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Center for Nonlinear Studies |
Exploiting the recent availability of comprehensive data on all recent NBA basketball games, the statistics of scoring and the statistics of lead changes are investigated. Except for anomalies at the very start and the very end of the game, basketball scoring is well described by a continuous-time anti-persistent random walk. There are essentially no temporal correlations between successive scoring events. We also determine the criterion for when a lead of a specified size is "safe" as a function of the time remaining in the game. Finally, we show that the distribution of times when the last lead change occurs is given by the celebrated arcsine law, a prediction that is in excellent agreement with basketball game data.
Host: Robert Ecke