March Madness 'Anomalies': Are They Real,and If So,Can They Be Explained?

摘要

Previously published statistical analyses of NCAA Division I Men's Basketball Tournament ("March Madness") game outcomes since the 64-team format for its main draw began in 1985 have uncovered some apparent anomalies, such as 12-seeds upsetting 5-seeds more often than might be expected, and seeds 10 through 12 advancing to the Sweet Sixteen much more often than 8-seeds and 9-seeds-the so-called middle-seed anomaly. In this article, we address the questions of whether these perceived anomalies truly are anomalous and if so, what is responsible for them. We find that, in contrast to conclusions drawn from previous analyses, the statistical evidence for a 12-5 upset anomaly actually is very weak, while that for the middle-seed anomaly is quite strong. We dispel some (but not all) theories for the former and offer an explanation for the latter that is based primarily on the combined effects of a nonlinear relationship between team strength and seed, the lack of reseeding between rounds, and a strong quasi-home advantage accorded to 1-seeds. We also investigate the effects that hypothetical modifications to the tournament would have on the anomalies and explore whether similar anomalies exist in the NCAA Women's Basketball Tournament.