Gaming Out Some Game Theory Under the New NFL Overtime Rule

by Hollywood Sports

I have previously offered my proposal for a change to the NFL overtime rules:

I have also written my thoughts about how the recent NFL change to the overtime rule may only kick the can regarding the problem they are attempting to solve:

In that second article, I identified some interesting Game Theory circumstances that coaches will now have. These decisions do not solve the inherent structural problem from the advantage of winning the coin flip award, but it does offer some avenues for good or bad coaching decisions to determine the ending of the game. I see three questions that head coaches will now encounter.

(1) We just won the flip — do we want the ball first or second?

The answer to this one may initially seem pretty straightforward since years of the college football overtime system have provided many examples to analyze how this dynamic plays out. Most college football teams who win the right to choose the first option in overtime choose the second possession. The logic is that the offense that understands exactly what they need to accomplish to win or extend the game has an advantage. What should an offense do if confronted with a fourth down? The team with the ball first may decide to simply kick the field goal. But this could be a mistake since their opponent now knows they can win the game with a touchdown — and change their play-calling to be more aggressive. On the other hand, if the team with the ball first attempts to go for it on fourth down — and fails — then their opponents seize a huge advantage since they can play conservatively and win the game with a short field goal. 

An important concept within Game Theory is this: it is disadvantageous to make the first critical (potentially game-defining) decision. 

Why is this? Putting yourself at unnecessary risk foregoes the opportunity for your opponent to offer you an advantage, free of charge (without taking a risk). Think of these scenarios as a game of chicken — the first one that blinks puts themselves at a disadvantage. This is the strategic foundation in chess to delay the deployment of the queen (with the Game Theory exceptions of this norm, notwithstanding). This is why college football teams choose the second possession in the overtime period. This is (one of the reasons) why it is more successful to avoid choosing big underdog upsets in the first round of your March Madness bracket (for every Saint Peter’s Hail Mary, there are far more misses — so let everyone else choose UAB while you retain the sizable haul from Houston). This is also a foundational reason that aggressive play in poker is advantageous when it forces your opponent to put all their chips at risk. 

Yet the “obvious” Game Theory decision within the new NFL overtime rules is not so obvious in practice. While the college system rotates who gets the ball first and last from round to round, the NFL system maintains the same order from round to round — but without a guarantee that that the team going last in round one will ever get the ball again (if their opponent scores first in that hypothetical round two). Opting for the ball last in the first round might doom that team to never getting a second chance at the football. This brings us to the second question.

(2) If trailing by seven points in overtime, should you attempt a two-point conversion if you score a potential game-tying touchdown. 

If the team chooses (to attempt) to simply tie the game with an extra point, then all their opponent needs is a field goal to win the game. Is the team better off by simply trying to win the game with a two-point conversion now? 

The real question is simple: does the team have a higher chance of successfully converting the two-point conversion than they do in stopping their opponent from scoring a touchdown or field goal? In practice, determining the true answer is very hard. Game Theory suggests the more opportunity you offer your opponent to make a mistake, the more likely they will. But the margins are getting thinner. 

(3) Should the team getting the ball first in overtime attempt a two-point conversion after their touchdown with the knowledge that their opponent could hypothetically win the game with a two-point conversion if they counter with a touchdown?

The real question posed to this team seems to be: are their odds of missing the two-point conversion lower than the risk assessment of (a) the probability that their opponent would choose to win the game with a two-point conversion rather than tie with an extra point (question (2), above; there is no risk of going for the two-point conversion if your opponent will always play for the tie) and (b) the probability of the success your opponent has in converting this two-point conversion. In poker, these risk assessments take place all the time in assessing pot odds regarding staying in a hand or folding. 

This is getting pretty complicated. Game Theory suggests that the more complicated the situation gets, the more likely someone will make a mistake. I don’t know how this will play out (besides knowing what Brandon Staley will choose in every instance). And the sample sizes are small. Even if the success rate of two-point conversions drops to 35% in overtime given the pressure of the moment, the depletion of a team’s best plays (that were already burned), and injuries impacting optimum effectiveness, teams that go for two will find some success. 

After playing these scenarios out, I still tend to defer to the assumption that the team that provokes their opponent to blink first will then be at an advantage. We have five months to game this out some more, maybe my thoughts will evolve?

Best of luck — Frank. 

All photographic images used for editorial content have been licensed from the Associated Press.

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