A model-based approach to football strategy.
|June 26, 2004|
The "coffin corner" kick, in which a punter tries to kick the ball out of bounds near the opponent's goal line, has largely gone out of style. These days, when punting from just outside field goal range, punters kick more or less down the middle -- the so-called "pooch kick" -- hoping to down the ball or have a fair catch near the opponent's goal.
Although it has been suggested that coffin corner kicks are more likely to be blocked, the choice mostly comes down to accuracy. Roughly speaking, the coffin corner kick requires the punter to control the kick's direction, whereas the pooch kick requires the punter to control the distance.
The most natural way to analyze this choice would be to examine data on a large number of coffin corner kicks, and a large number of pooch kicks, to see which approach leaves the opponents closer to their own goal line on average. However, since the optimal strategy might depend on exactly where the line of scrimmage is, one would have to condition the analysis on the field position. In addition, since some punters are more accurate than others, one would have to perform the analysis separately for each kicker. Hence, the amount of data available for each situation is small. And since the coffin corner kick has been largely abandoned in recent years, it's unlikely that examination of the results of punts in games will allow us to determine the optimal strategy for short punts.
In this article we will present a different approach, based on a simulation model. In the context of the model, neither pooch kicks nor coffin-corner kicks have any special status. Instead, we search over all possible spots on the field (or out of bounds) at which the punter could aim the kick, and find the aim point that gives the opponents the worst starting field position, on average.
The model's inputs can be determined on the practice field. The first piece of required information is the accuracy of the punter. This can be estimated by giving the punter a target roughly 45 yards down the field, and asking him to come as close as possible to hitting the target on the fly. For each attempt, an observer records both how long or short of the target the punt was, and also how far off line. From a large number of such attempts, one can estimate the probability distributions for that kicker's distance and direction, relative to the aim point.
The other type of information that we need has to do with the way the ball bounces. To get applicable data, we don't even need the team's actual punter. It's sufficient to have any punter repeatedly kick the ball about 45 yards down the field, and have someone record, for each kick, the direction and distance in which the ball bounces after landing. From such data on a large number of punts, one can estimate the probability distributions associated with the action of the ball after it bounces. (Strictly speaking, these data should be collected for various field conditions: The ball tends to bounce farther on an artificial surface than on rain-soaked grass.)
Teams presumably stopped attempting coffin-corner punts because they weren't happy with the outcomes. Before describing the simulation model and presenting some illustrative results, it's worth examining why coffin corner kicks are so difficult. Recall that a football field is 160′ wide, and that the hash marks are separated by
If instead the punter aims for the 6 yard line, the angle θ satisfies
What about aiming the kick toward the far sideline? This changes the situation in two ways, only one of which is helpful. Certainly, the angle is better if the kick is toward the far sideline. However, the ball has farther to travel. Repeating the trigonometric calculation using 29.75 yards to the sideline rather than 23.583, we find that it actually is a bit better to aim a coffin-corner kick toward the far sideline. However, in either case, the kick cannot deviate very much from the intended direction to be successful.
Of course, pooch kicks aren't easy to execute either. In the next section we will present a model that can evaluate both kinds of kicks in a unified framework.
In this section we will give a cursory description of the simulation model. A more precise description is contained in the mathematical appendix. Those who want the full details of the model, including all the specific parameter values, can consult the source code, which is written in MATLAB®.
The model works as follows: The punter chooses his aim point, which is characterized by the desired direction, and the desired distance that the ball travels in the air. The actual distance and direction are random variables, with means equal to the desired values. If the ball flies out of bounds between the goal lines, it is spotted at the yard line at which it crossed the sideline, in accordance with Rule 7-5-1. If the punt doesn't go out of bounds between the goal lines, but flies into or over the end zone, it is a touchback, and the opponents take over at their 20 yard line.
If the ball lands in the field of play short of the end zone, there may be a fair catch. We assume that the opponent's strategy is to call for a fair catch unless the ball comes down too close to their goal line, in which case they let it bounce. If the ball bounces, there are probability distributions for the direction of the bounce, and for the distance that the bouncing ball would travel if untouched. If the ball bounces out of bounds, or if it comes to rest in the field of play, the opponents take over at that point. If the bouncing ball is headed into the end zone, there is a chance that it will be downed by the kicking team. Roughly speaking, the probability that the ball is downed before reaching the end zone depends on how much time the punting team has to do so. Of course, if the ball bounces into the end zone, it is a touchback.
For each aim point, we simulate a thousand punts, and compute the opponent's average starting field position. We then search over all aim points to find the one that (on average) pins the opponents closest to their own goal. (Strictly speaking, the objective should be to minimize the opponent's probability of winning the game, so that the optimal aim point actually depends on the score and the time remaining. However, the expected yard line should be a reasonable enough proxy for our purposes.)
For the results presented in the next section, we set the standard deviation for the distance of the kick equal to 15% of the intended distance. (This corresponds to almost 7 yards on a kick intended to travel 46 yards in the air.) We used 10° as the standard deviation for the direction of the punt. These are the most important parameters in the model. We must emphasize that in an actual application, these parameters would be set to match the punter's experimentally estimated accuracy, and the parameters related to bounce would correspond to the particular surface on which the game is being played.
For punts that land in the field of play, we assume that the opponents let the ball bounce if it comes down inside their 5 yard line, and otherwise call for a fair catch. This rule proved to be roughly optimal for the opponents in the context of the model.
We have not modeled the possibility of a runback. For coffin corner kicks, of course, the punt goes out of bounds or into the end zone. On a pooch kick, the receiving team almost always calls for a fair catch or lets the ball bounce. However, poorly executed kicks or coverage lapses by the punting unit (or both) do occasionally permit a substantial runback. It wouldn't be difficult to expand the model to incorporate this possibility.
For the results presented here, we will suppose that the ball is spotted at one of the hash marks, and that the line of scrimmage is the opponent's 39 yard line. In this case, the optimal aim point turns out to be the spot on the field that is on the opponent's 7 yard line, 16 yards from the nearer sideline. With this aim point, the opponent's expected starting field position is the 12 yard line. Interestingly, in a random sample of pooch kicks from the 2003 season, the 12 yard line was the observed average starting field position for the receiving team. This suggests that the parameters we are using are reasonable.
The optimal yard line to aim at remains close to the opponent's 7 even if the line of scrimmage differs a bit from the 39 yard line. However, the distance between the optimal aim point and the sideline changes. For example, from the opponent's 41 yard line, the punt should be aimed about 20 yards from the sideline, rather than 16.
The reason why the optimal aim point is angled toward the sideline is that this slightly mitigates the randomness of the length of the kick. Indeed, if a punt travels straight downfield, each yard more or less of distance has an equal impact on the yard line at which the ball lands. However, if the kick is at an angle, an extra yard of distance in the direction of the kick translates to less than a yard in the direction of play.
One of the comforting results of the model is that there is a fairly wide range of aim points that are nearly equally effective. For example, the punter can aim the kick straight ahead, rather than angling it slightly toward the sideline, without significantly enhancing the opponent's expected starting field position. Similarly, he can aim for the 5 yard line, or the 9 yard line, without much expected cost.
However, this robustness doesn't extend to punts aimed out of bounds -- in other words, coffin corner kicks. Among coffin corner kicks, the best choice according to the model is to aim toward the far sideline, at the opponent's 2.5 yard line. However, with this aim point, the opponent's expected starting field position is the 15 yard line -- substantially worse (for the kicking team) than what can be obtained with a pooch kick. In order for a coffin corner kick to be optimal, the punter's standard deviation for direction has to be about 4°, which seems implausibly low.
Alternatively, coffin corner kicks become optimal if the punter has very poor distance control. However, the standard deviation for the distance of the punt would have to be 30% of the intended distance before intentionally kicking out of bounds is as effective as a pooch kick. If the punter's distance control is that bad, replacing the punter seems preferable to resorting to coffin corner kicks.
Copyright © 2004 by William S. Krasker