## Sunday, November 17, 2013

### NBA Win Probability Calculator

This past summer, I rolled out my initial attempt at a win probability model for the NBA (introductory post | the insanity that was Game 6 | graphs for all playoff games | win probability added). Since that time, I have refined the model somewhat via more rigorous cross-validation of the model parameters. And while I may still have some tinkering to do, I'm ready to share a beta version of an online Win Probability calculator.

Much like the Win Probability tool from Advanced NFL Stats, this tool allows you to input the game state (time remaining, margin, possession) and it will return the win probability of said game state.

So what's the point? From my perspective, a win probability model has three main potential uses:

• Entertainment Value - A win probability model allows you to put a precise number on the outcome everybody cares about most: winning. You can then track and chart that number throughout the course of the game, giving each game its own visual fingerprint. You can see where the turning points where, where the low points were, and where things just went batshit insane.
• Player Evaluation - Looking at Win Probability Added on a player level is the most direct way to measure and quantify those eternally debated questions regarding who is "clutch" and who is "most valuable". Win Probability Added can tell you that very clearly (although its usefulness as a predictor of future performance remains to be seen).
• In Game Decisions - Compared to baseball, and especially football, there are relatively few strategic decisions a coach must make in the course of a basketball game which would be informed by a win probability model. One that does come to mind though is when a team that is trailing late should start fouling, and it's a topic I intend to address in a future post.
Once again, here is a link to the calculator. I hope some of you find it useful. More updates to come regarding player evaluation and in-game decision making.

### Appendix - Methodology Overview

• Data source: All NBA games from the 2004 through 2011 seasons
• Modeling Approach: Locally weighted logistic regression. I used R's Locfit package for the heavy lifting, with bandwidths optimized via cross-validation.
• Model inputs: Betting point spread, time remaining, margin, possession. While the tool I'm sharing here does not provide probabilities as a function of point spread, I am controlling for point spread in the modeling, such that the probabilities shared with this tool should properly reflect win probability for evenly matched teams. In other words, I am eliminating selection bias in the results and calculating probability as a function of pure game state.
• Overtime: This is a bit of a cheat, but I am modeling overtime as if it was the fourth quarter. So, a team being down by 2 with 2:30 to go in the fourth quarter has the same win probability as a team down 2 with 2:30 to go in overtime.