When to Intentionally Allow a Touchdown

This study examines a team's chances of winning at the end of the game when an opponent is in potentially game-winning FG range. It's a dire situation for the team on defense because the offense could run enough time off the clock before its FG attempt so that there is no time to respond.

The Field Goal Choke Hold situation looks like this:  The defense has a lead of 1 or 2 points with less than 3 minutes to play. The opposing offense has just converted a first down inside FG (attempt) range. Through week 13 this season there have been 12 games that qualify, which makes this situation about as common as overtime. (There were 12 more games with similar circumstances except the game was tied, a situation nearly identical but that requires some slightly different math.)

Two strategies are compared. The first is playing for the stop and forcing the FG attempt. This may be dangerous due to the ability of the offense to burn clock. The second strategy is to allow an immediate TD. This strategy forfeits points to the opponent in exchange for enough time to respond with a game-winning TD drive.

There is no guarantee the offense will take the bait and score a TD. If the offense is cognizant of the strategy, they may take a knee close to the goal line. So strictly speaking, this analysis merely estimates which combinations of circumstances make an immediate TD preferable to forcing a FG attempt. Even if all offenses were prepared for this contingency and were inclined to take a knee, this analysis lays out when that would be the smart move.

Analysis Overview

There are many considerations in the analysis:

1. The current time on the clock
2. How many timeouts you have
3. When you would get the ball back given a series 'stop' and a FG
4. The current field position of your opponent
5. The accuracy of a FG attempt from the expected attempt distance
6. The chance of scoring either a FG or TD after the 'stop' and FG
7. The chance of scoring a TD from your own 20 given an intentionally allowed TD at the current clock time, minus the time for the TD play itself

The problem boils down to a single comparison: A defense would prefer to intentionally allow a TD whenever the probability of scoring a TD in response exceeds the total probability of the offense missing the FG attempt plus the possibility that either a FG to TD can be scored in response to a successful FG.

Assumptions

It's a very complex problem with many moving parts. To simplify the analysis, there are several assumptions needed. The intent here is to begin to get our arms around a seemingly impenetrable problem. First, for now, I'll only look at first downs as decision points. In other words, we'll decide whether to play for the stop or to allow a TD immediately following a series conversion by the offense.

Second, once within reasonable field goal range, the offense will only run the ball and will not make another conversion. Of course they could convert, but this would be the least preferable outcomes for the defense. The possibility of a series conversion would only add weight to the scale on the side of intentionally allowing a TD. As with other analyses questioning conventional wisdom, it's best to choose simplifying assumptions that count in favor of the conventional choice and against the unconventional choice. In other words, this analysis says, "Coach, even if you were to certain to get the stop, you would still want to allow the TD..."

Another assumption is that the team on offense will play smartly enough not to commit a significant penalty or turnover.

Also, the offense will gain a modest amount of field position on its three plays prior to a FG attempt. For the sake of simplicity, I'm going to say there will be 5 yards gained between 1st and 4th down prior to the FG attempt. Unless the offense is at a very long FG attempt range, a few yards in either direction will not make a large difference in the final analysis. Additionally, the offense will use 39 seconds between plays (whenever a timeout is not called or two-minute warning does not occur), and plays themselves will take 6 seconds.

Lastly, the analysis assumes that after a score, the subsequent drive will start very near a team's own 20-yard line. This is plausible because touchbacks are now so common that the average starting position following a kickoff is a team's own 22, and touchbacks would be preferred by the receiving team because no time elapses on the play.

Analytic Approach

If a team does allow a TD, it would need its own in response to win. The probability of scoring a TD is a function of only time remaining. The probability estimates for scoring are based on recent history where teams need a TD to tie or win on a final possession.

If the team on defense forces the FG attempt and it's successful, a TD or FG in response would be needed to win. The probability of scoring either a TD or FG is also a function of time and based on recent historical scoring rates for teams that need a score to tie or win in the endgame.

The main question boils down to three possibilities:

A. Forcing a stop and hoping for a FG miss
B. Given an opponent's made FG, getting your own FG or TD in response after the opponent has burned as much time as possible
C. Getting your own TD in response to an intentionally allowed TD at the current time remaining (minus the duration of the play).

Possibilities A and B comprise the win probability (wp) for forcing the stop and the FG attempt. Possibility C directly relates to the chances of winning after allowing an intentional TD. [I left wp in lowercase to distinguish it from the global Win Probability model I often use. This analysis estimates the chances of winning indirectly using scoring probabilities in the endgame. This is necessary because the number of timeouts is so critical.]

Or alternatively:

wp[force FG] = p(FG fail) + p(scoring | made FG)

wp[allow TD] = p(scoring own TD in response)

The decision should be whichever wp is higher:

Decision = max{wp[force FG], wp[allow TD]}

The next four parts of this series will estimate the time that the team on defense will regain possession (part 2), estimate the probability of a failed FG attempt (part 3), estimate the probabilities of the team on defense responding with its own score (part 4), and present the final results (part 5).

9 Responses to “When to Intentionally Allow a Touchdown”

1. j holz says:

At the risk of making it even more complicated, if the defense has a one point lead, don't we need to account for the offense potentially going for two and making it?

2. Brian Burke says:

That's true. The Giants did that in the SB last year.

3. Anonymous says:

Shouldn't we have an extra p(made FG) on the end of wp[force FG], so it becomes:

wp[force FG] = p(FG fail) + p(scoring | made FG) * p(made FG)

Otherwise, it's possible to have wp[force FG]>1! For example, suppose
p(FG fail)= .5
p(scoring | made FG) = .6

Then the formula given in the article calculates wp[force FG] .5 + .6 = 1.1, instead of the correct wp[force FG]= .5 + .6 * .5 = .9.

4. Nate says:

Is refusing to take the touchdown if the defense leaves the field a 'palpably unfair act'?

Could the defense put 15 players on the field (or use some other deliberate dead ball foul) to advance the offense to the goal line without using the clock?

There's some strangeness with the way that the clock works in football. In yesterday's blow out, the Seahawks offense could have kneeled the entire fourth quarter, but that would not have gone over well.

5. mike says:

Rather than entering situations where it is correct to "let them score" it is more intelligent to know in advance when you will enter those situations and design a gameplan accordingly to prevent it.

The game plan is designed to either:
1) stops opponent, or
2) give up a TD rather than a conversion
3) Gives up a big enough play to force a 1st and goal, rather than a 1st and 10.
The 2nd option is for when a conversion would put defense in "let them score" territory, or close enough to it that providing the extra coverage short and intermediate and/or pressure will be worth sacrificing the deep zones.

The 3rd option would be buying you more time by preventing opponent from being able to get ANOTHER conversion after this one. The third option would be relevant when two conversion allows opponent to run out the clock or leave you with such little time that you have minimal time to get a fieldgoal, but one does not IF opponent converts on the next play.

Of course, this game-planning would require a good understanding of when those "let them score" opportunities are so you can construct coverages and plan on aggressive "all or nothing" blitzes, so this point actually strengthens the need for this information.

Intuitively, I suspect teams should consider playing a "goal line" style of defense where they don't defend deep routes and they come hard into the backfield, or a "cover zero" blitz and more aggressive strategies just before entering this point to essentially either STOP them OR let them score (Or in some cases, prevent them from being able run out the clock by forcing one or more fewer conversions).

In some situations a traditional cover two is best. This way the "hole" in the zone of the coverage is deep to the sidelines, while also eliminating short and over the middle. Ideally this coverage IF it doesn't stop the opponent from converting, will set up a first and goal rather than a first and 10 for reasons discussed above.

6. Brian Burke says:

Mike, some very smart thoughts there.

Anonymous above, no. Your total probability math is incorrect. If p(FG success) = .5, then you need to multiply the p(responding score) by (1 - .5) for that term.

7. Sam Shainsky says:

And when adrian peterson needs to break the nfl rushing record :)

8. Brian Johnson says:

I took a look at this post after your session at the MIT Sloan Sports Analytics Conference today. My thoughts were similar to Herm's on this. It's very difficult to ask a defense to allow the opponent to score, even if this is statistically the best decision. I was thinking that it might be better to just go with the defense that has the highest chance to cause a turnover, assuming the offence will score if you fail.(And I see that Mike covers this well above.) The question is, is there a high percentage turnover defense? Could one even be designed for this situation?

9. Anonymous says:

I would think if a defense were on the brink of being faced with a "let them score situation" you would want to go with a high risk/high reward defense. A lot of teams play bend but don't break (cover 3/cover 1 blitzes, etc). I would blitz 6 and try to make a big play on defense, if you don't, they score before they have time to think about a situation where they might take a knee at the 1.

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