By analyzing recently available data from nearly ten NBA basketball seasons, we argue that basketball scoring during a game is well described by a continuous-time anti-persistent random walk, with essentially no temporal correlations between successive scoring events.  As illustrations of this random-walk picture, we show that the distribution of times when the last lead change occurs and the distribution of times when the score difference is maximal are both given by the celebrated arcsine law--—a beautiful and surprising property of random walks.  We also use the random-walk picture to construct the criterion for when a lead of a specified size is "safe" as a function of the time remaining in the game.  The obvious application to game-time betting is left as an exercise for interested gamblers.