrete) uniform probability density functions. We determine the probability that Player A could lose paradoxically to a player with a lower first-half batting average, as well as the probability that Player A could lose (not necessarily paradoxically) to such a player. We close with some comments about more realistic models, some philosophic musing about paradoxes, and a theorem that reinforces one’s intuition about fractions. Conrad Plaut Professor, Director of UT Math Honors Math Department Aconda Ct. 104 1534 Cumberland Ave. University of Tennessee Knoxville, TN 37996-0612 Office: Aconda Ct. 401A Phone: 865-974-4319 http://web.utk.edu/~cplaut