Payton's Gamble

In last Sunday's game between New Orleans and Denver, down 24-17 with 30 seconds left in the 2nd quarter, the Saints faced a 4th down and goal from the 1 yard line. Normally, all the numbers say 'go for the touchdown,' and this was indeed what the Saints' decided to do. I love aggressive decisions on 4th down, but we'll see why going for the field goal would have been the slightly better decision.

According to the Romer paper, going for it on 4th goal makes sense anytime the offense is inside the 6 yd line. The key to the advantage in going for the TD is that a failed attempt leaves the ball deep in an opponent's own territory. It's likely that the opponent will end up punting and giving the ball back in excellent field position, or even allowing a safety.

And that's exactly what happened Sunday. The Saints failed in their attempt, leaving the ball for the Broncos at the 1. On the very next play, the Saints stuffed a run and scored a safety. And even though they got 2 points out of the situation, it was a highly improbable outcome. They should have kicked the field goal.

The fundamental difference between the normal Romer-type expected points analysis and this situation is that there was under 30 seconds left in the half. Neither team had any time outs remaining, so neither team had time to mount a follow-on drive. The lack of time means that the benefits of the follow-on field position are very limited. It also means that the value of the ensuing kick after a score doesn't have to be factored in. With only a few seconds remaining in the half, a kick off would undoubtedly be of the 'squib kick to the 3rd string TE' variety. There's no chance it would be returned.

We can evaluate the decision in a simple expected utility calculation. The chance of scoring from the 1 yd line is 39%, and field goals are 99% successful from that range. The chance of forcing a safety from the 1, given an unsuccessful TD attempt, is 4%. (In the past 8 years, there have been 267 runs from the 1, featuring 12 safeties and zero fumbles. The Broncos would have been crazy to pass, so I'll ignore the possibility of an interception.)

Value(TD attempt)= 7 * P(successful TD attempt) + 2 * P(unsuccessful TD) * P(Safety)
= 7 * 0.39 + 2 * (1-0.39)(0.04)
= 2.73 + 0.05
=2.8 points

Value(FG attempt)= 3 * P(successful FG attempt)
= 3 * 0.99
= 3.0 points

The percentage play for the Saints would have been the field goal in this situation, but not by much. If for some reason Sean Payton thought his offense had a much better than the league-average chance of scoring from the 1, it would have made sense. But that would be a stretch given New Orleans' lack of a power running game.

To prevent a safety, Shanahan might have called for the QB sneak. The Broncos only needed to take a single snap, and the sneak is probably the most safety-proof type of play. I suspect that he feared a fumble more, and didn't want the ball in Cutler's hands in that situation.

This situation is a good example of how the end of the half alters the equation for decision making. Early in the half, we can treat the flow of the game as effectively infinite. But as the clock winds down, we have to account for the effect of an approaching time horizon.

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7 Responses to “Payton's Gamble”

  1. Anonymous says:

    Hi - Great articles. I had a question (unrelated to this particular article) for you. How do you get the data for your analyses ? Do you buy it from STATS or procure it get it from some other source.. (especially the esoteric stats around details of each play (yardage, down info, etc.)

  2. Brian Burke says:

    Thanks. I taught myself PHP and wrote a program that parses gamebook files. Excel Pivot tables make the analysis a breeze. It's one of those incredibly powerful tools in MS Office that most people never use.

  3. JKL says:

    Is the success rate on plays from the 1 really only 39%? I knew it would be lower than in the middle of the field, but that seems low. I would have guessed closer to 50%.

    It probably doesn't matter materially, but I think your assumption on the safety rate in the particular situation is low for the same reason that you assume Denver should not pass. New Orleans wasn't trying to prevent a first down and force a punt to get good field position. They were trying to penetrate and get a safety. Gap control was less important, because what difference does it make if Hall gains 10 yards or 2?

    For grins, I do think Denver should have thrown an intentional incompletion on a 3 step drop by sailing it over the receivers head on a sideline route, precisely to give the Saints something to think about instead of just selling out on the run. With no timeouts, what difference does it make if Denver runs out the clock on first or second down?

    At what point, in this particular game, did maximizing win expectation and maximizing points diverge? As an extreme example, going for it on 4th and 20 at the opponent 20 has a lower point expectation than kicking the field goal, but if there is 1 minute left and you are down 6, you go for it.

    The Broncos had scored 24 points in one half, and were the highest scoring team coming in. The Saints D is below average. They trailed by 7. I think there is a good argument that the difference between scoring a touchdown and getting a field goal and being down 4 still was more valuable than the difference between getting 0 and getting 3.

  4. Brian Burke says:

    I thought it would have been higher too. The 39% is for all runs from 4th and goal on the 1.

    That's a good point about the Saints' D selling out for the safety. I didn't consider that. To make up that extra 0.2-pt difference, they'd need at least a 14% chance at the safety. I doubt that's realistic, but there's no way to tell.

    I'm not 100% sure at what point the game switched from 'point maximization' to 'win probability.' In general, it seems like the late 3rd quarter. (See my post on 'The End Game.') But it's not a distinct moment. It's a gradual transition that partly depends on the score difference.

    At halftime, teams down by 7 have about a 35% WP, and teams down by 4 have about a 43% WP. (Tied would obviously be about 50% depending on who receives the kickoff).

    My intuitive sense is that the game was still in the point-maximization phase. If you look at my WP graph, it looks like the divergence for a 7-point score difference occurs at about the 5-min mark in the 3rd quarter. That's when the WP drastically drops for the trailing team.

    Really interesting question...

    (As an aside, teams down by 4 usually have a better WP than teams down by 3. Why? My guess it's because teams down by 4 are playing for a TD and are more aggressive, and teams down by 3 are playing for the tie and are too conservative.)

  5. Tommy_Grand says:

    Another great article!

  6. Anonymous says:

    How do you think coaches should think about their specific team (and the opposition) v average? If Payton thinks that hiss team is above average, is that enough to make up for the .2? If the opponent is below average? My sense is there is some difference in the probabilities where the answer is a wash, and the non-measured functions need to play a huge role (how is our O-Line v Dline doing? Think our RB out leap their LB? Can our QB look for enough of a Oline push to get the yard?

  7. Tarr says:

    Good point about the lack of benefit of field position. That said, I have two objections to your analysis that may tip the scales slightly in favor of the agressive decision:

    1) I don't think it's fair to simply assign a 4% chance of a safety and leave it at that. Teams DO attempt passes from the 1, and it's obvious from a game theory perspective that you must be at least potentially willing to attempt a pass. I would be a lot more comfortable with a broader analysis of all (non-punt) plays run from the 1, 2 or 3 yard line, which would surely reveal some fumbles and picks.

    2) The Saints were down 7 at the time. As the trailing team, there is some increased incentive to play high-risk, high-reward football. After all, losing by 4 is really no better than losing by 7. Rather than simply calculating expected score, how about looking at the probability of winning a game when down by 7, 5, 4, and 0 points at halftime, starting the second half kicking off to the other team?

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