[BostonCard]

Good analysis; it has made me rethink my priors that despite the result, returning was clearly the better move.  To do this properly, you’d have to look at the integral of probability of return times the change in win probability.  That’s obviously not going to be straightforward.  As a shorthand, you can look at it two ways, which I think looks like your apporach. First look at low probability extreme events: fumble versus a return that gets the ball to field goal range or TD. Fumble takes your probability from roughly 1/3 to close to 0, while a TD or field goal range return takes it from 1 in 3 to close ish to 100 (minus the probability the Rams go the other way). So roughly your TD/FG range return probability has to be somewhat less than half the probability of a fumble.

The other place to look at is the more likely outcomes, a return that winds up somewhere between the 10 and 40 yard line. Going by your probabilities, a 20 yard return costs you about 2ish percent in win probability, while a 40 yard return buys you a 5ish increase in win probability or a bit under 2% per 5 yards. I will admit that surprised me, since I expected the distribution to have a skewed distribution favoring returns past the 25 (maybe the time was the difference, and I will admit to have not factored that in), the logic is that assuming the Packers had to make it to the Rams 30, the difference between needing to make a 30 yard drive (starting on the 40) versus a 45 yard drive (starting on the 25) should be larger than the difference between a 45 and a 60 yard drive (starting on the 10). That being said you’d have to calculate the probability of those outcomes. I think the average return from the end zone gets you to the 20, and most returns are between 15 and 25 yards.

BC

[BostonCard]

Good analysis; it has made me rethink my priors that despite the result, returning was clearly the better move.  To do this properly, you’d have to look at the integral of probability of return times the change in win probability.  That’s obviously not going to be straightforward.  As a shorthand, you can look at it two ways, which I think looks like your apporach. First look at low probability extreme events: fumble versus a return that gets the ball to field goal range or TD. Fumble takes your probability from roughly 1/3 to close to 0, while a TD or field goal range return takes it from 1 in 3 to close ish to 100 (minus the probability the Rams go the other way). So roughly your TD/FG range return probability has to be somewhat less than half the probability of a fumble.

The other place to look at is the more likely outcomes, a return that winds up somewhere between the 10 and 40 yard line. Going by your probabilities, a 20 yard return costs you about 2ish percent in win probability, while a 40 yard return buys you a 5ish increase in win probability or a bit under 2% per 5 yards. I will admit that surprised me, since I expected the distribution to have a skewed distribution favoring returns past the 25 (maybe the time was the difference, and I will admit to have not factored that in), the logic is that assuming the Packers had to make it to the Rams 30, the difference between needing to make a 30 yard drive (starting on the 40) versus a 45 yard drive (starting on the 25) should be larger than the difference between a 45 and a 60 yard drive (starting on the 10). That being said you’d have to calculate the probability of those outcomes. I think the average return from the end zone gets you to the 20, and most returns are between 15 and 25 yards.

BC