|I can't believe this movie is 20 years old.|
This is a continuation of Saturday's post on in-game squares probability. The original post covered in-game probability for the first quarter square, using last year's Giants-Patriots Superbowl as an illustrative example.
This post covers in-game probability for the second quarter square, where again I use last year's Superbowl as illustration, and validation, of the probabilities. The model I have built calculates probability of each square paying out as a function of current score, possession, time remaining, yardline, and down. It is built from actual game results and a lot of smoothing. My original post (linked above) has additional details on the methodology.
The winning square for the second quarter was 0-9, same as the winning 1st quarter square. The graphs below show how the probability of 0-9 paying out evolved over the first half. The first graph shows the entire first half, while the second just zooms in on the last six minutes, so the play by play movements are easier to see.
The second quarter square is probably the most highly leveraged of the four quarters, as any team with the ball near the end of the half is most likely trying to score. There is no similar urgency at the end of each quarter. And at the end of the game, a team with the lead is most likely trying to run out the clock.
You can see the impact of that leveraging below, with the probabilities shifting fairly dramatically from play to play in the last minute. In that last minute, the score was 3-9 in favor the Giants, but the Patriots had driven deep into Giants territory, so there was a decent chance of a 3-9 (no score), 0-9 (Pats touchdown), or 6-9 (Pats field goal). In general, the movement in the probability graph seems to make sense. 0-9 spikes up after the Patriots get to the 2 yard line on 2nd down. It dips down when the Pats fail to score on 2nd down, and then spikes up once again when Tom Brady finds Danny Woodhead for a touchdown with 15 seconds left to go in the half.
What's the Point
If I am able to put all the pieces together (including 4th quarter probabilities), I plan to have a tool on this site that will update the probabilities realtime during the Superbowl this Sunday.
I realize that there is probably not a lot of demand, or general use, for an in-game squares probability model, but I viewed this as one step in the process of building an in-game cover probability model. Working on this somewhat simpler problem has helped me test out approaches that I can then apply to a cover-probability model. For example, cover probability requires projecting out the probabilities of multiple scoring margins, so standard linear or logistic regression techniques don't work. But the multinomial logit approach I built for the squares model could be extended to predicting these types of non-binary outcomes (although I think ordered logistic regression may still be the best bet).