arXiv:1503.03509physics.data-an
Safe Leads and Lead Changes in Competitive Team Sports
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Abstract
We investigate the time evolution of lead changes within individual games of competitive team sports. Exploiting ideas from the theory of random walks, the number of lead changes within a single game follows a Gaussian distribution. We show that the probability that the last lead change and the time of the largest lead size are governed by the same arcsine law, a bimodal distribution that diverges at the start and at the end of the game. We also determine the probability that a given lead is "safe" as a function of its size $L$ and game time $t$. Our predictions generally agree with comprehensive data on more than 1.25 million scoring events in roughly 40,000 games across four professional or semi-professional team sports, and are more accurate than popular heuristics currently used in sports analytics.
Related research on basketball: https://www.physics.umass.edu/events/2015-09-09-statistics-b... (arXiV: https://arxiv.org/abs/1503.03509) I had the pleasure of attending the mentioned colloquium by Sid Redner back in 2015 and I was absolutely blown away by the effectiveness of a…
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