An alternative method to compute win probabilities and to measure player productivity in basketball

Abstract

This paper has proposed an alternative method to compute win probabilities which has been theoretically based, and that has been built upon the concept of estimated possessions. After taking into account the moment of time of each game action and the scoreboard differential, estimated possessions has been computed using a truncated Poisson regression model on a sample of 5,622 play-by-play observations. Once obtained the estimated possessions, the value of each action has been derived from the difference in theoretical probabilities of the potential value of each action reflected in a change in the score differential. Therefore, box-score statistics can be weighted using a context-dependent system of evaluation, and then computing a global index of productivity. As an empirical example, Player Total Contribution (PTC) was taken as an index summarizing the main box-score variables, and it has been showed how this index can change depending on the variations in the time and scoreboard for every play of the game. Consequently, two players with the same box-score performance could have really contributed very different to the winning probability of a team. Future research is needed to make this procedure more easily implemented.