I love following Brian Burke's work over at Advanced NFL Stats, and in particular, his win probability graphs for NFL games. Using down and distance, yards to go, and time left in the game, Brian can model the probability of each team winning in any game situation. Using the handy Win Probability Calculator he provides on his site, I took the opportunity to graph Illinois' probability of winning over the course of their 38-13 defeat of Michigan on Saturday. Be warned, the following chart is rough because my Excel graphing skills are somewhat lacking:
I had to keep the model simplified (both because of lack of data and time constraints), so the win probability is modeled drive-by-drive as opposed to play-by-play like Brian models it. Even so, you can see that llinois' odds of winning were around 20% early in the second half (when Michigan was leading 13-7 and also had the ball). And in fact, when Michigan achieved first and goal on the 1, Illinois' odds of winning were down to just 10% seeing how they were almost certainly about to fall behind either 16-7 or 20-7. Although Terry Hawthorne's stop of Roy Roundtree on the Illinois 1 proved to be a huge play, it didn't make much of an impact on Illinois' win probability since Michigan was still expected to score 92% of the time from first and goal on the 1.
I didn't think much about it during the game, but now I wonder if Rich Rodriguez' decision to go for it on fourth and 1 was a good idea or not. I'm not going to judge by the results but by the probability going in. Let's look at the scenarios:
4th and 1, Michigan scores a TD to go up 20-7: Illinois' odds of winning are 4% if they get the ball on their own 20.
4th and 1, Michigan kicks a FG to go up 16-7: Illinois' odds of winning are 25% if they get the ball on their own 20.
4th and 1, Michigan goes for a TD and doesn't get it, giving Illinois the ball at their own 1: Illinois' odds of winning are 19%.
So according to this model, had Michigan attempted a field goal, they would have been better off missing the attempt rather than making it. This is rather counterintuitive, but there is a logical explanation, which is that the negative value of Illinois' field position backed up on their own 1 was greater than the positive value of Michigan scoring 3 points and giving Illinois much better field position after a kickoff. Clearly, Rich Rodriguez made the right decision because going up 20-7 would have been decisive and going up 16-7 wouldn't have been. Furthermore, even if they didn't get the touchdown, by far the most likely outcome was that Illinois would punt and Michigan would have great field position to attempt another score. So don't blame Rodriguez for not taking the easy points. There was enough time left in the game that he was best off trying to maximize his team's margin rather than playing it conservative. What really changed things was Mikel LeShoure's 70 yard touchdown run, and that is all on the Michigan defense.
