Examples from 2011 NBA Playoffs -, Vol1. No.1, JIC, Journal Of
ISSN 1750-9823 (print) International Journal of Sports Science and Engineering Vol. 05 (2011) No. 03, pp. 145-154 Simpson’s Paradox and Other Reversals in Basketball: Examples from 2011 NBA Playoffs Y. Zee Ma 1 and Andrew M. Ma 2, 1 Schlumberger, Greenwood Village, CO, USA 2 Campus Middle, Greenwood Village, CO, USA (Received July 12, 2011, accepted August 11, 2011) Abstract. Simpson’s paradox has been discussed in many scientific and social studies, including analysis of sports’ data. Yet it is not well known in basketball, except in some limited cases. One reason is that the NBA official box scores of basketball games do not list the 2-point shooting statistics. In this article, we show that by decomposing the 2-point statistics from the combined field goals, Simpson’s paradox appear quite frequently. Using this method, we have found many instances of Simpson’s paradox from the 2011 NBA playoffs, which seem to be one of the best NBA playoffs. Other reversal phenomena are also discussed to highlight excitements in these playoffs. Moreover, we propose a method of scoring normalization to more accurately combine the three scoring types in basketball. Keywords: Sports statistics, Data mining, Basketball, Simpson’s reversal, Scoring normalization. 1. Introduction Simpson’s paradox refers to the reversal of statistical relationships when two or more groups of data are combined. For this reason, it is also called Simpson’s reversal. This reversal paradox has been discussed in several sports, including baseball [1] and cricket [2]. In basketball, however, it has been discussed only for some limited cases, such as the controversy regarding the hot-hand phenomenon [3-5].
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