One area of basketball I’m interested in researching and modeling is how a team’s probability of winning changes over time.
The first such movement in that direction are the NBA win probability graphs.
These graphs are based on the 1994 paper A Brownian Motion Model for the Progress of Sports Scores by Hal S. Stern that was published in the Journal of the American Statistical Association, Vol. 89, No. 427. (Sep., 1994), pp. 1128-1134.
Each team’s strength is determined by Pinnacle’s closing line. This gives the team’s probability of winning which is then used to calculate the game’s drift for use with the Brownian motion model.
Here is a sample graph:
There are some obvious limitations that I will note here:
- The probabilities listed assume that overtime does not take place. Therefore, end game probabilities can be misleading.
- On the same note, the model does not identify which team has possession. Thus end game probabilities are likely misleading for this reason as well.
- It is assumed that a team’s drift is constant regardless of the situation. This isn’t likely to be true in reality, as a team with a large lead early may change strategy that will affect their drift. How this changes the actual probability of winning is something to look at in the future.
- The expected number of possessions remaining is not taken into account. I suspect that a faster paced game will have different drifts (specifically higher variance) than a slower paced game. Hence I suspect a large lead in a fast paced game is easier to overcome compared to one in a slower paced game. This is also something to look at in the future.
I intend to model the game based on actual game observations that is similar to Ed Küpfer’s within game win expectancy, but I hope that these graphs are a good illustration to start.
Posted by Ryan as NBA Basketball at 4:08 PM EDT