...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|
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|
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.