It’s a classic football conundrum. You’re down by two scores and need a touchdown and a field goal to survive. With time dwindling, you move the ball inside field goal range with a fresh set of downs. Should you:

a) attempt the field goal right away to save time for a possible last-minute touchdown drive? Or,
b) should you continue to drive for a touchdown, and hope to get a quick field goal later?

It seems like a question we could answer with empirical win probability, but there cases of relevant situations leave the intent of the offenses unclear. Teams overwhelmingly prefer option b. The answer is dependent on a number of important factors, including score, time, field position, and timeouts. We would need a large sample size for each combination of factors to build a reliable model for when (if ever) it would be a good idea to try an immediate field goal. It’s definitely a question outside the box of convention, and a perfect problem for my simulation model, the WOPR.

The WOPR can create as large a sample as desired for each combination of relevant factors. We can then compare the win rates for the two alternative strategies—immediate field goal attempt, or continue to drive for the touchdown.

Judging by recent examples, the conventional strategy is to forgo the immediate field goal attempt and continue to drive. I’ll call this the standard strategy. In my formulation of the standard strategy in the simulator, I programmed the offense to continue its drive as it otherwise would and try a field goal any time it reaches 4th down. For the FG first strategy, I programmed the offense to attempt an immediate field goal and then proceed as it otherwise would according to general onside kick guidelines other end-game tactics.

I created 30,000 games for each strategy starting from all combinations of the following

-11 through -9 points score difference

3 timeouts to 0 timeouts for the offense

Starting yard line from the 35 to the 5 in 5-yard increments

From 6 minutes to 30 seconds remaining in 30-second increments

The number of timeouts for the team on defense (the team ahead) would be a very minor factor and would come into play only in the most freakish sequence of events. For these sim runs, I left the defense's timeouts at 3. Together the initial parameters comprise 960 various scenarios, so I’ll present the results for only a handful of representative examples. But it should be enough to convey the general pattern and gain some insight.

The first example situation is down by 10 points, 1st down & 10 at the 30 yard line, 2 timeouts. In this scenario, the preferred option is to continue the TD drive until about 4 minutes remaining, when the FG first strategy becomes the preferred option. By the 3-minute mark, the advantage for attempting an immediate FG becomes quite pronounced—5.5% to 3.5%.

Now let’s change one parameter. The next example moves things to the 15-yard line, keeping everything else the same. The FG first strategy loses much of its advantage as we get closer to the end zone, which makes intuitive sense. It becomes preferred much later--inside 3 minutes to play--and by a slighter degree.

Next we’ll go back to the 30-yard line and take away a timeout. Win probabilities for both strategies suffer due to the fewer number of timeouts, but the standard strategy suffers slightly more. The advantage for the FG first strategy is more pronounced, at least in relative terms.

The last example changes the deficit to 9 points. The FG first strategy is preferred as early as almost 5 minutes to play.

These results surprised me. Going in, I thought there would likely be very few scenarios when a FG first strategy would be preferred. I thought something was wrong with the model, so I watched the simulated play-by-play for several games. When a team was able to tie or win, they were able to do one thing almost every time. They avoided a situation that called for an onside kick.

That’s what’s driving these results. Onside kicks require the pathway to victory to pass through a narrow probability corridor. Successful recoveries are especially unlikely when the receiving team is expecting them. Continuing a drive intending to get a touchdown, even if successful, forces a team into a situation when they have little choice but to kick onside. The bottom line is to do whatever is needed to avoid needing an onside kick.

Notice how the 15-yard scenarios don't indicate as much of an advantage for taking the field goal first. That's because the amount of time an offense seeking a touchdown could burn from the 15 isn't as much as much it could burn from the 30. The probability for the need of an onside kick diminishes the closer an offense is to the end zone, given the same time remaining in the game.

The second most important factor is the need for a stop. Assuming an onside isn't required, a team down by two scores will need to make a stop between scoring. Kicking an immediate field goal allows for the possibility that the opponent is able to get a first down or possibly more before the trailing defense is able to get the ball back. That's why the advantage for the field goal first strategy begins as early as five minutes left to play.

I wonder if the best thing to do might be to take three quick shots into the end zone with a low-risk mindset prior to attempting a field goal. If the play isn't there, the quarterback should be quick to throw the ball away. That strategy burns only a handful of seconds off the clock but gives the offense a realistic chance of getting a quick TD and then only needing a field goal to survive.

As with most strategic questions, the difference might seem minor. One option might offer a 6% chance of winning and the other a 3% chance. But as I always say, every little bit helps. A team could get an extra couple percent here, another few percent there, and pretty soon you can build a 10% edge each game.

The next step is to create something useful for coaches. Coaches shouldn't care whether one tactic would result in a 0.05 WP and another would result in a 0.03 WP. They just need to know which one is better, and when. The actual WP numbers themselves aren't critical. So a table or set of tables that lists the time at which the field goal first alternative becomes preferred, based on score, field position, and timeouts, might be handy.

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• ### Brian Burke

A couple things I had intended to mention:

1. Thanks to Hugh for first asking this question several months ago.

2. All simulated results, like this, need to be looked at with a skeptical eye. Outputs can be very sensitive to small changes in the model underneath. If I don't have a realistic 2-minute offense or a 4-minute offense represented well, the results could be meaningless. I trust the results because I know how the sim works, but it would be proper for readers to be less confident.

3. Simulated output might not give us perfectly accurate results. I wouldn't want to claim that an offense would have exactly the WPs illustrated in the charts above. But that's ok. All that matters to a decision maker is which alternative is better. That's a much lower bar.

• ### Nate

Considering that winning from a 10-point deficit requires overtime or a 2-point conversion, the win probability seems like it should be around half of what it is when the team is down 9, but the simulation shows something closer to a fixed offset. That makes me wonder how confident we should be in the .02 difference the model predicts for 'kick first'.

It seems like there are two rules of thumb:
* It's better to kick a field goal, and kick off conventionally than score a touchdown and kick on-side.
* You can score touchdowns on a punt return.

• ### Guest - Tron

It all comes down to clock / game management. Coaches are generally very short sighted and don't see the big picture.To win, you need at least 3 things:
a) a touchdown drive
b) a field goal drive
c) a defensive stop / onside kick. Manage your game plan according.

If you are onside kick when it could have been avoided, you have failed at managing the game.
If you spend 3 minutes to move the ball from the 30 yd line to the 2 yd line, and STILL opt for a FG, then you also fail.

• ### Keith Goldner

I feel like a huge portion of this analysis hinges on the assumption that opposing teams will run the ball three times and punt when up by a touchdown in the closing minutes of the game. This is certainly true with many teams and causes a huge inefficiency for those teams trying to run out the clock. I would guess if opposing/winning offenses were treated as non-under 5-minute offenses and rather as regular offenses, these results wouldn't hold. Would be interesting to see though and definitely seems like something coaches could take advantage of for now.

• ### Guest - Rog

I agree with Keith - these results don't make a lot of sense mathematically unless the opposing coaches are allowing their play selection to be detrimentally influenced by game state. I feel this result is probably related to the way it is better to be up by 3 than by 4-6 near the end of the game - that should never be the case, but is because of poor coaching.

• ### Brian Burke

Keith/Rog--Not claiming it's perfect, but the sim directly samples from actual 4-min offense play, including play type (pass/run), elapsed time, and yardage based on down/dist/field pos. It is very run heavy, but not 100%.

Nate-I also noticed that. The reason that being down 9 isn't twice as good as being down 10 is because of certain 'freak' outcomes. Kick returns. Pick-6s. Fumbled kick returns. Stuff like that.

• ### James Sinclair

Very interesting. I'd like to see the what the numbers look like for a team down by 8. I wouldn't be totally shocked if, even then, there are some scenarios where a field-goal-first strategy makes sense (not that any current coach would dare to do it).

Most coaches seem to take the same strategic approach to an 8-point deficit late in the game as they would for any other margin from 4 to 7—they assume scoring a touchdown is the most important immediate goal, and anything else can be sorted out later. But if you have a 50% chance of making the two-point conversion, and a 50% chance of winning if the game goes to overtime, your WP even after scoring the late touchdown isn't going to be much more than 25%. Possibly significantly less, depending on how much time is left for the other team to drive for a last-second field goal.

It seems like, for a team down 8, with all three timeouts and a first and 10 on the opponent's 20 with, say, three minutes left, kicking a field goal right away has to at least be worth considering. Or, even better, taking three quick, low-risk shots at the end zone and then kicking.

• ### Nate

> Nate-I also noticed that. The reason that being down 9 isn't twice as
> good as being down 10 is because of certain 'freak' outcomes. Kick
> returns. Pick-6s. Fumbled kick returns. Stuff like that.

Kicking a field goal with 150 seconds left has a difference of around 0.01 on the two charts. So the implied win equity from 'freak' incidents is around 0.03 - more than from getting the stop and a touchdown conventionally.

More generally, it occurs to me that while it's easy to run 30,000 iterations of a simulator, the league's only played about 3000 games since 2002, and many of those won't have been close in the last minutes. Is there really enough raw data to produce a model that's credible down to these single-digit percent differences?

• ### Guest - Tron

I think your hypothesis needs to be clarified. If you are testing your claim based on empirical data, then you NEED to account idiotic conservative coaching by the other team. If you are basing it off of theory, then it's a no-brainer that you should go for the TD first. If you immediately go for the FG, you are simply wasting yardage/downs. It is a DOMINATING strategy to go for the TD.

• ### Nate

In reply to: Guest - Tron

> ... If you are basing it off of theory, then it's a no-brainer that you
> should go for the TD first. If you immediately go for the FG, you are
> simply wasting yardage.downs. ...

"There are more things in heavy and earth, Horatio, than are dreamt of in your philosophy" -- Hamlet

I have my doubts about the numbers posted here, but even with 'theoretically optimal variance indifferent coaching' there are factors that make the decision more complex than that:

By kicking a field goal early you can get a free time out from the 2-minute warning. Since this is clearly a scenario where time and timeouts matter, that could be a significant factor. (How often do you think a losing coach would be willing to trade 30 yards for 40 seconds?)

The timing rules change over the course of the game. For example, things like inentional fouls to stop the clock aren't allowed in the last minute of the game. That means that the time equity of possession can change (and is probably higher in the last minute.)

We don't have a particularly large sample of desperation on-side kicks which means that we have limited confidence in the expected recovery rate.