[Goose]

Eh, I could buy those arguments if the analysis indicated that going for it was a close decision. But for the most part it's just not.

If you're well away from the boundary line, then it's not that close of a decision. The second one (the 4th and 7) is in "go for it" territory, but only just. I sort of understand the rationale, though given the game situation I still think you ought to go for it. But the other one, the 4th and 1, was just bad. There was really no choice but to go for it.

I have looked at the article previously. I have two issues with it. First, the value of EP (expected points) is computed using data gathered from games where coaches make decisions as they do today. If the coaches used the model presented in this document, the data would change. We would for sure have lots more data on EP of 4th downs when they don't punt. So, the "actual" EP on 4th down from a given place on the field is probably significantly different from the measured average in today's game.
Second, using EP is an attempt to model a complex non-random quantity as a random variable. We are often forced to do this when the actual problem is just too complex to analyze. However, relying on this type of analysis can lead to seriously incorrect conclusions in "corner cases" like this. The problem is that there may be hidden structure that is not reflected in the measured expected value. For instance, (from the article), the time to get to the office on the back roads may be a function of the weather, or a function of your neighbors making the same choice you do. If you don't know about the other factors, using the expected value may make good sense. However, it may not ever produce an "optimal" strategy. You can actually do better if you include the other factors. That may be true even if you don't know what those factors are. Over the history of the game, the coaches have done a Monte Carlo simulation of what happens if you go for it on 4th down. The results of that simulation have convinced them that the actions indicated in the graph are in fact not optimal. It may be that their objective function isn't EP, but rather staying employed  :), which may not be the same thing. Anyway, the graph hasn't convinced them, at least not yet.

A minor point, but the distance from the boundary where EP is greater if you go for it than punt may mean very little. You would have to know what the two PDFs actually looked like. All you are sure of is the EP doesn't decrease. It may not increase very fast. In addition, the fact that the graph isn't non-decreasing from 90 yards down to 35 yards is very suspect. It is probably due to lack of meaningful data at the larger yardages because nobody goes for it there unless really forced to.

[Goose]

Eh, I could buy those arguments if the analysis indicated that going for it was a close decision. But for the most part it's just not.

If you're well away from the boundary line, then it's not that close of a decision. The second one (the 4th and 7) is in "go for it" territory, but only just. I sort of understand the rationale, though given the game situation I still think you ought to go for it. But the other one, the 4th and 1, was just bad. There was really no choice but to go for it.

I have looked at the article previously. I have two issues with it. First, the value of EP (expected points) is computed using data gathered from games where coaches make decisions as they do today. If the coaches used the model presented in this document, the data would change. We would for sure have lots more data on EP of 4th downs when they don't punt. So, the "actual" EP on 4th down from a given place on the field is probably significantly different from the measured average in today's game.
Second, using EP is an attempt to model a complex non-random quantity as a random variable. We are often forced to do this when the actual problem is just too complex to analyze. However, relying on this type of analysis can lead to seriously incorrect conclusions in "corner cases" like this. The problem is that there may be hidden structure that is not reflected in the measured expected value. For instance, (from the article), the time to get to the office on the back roads may be a function of the weather, or a function of your neighbors making the same choice you do. If you don't know about the other factors, using the expected value may make good sense. However, it may not ever produce an "optimal" strategy. You can actually do better if you include the other factors. That may be true even if you don't know what those factors are. Over the history of the game, the coaches have done a Monte Carlo simulation of what happens if you go for it on 4th down. The results of that simulation have convinced them that the actions indicated in the graph are in fact not optimal. It may be that their objective function isn't EP, but rather staying employed  :), which may not be the same thing. Anyway, the graph hasn't convinced them, at least not yet.

A minor point, but the distance from the boundary where EP is greater if you go for it than punt may mean very little. You would have to know what the two PDFs actually looked like. All you are sure of is the EP doesn't decrease. It may not increase very fast. In addition, the fact that the graph isn't non-decreasing from 90 yards down to 35 yards is very suspect. It is probably due to lack of meaningful data at the larger yardages because nobody goes for it there unless really forced to.