Would Auburn Have Been Better Off Not Scoring a Touchdown?

Slate asked me to take a look at the possibility that Auburn would have a higher win probability had they not scored on Tre Mason's go-ahead touchdown run, and instead taken a knee at the 1-yard line with 1:19 to play. It was a difficult analysis, and required some unsatisfying assumptions, but in the end the results confidently pointed toward one conclusion.

...Nevertheless, Auburn had about an 81 percent chance of winning after Mason’s score, as teams in Florida State’s position are able to score a touchdown about 19 percent of the time. (These numbers are based on analogous situations in the NFL, though I’ve made slight adjustments for the differences in pace between college and the pros, and to include the chance of a kick return for a touchdown.)

So, the question we’re evaluating is whether having a first down at the 1-yard line would have given Auburn more than an 81 percent chance of winning. It’s a tricky question because it needs to be analyzed backwards...

(What I didn't explain in the article is that it's easiest to work backwards because the Auburn WP on 3rd down is depending on the results of a potential 4th down. And the WP on 2nd down are dependent on the potential results of 3rd down, which in turn depend on 4th down. And so on.)

For the Slate articles, I can't get away as much math and equations as I like, so here's a table of the relevant probabilities I used. It was complicated because the deeper into the goal-line series Auburn went, the lower Auburn's chances of getting the TD went BUT the lower Florida State's chances of responding went too. This edition assumes Auburn goes for it on the 4th down on what would be a single make-or-break play for championship.

 Down Snap time Stop time P(occur) P(TD) P(FSU Response) AUB WP if successful AUB WP if fail Total AUB WP 1 1:19 1:13 1 0.35 0.18 0.82 0.68 0.73 2 1:13 1:07 0.65 0.35 0.10 0.90 0.57 0.68 3 0:28 0:21 0.42 0.35 0.02 0.98 0.35 0.57 4 0:21 0:00 0.27 0.35 0.01 0.99 0.00 0.35

And here's the same table if Auburn decides to kick a field goal.

 Down Snap time Stop time P(occur) P(TD or FG on 4d) P(FSU Response) AUB WP if successful AUB WP if fail Total AUB WP 1 1:19 1:13 1 0.35 0.18 0.82 0.73 0.76 2 1:13 1:07 0.65 0.35 0.10 0.90 0.63 0.73 3 0:28 0:21 0.42 0.35 0.02 0.98 0.47 0.63 4 0:21 0:00 0.27 0.95 0.01 0.45 0.00 0.47

The most interesting thing about this situation was that no matter how high I cranked Auburn's probability of success to score from the 1-yard line (within reason), the strategy never exceeded their win probability for simply scoring on the long Mason run in the first place. If you think about the extreme case of a 99% chance of scoring the TD from the 1, it's little different than scoring on the Mason run. The only difference is it burns a couple seconds and forces FSU to use a timeout.

Anyway, it was an interesting analytic exercise however absurd the suggestion. And yes, I know college is different, especially when it comes to the clock. Slate asked me to do the analysis anyway, and I made adjustments to the numbers I thought most reasonable.

6 Responses to “Would Auburn Have Been Better Off Not Scoring a Touchdown?”

1. Chase says:

Great stuff, Brian.

The more interesting question, at least to me, is what is the optimal strategy assuming he takes a knee at the 1.

Is it take a knee on 1st down? Then run 2 plays + FG? (well, presumably it will always be better to go for it on 4th-and-G than a FG if we're at the 1).

My gut tells me the best thing to do is take a knee, with the hope that having to gain 2 yards on 2-3 plays is the best trade-off.

2. j says:

I honestly think that if Mason had been tacked when he was hit around the 20 yard line, Auburn wins. Florida State was unable to stop the short run game. However, it is hard to take 7 points off the board when you are behind.

3. David Ohsie says:

The most interesting thing about this situation was that no matter how high I cranked Auburn's probability of success to score from the 1-yard line (within reason), the strategy never exceeded their win probability for simply scoring on the long Mason run in the first place. If you think about the extreme case of a 99% chance of scoring the TD from the 1, it's little different than scoring on the Mason run. The only difference is it burns a couple seconds and forces FSU to use a timeout.

But isn't that because if the scoring chances are very high (99%), then the strategy you've listed (going for on a TD on all 4 downs) is not the correct one? If you really know that you have a 99% of scoring from the 1, then burn down all the clock and you have a 99% chance of scoring on the last play of the game (or near the last play), so your chances of winning go from 81% to 99% (or near 99%).

One narrative with Malzahn's offense (not sure how true) is that he sets up plays better than anyone. So if anyone in college football can run 3 semi-intentionally unsuccessful plays in order to set up a fourth 99% successful play, it's probably Auburn.

i.e.
1st down: dive for 0 yards
2nd down: obvious counter for 0 yards
3rd down: qb sneak for 0 yards
4th down: brilliant non-obvious counter for WIN

Whether Auburn is really that good at play-calling is... doubtful. :)

5. Brendan Scolari says:

I believe Brian was saying that Auburn would have a 99% chance of scoring from 1st and Goal at the 1, not that they'd still have a 99% chance on subsequent downs. If they did, then it'd be clearly best to wait until 4th down and take the 99% win probability. :)

6. phil zimmermann says:

"Nevertheless, Auburn had about an 81 percent chance of winning after Mason’s score, as teams in Florida State’s position are able to score a touchdown about 19 percent of the time. (These numbers are based on analogous situations in the NFL, though I’ve made slight adjustments for the differences in pace between college and the pros, and to include the chance of a kick return for a touchdown.)"

You don't really go into your adjustments for NFL-college calculation, but that seems off to me, I think FSU's chances of getting the TD coming back were higher than 19%

- biggest factor - college clock stops on 1st down, make 2 minute drills far easier than in the NFL

-less important factors - college offenses are generally higher scoring than NFL offenses, also FSU's offense being historically high scoring and all...