Friday, April 17, 2015

The Game that Broke My Win Probability Model

On the eve of the playoffs, I take a look at the most improbable game of the 2014-15 NBA regular season.

Earlier this year, I rolled out an improved version of my NBA win probability model. The new model resulted in better predictive accuracy in out of sample testing. It also reduced the number of "impossible" comebacks. Prior to the upgrade, there were several games in which a team with a win probability of zero ultimately came back to win the game. This would indicate an overconfident model.

After the new model was rolled out, most of those "impossible" comebacks were downgraded to merely "improbable". Except for one.

On November 13, the Memphis Grizzlies trailed the Sacramento Kings by one point, with six seconds left in regulation. With two seconds left, the Grizzlies' Zach Randolph missed a 7 foot shot that would have given Memphis the lead. The Kings' Ben McLemore pulled down the rebound with 0.9 seconds left in the game.

At this point, the Kings have the lead, possession, and just nine tenths of second left on the clock. My win probability model pronounced the Grizzlies dead. Odds of winning: 0%.

McLemore is immediately fouled, but not before 0.3 more seconds tick off the clock. But McLemore misses both free throws and Randolph gets the rebound off the second miss. An additional 0.3 seconds bleed off the clock, but the Grizzlies have a pulse: they have the ball, and 0.3 seconds of game time to do something with it. Their win probability rises, zombie-like, to 5%.

After a timeout that advanced the ball to the Grizzlies side of the court, this happened:

Here is the complete win probability graph:

This game was stupid-ridiculous. The Grizzlies trailed by 26 points early in the second quarter (win probability 6.9%). The deficit was 20 points late in the third (win probability: 1.9%). And with 7:37 left in the fourth quarter, the Grizzlies were behind by 18. Their win probability was a barely finite 0.4%.

You can use the Top Games Finder to find other improbable comebacks for any game over the past four seasons. Filter by team, date, and regular season vs. playoffs.


  1. The logistic model your're using for the bulk of the game should never give a 0% win probability estimate. Perhaps there's some oversight in the late game decision tree that you set up to handle the closing moments. (0% isn't an outrageous an estimate for the win probability in that context, but with this example in front of me it seems a little low.)

    I'm a little surprised that the game that should have cost Mark Jackson his job ( is only the third biggest comeback in the game finder.

    1. True. The raw probabilities never go to zero. But since I round to four decimal places, the rounded versions do. So saying my win probability model was "broken" may be a bit dramatic.

      Part of the issue is that my model doesn't have game time at the tenth of second level. So all situations between 1.0 and 0.1 seconds are counted equally (McLemore got the rebound at 0.9 seconds, but the model doesn't know that).

    2. Yeah. There's a world of difference between 0.9 and 0.0. Similarly, there's a world of difference between 1 yard and 1 inch on fourth down in football.

      I do think the win probability there should have been closer to 0.005.

      Two missed free throws is around 1/16, the defensive rebound is around 3/4, and let's say the closing shot is 1/15 for an aggregate of chance of 1/320, and they could still have tied if one free throw went in.

    3. How do you come up with a 1/320 chance, Nate? Just curious

    4. I thought that was clear, just multiply out the fractions:

      1/16 * 3/4 * 1/15 = 1/16 * 1/4 * 1/5 = 1/320.