There's this high school football coach somewhere who will always go for it on fourth down. I can see his reasoning pretty clear in high school, every punt is this adventure of teenage-level talent, of bad kicks and bad coverage and botched long snaps and botched blocking. He would just rather risk giving the other team the ball at the thirty, and like his chances of converting a fourth-and-whatever. And in certain situations I can side with him. I mean, how likely is it that an offense will convert a fourth and inches? At the very least, I kind of like the wacky play where a team will fake going for it to just draw the other team offsides. If they fail, take the delay of game penalty. The scene is a quarterback yelling like mad while all the players pretend to be involved. I don't know, it's something. Anyway, in this post I'll go into all the statistics I can think of for when a team should punt or go for it. If anyone's curious, the data I'm using are from all NFL games from 2002 on, throwing out meaningless plays (taking a knee, hail marys at the end of halves, etc).
Below I've plotted up the average net change in yards (the distance of the punt minus the return yardage) based on field position. My frame of reference is yards to go for a touchdown; so if a team's on their own 20, then the yards-to-go would be 80.
On average a team will gain roughly 40 yards in field position if they punt. Things start to break down around 55 yards as touchbacks begin to occur.
So, if a team doesn't go for it, and punts instead, what are the odds that the opposing team would make it back to that original ling of scrimmage anyway? I've plotted out the odds that the opposing team makes it back to the original punting location, again, broken down by the kicking team yards-to-go. This data is all based on average drive lengths from a given field position (in this case, the field position dictated by a punt). I define "making it back" to the original line of scrimmage as the opposing (or receiving) team having a first down past the punting line of scrimmage, or scoring a touchdown.
For the most part, there's about a 35% chance that punting (instead of failing on a fourth-down conversion attempt) will make no difference in net yardage, and a 65% chance that punting is worth it. Things start to tick up right around mid-field (pretty soon after we start seeing touchbacks appear). So, generally, the benefit a team sees in punting (instead of just going for the 4th down attempt) starts decaying at mid-field.
Now all the data above is predicated on failure. What are the odds that a team will actually convert on fourth down? There's really not enough fourth down attempts to achieve a statistically significant result, so below I've plotted out the third down conversion rates for a number of different yards to go for a first down. I looked at fourth down conversion rates, and when I exclude the red-zone area, there's not much of a difference from third down. I went ahead with the third down numbers, as it's a bigger sample set.
So for anything a yard or shorter to go, there's nearly a 70% chance that the down is converted, and for anything shorter than 3 yards, that percentage drops to 50%. If you kind of squint at the data, if a team only has a yard to go they should always go for it. After that, it's a gray area; but if a team's on the opponent's side of the field, they should more or less never punt if there's only 1-3 yards to go.