[CardinalSagehen]

I think the formula is the value for going it if successful times the probability of success minus the value of going for it but failing times (1 - p) has to be greater than the value of punting.

So it becomes 3.83p - 2.72(1 - p) > -1.8 (the value to the other team of having the ball on the 20, if you punt).  Solving for p, you get

p > 0.92 / 1.11; p > 83%

It's a bit late, so I could be wrong on the math; I would have thought the breakeven point would be lower, but maybe that's because I would have expected the value of being on the 40 compared to the 20 to be smaller.

BC

UPDATE: Your equation is correct. My short-lived initial response was nonsense :-). I was evaluating play as if there was an option to do nothing. There isn't. If you don't go for it, you have to punt, which has a presumed -1.8 fixed value. 3.83p - 2.72 + 2.72p > -1.8 becomes 6.55p > 0.92 or p > 0.140. That yields a pretty low 14% success probability as the point above which going for it makes sense. My guesstimate of our success probability being zero still says don't do it, but it makes it much more arguable. I have evaluated the formula at p=90% and p= 20% with reasonable results.  Of course if one believes the ball can be downed inside the 20 that moves the required success probability up.

A more "conservative" result that may have some value as a "worst case" scenario is what does p need to be completely discounting the benefits of not giving the ball back to your opponent. IOW -2.72 (1 -p) > -1.8 or 2.72p > .92. That yields a p of .338.

Coach TT addressed this question directly in today's presser at this timestamp: https://youtu.be/tTYW3dpIEVA?t=386

He said that there's an analytics person who runs numbers for fourth down based on everything including "the book", our strength up until this game, and the opponent's strength up until this game. This person provides a number such as "3", which means the analytics favor going for it in this situation with 3 or fewer yards to go. But sometimes the differences in win probabilities between "go" and "punt" are very close (e.g., within 2%), and TT says that he sometimes overrides the recommendation based on other in-game factors. 

If the system is everything he says it is, it's similar to what I imagined and was trying to describe above, in that it personalizes "the book's" recommendation based on the relative strength of this offense and this defense. But I somewhat doubt that the system is really everything he says it is.

Sounded like, if I heard Coach right, that the analytics calculation does not take into account the stats of the current game so far. So that seems a significant limitation to it. Your calculation might say you should average a 3 yard gain per run play for this situation for that opponent based on their defensive history, but does it take into account one of our own key OLineman is out injured and that one of their key DLineman is just returned having missed games, and that so far this game you've averaged no gain on such run plays?

Yes, that's exactly what I heard, too. But I think that's part of his argument for why he overrides the analytics sometimes. It would be much more difficult and arguably not very valuable to have accurate, real-time, in-game updates to the model. TT's approach, if it's really as he described, sounds reasonable and balanced to me.

[CardinalSagehen]

I think the formula is the value for going it if successful times the probability of success minus the value of going for it but failing times (1 - p) has to be greater than the value of punting.

So it becomes 3.83p - 2.72(1 - p) > -1.8 (the value to the other team of having the ball on the 20, if you punt).  Solving for p, you get

p > 0.92 / 1.11; p > 83%

It's a bit late, so I could be wrong on the math; I would have thought the breakeven point would be lower, but maybe that's because I would have expected the value of being on the 40 compared to the 20 to be smaller.

BC

UPDATE: Your equation is correct. My short-lived initial response was nonsense :-). I was evaluating play as if there was an option to do nothing. There isn't. If you don't go for it, you have to punt, which has a presumed -1.8 fixed value. 3.83p - 2.72 + 2.72p > -1.8 becomes 6.55p > 0.92 or p > 0.140. That yields a pretty low 14% success probability as the point above which going for it makes sense. My guesstimate of our success probability being zero still says don't do it, but it makes it much more arguable. I have evaluated the formula at p=90% and p= 20% with reasonable results.  Of course if one believes the ball can be downed inside the 20 that moves the required success probability up.

A more "conservative" result that may have some value as a "worst case" scenario is what does p need to be completely discounting the benefits of not giving the ball back to your opponent. IOW -2.72 (1 -p) > -1.8 or 2.72p > .92. That yields a p of .338.

Coach TT addressed this question directly in today's presser at this timestamp: https://youtu.be/tTYW3dpIEVA?t=386

He said that there's an analytics person who runs numbers for fourth down based on everything including "the book", our strength up until this game, and the opponent's strength up until this game. This person provides a number such as "3", which means the analytics favor going for it in this situation with 3 or fewer yards to go. But sometimes the differences in win probabilities between "go" and "punt" are very close (e.g., within 2%), and TT says that he sometimes overrides the recommendation based on other in-game factors. 

If the system is everything he says it is, it's similar to what I imagined and was trying to describe above, in that it personalizes "the book's" recommendation based on the relative strength of this offense and this defense. But I somewhat doubt that the system is really everything he says it is.

Sounded like, if I heard Coach right, that the analytics calculation does not take into account the stats of the current game so far. So that seems a significant limitation to it. Your calculation might say you should average a 3 yard gain per run play for this situation for that opponent based on their defensive history, but does it take into account one of our own key OLineman is out injured and that one of their key DLineman is just returned having missed games, and that so far this game you've averaged no gain on such run plays?

Yes, that's exactly what I heard, too. But I think that's part of his argument for why he overrides the analytics sometimes. It would be much more difficult and arguably not very valuable to have accurate, real-time, in-game updates to the model. TT's approach, if it's really as he described, sounds reasonable and balanced to me.

[fullmetal]

You can use analytics to prep your gameplan, choose formations and plays, etc. before the first snap.  But you know, everyone has a plan until they get punched in the face.  Adapt or die.  Bias toward the most recent data you have...which means in-game results.

[fullmetal]

You can use analytics to prep your gameplan, choose formations and plays, etc. before the first snap.  But you know, everyone has a plan until they get punched in the face.  Adapt or die.  Bias toward the most recent data you have...which means in-game results.