Over for NFL Overtime?

In recent years a growing outcry has built up against the current sudden death overtime system in the NFL. The vast majority of the complaint comes from the power of the opening overtime coin flip in determining the winner. It is unnecessary to rehash all of the statistics supporting the ‘power’ of the coin flip when sites like NFL.com, AdvancedNFLStats.com, pro-football-reference.com and others have already done it in far more detail than is necessary here. The simple fact is that over the last 10 years the winner of the coin flip wins the game approximately 61% of the time with 60.4% of those wins coming on the first possession without the other team ever receiving an offensive possession. Basically 37% of overtime games end with only one team getting an offensive possession. Clearly opponents of the current system believe these numbers provide enough support to demonstrate how unfair the system is and that it needs to be balanced.

The possible outcomes for the current overtime system are shown below for the first two possessions;

Assume that Team A wins the coin flip and elects to receive –

Team A scores a touchdown, Team B receives no possession, Team A wins;
Team A kicks a field goal, Team B receives no possession, Team A wins;
Team A does not score, Team B does not score, game continues;
Team A does not score, Team B kicks a field goal, Team B wins;
Team A does not score, Team B scores a touchdown, Team B wins;

There are two popular counter-arguments to the cry for overtime reform. First, if the team that lost the flip and then later losses the game had done their job in regulation there would have been no need for overtime. Therefore, if a team cannot win in the first 4 quarters there is no justification to complain about losing in overtime and never receiving an offensive possession.

Second, the age-old statement of: ‘if you want the ball stop the offense.’ Defenses in the NFL are paid to stop the opposing team’s offense. If a team loses the coin flip and wants to win the game then the defense should be able to stop the offense and get it back, otherwise the defense has failed in its job limiting the ability to complain about the system. Although valid, neither argument actually addresses any inherent ‘unfairness’ of the overtime system. Instead they attempt to avoid the issue in effort to focus on the team’s responsibility for the situation. Basically the attitude is: ‘do not complain about the circumstances of the scenario because you are responsible for the occurrence of the scenario in the first place.’

With that said suppose a change would be made to the overtime system in an attempt to neutralize the unfairness. The principle element of the solution would have to have a level of finality. It is probable that players would balk on a system that could go back and forth similar to the overtime system in college football both due to the additional potential for injury and a mindset of ‘unpaid overtime’. Also most would demand that both teams receive at least one possession. Unfortunately these two elements may initially contradict each other because of the reasonable possibility that both teams go back and forth with one taking the lead and then the other equalizing the previous score.

In addition to this potential back and forth, it would be useful for the change to alter the dynamic of the coin flip. As a vast majority of NFL teams select to receive the ball in the current system, almost all college teams select to play defense first if they win the coin flip. In a ‘each team gets the ball at least once’ situation clearly the team that wins the coin flip will simply select defense instead of offense. There should be more equality in selecting offense or defense by the team that wins the coin flip. One possible reform to the overtime system is described below:

In a given overtime period if both teams are guaranteed to have the ball once there are nine possible outcomes:

Assume that Team A wins the coin flip and elects to receive –

Team A scores a touchdown, Team B does not score, Team A wins;
Team A kicks a field goal, Team B does not score, Team A wins;
Team A does not score, Team B does not score, game continues as sudden death;
Team A scores a touchdown, Team B kicks a field goal, Team A wins;
Team A kicks a field goal, Team B kicks a field goal, game continues as sudden death;
Team A does not score, Team B kicks a field goal, Team B wins;
Team A scores a touchdown, Team B scores a touchdown, game continues as sudden death;
Team A kicks a field goal, Team B scores a touchdown, Team B wins;
Team A does not score, Team B scores a touchdown, Team B wins;

As statistically anticipated the results are broken down into three categories of three where Team A wins, Team B wins or the game remains tied and continues into sudden death. The first two categories are appropriate because the game ends; however, with a statistical probability of 1/3 and an actual occurrence probability exceeding 1/3 for a continuing game such a ‘each team receives 1 possession’ rule may not be suitable by itself. Fortunately the possibility of such a dilemma offers the opportunity to generate new conditions that would not only solve the problem, but also add a level of strategy to overtime in addition to diversifying coin flip selection. The addition of two new ending conditions could resolve these concerns by eliminating two of the three continuation conditions.

First, if the receiving team scores a touchdown then the game ends similar to if the sudden death system were still in place. Second, if the receiving team kicks a field goal and then the kicking team kicks a field goal in the next possession tying the game, the kicking team would win the game.

Initially it could be argued that these two new conditions destroy the point of the overtime reform. Application of the first condition revives the ‘unfair one team may not get the ball’ aspect of the current overtime system. Although true, most of the problems that opponents have with the current sudden death overtime system is that a field goal ends the game, not a touchdown. No one complains that it is unfair that the game ends after the team that wins the coin flip drives 70 yards for a touchdown. No, the complaints come from the fact that the team that wins the coin flip can drive 35 yards and kick a 52 field goal for the victory without the opposing offense getting the ball. Overall if the kicking team cannot prevent the receiving team from scoring a touchdown on their opening drive of the overtime period the kicking team has no reasonable ability to complain.

Application of the second condition would be criticized in that the game is once again tied so why should one team be awarded the victory over the other team? There is no explanation that will completely satisfy that complaint; however, such a condition is useful in both improving the variance of and shifting the power of the coin flip as well as reducing the probability of a prolonged overtime period. Think of it as a special overtime rule similar to the current sudden death system.

For instance if Team A wins the coin flip they now have an important decision to make. They can choose to receive the ball and try to end the game with a touchdown. However, if they fail and only end up kicking a field goal, then the opposing team can win the game with only a field goal instead of a touchdown. If Team A chooses to kick the ball they may never get a chance on offense if the opposing team scores a touchdown, but if they can hold the opponent to only a field goal or nothing then they have an offensive advantage.

The new breakdown of outcomes with these two new conditions:

Assume that Team A wins the coin flip and elects to receive –

Team A scores a touchdown, Team B receives no possession, Team A wins;
Team A kicks a field goal, Team B does not score, Team A wins;
Team A kicks a field goal, Team B kicks a field goal, Team B wins;
Team A kicks a field goal, Team B scores a touchdown, Team B wins;
Team A does not score, Team B does not score, game continues as sudden death;
Team A does not score, Team B kicks a field goal, Team B wins;
Team A does not score, Team B scores a touchdown, Team B wins;

Looking at the possible outcomes one may balk at the new conditions for now from a pure statistical standpoint with a 50% - 50% determinate when neither team scores on the opening possession the receiving team only has a 35.71% chance of winning (2.5/7) where as the kicking team has a 64.29% chance of winning (4.5/7). This new system simply flipped the percentages, how is that fair? Remember that 61% vs. 39% are the empirical percentages (the real outcome percentages) for the current overtime system even though the statistical theoretical percentage is 50% - 50%. Clearly if the statistical theoretical percentage were genuine to real conditions the controversy regarding the overtime system would not exist. Therefore, it is important to estimate the real outcome percentages in this new system through extrapolation from existing data to truly judge the outcome percentages.

Recall that in the current system there are two avenues of automatic victory for the receiving team, but in this new system there is only one. 37% of the games in the current system end without the kicking team having an offensive possession. Initially one may think that cutting that value in half is appropriate; however such a thought is not accurate. It would be more appropriate to suggest that 75% of the aforementioned 37% instant victories come from kicking field goals and only 25% come from scoring touchdowns. One may argue that field goals should account for more, but not all overtime first possession field goals are outside the red zone. There are a sufficient number of situations where a team drives to inside the 20 and then proceeds to kick a field goal prior to 4th down because it ends the game. However, would the team behave in the same manner if a field goal did not end the game? It is unlikely, therefore, those drives would continue with the team in question attempting to score a touchdown. Therefore, 75% field goal vs. 25% touchdown seems reasonable.

The above assumption leads to an extrapolated instant win percentage for the receiving team scoring a touchdown of 9.25% (37% * 25%). That is, under the new system 9.25% of the time the game will end without the opposing offense getting the ball instead of the current system of 37%. So what is the probability of winning on a field goal for the receiving team?

Assuming the same probability of kicking a field goal on the opening drive as current empirical evidence generates a probability of 27.75% (37% * 75%). However, because a field goal no longer ends the game automatically what is the probability that the opposing team responds with at least a field goal on their next drive? It is reasonable to assume a probability of 40% based on league averages when it comes to producing points on an average drive and factoring in a slight advantage due to the conditions of the drive allowing for 4 downs instead of 3 and a punt because a score is required. With that said the probability that the receiving team ends the game with a field goal and no response on the first two drives of the overtime is 16.65%. The probability that the kicking team answers is 11.1%. Note that the outcome of the score is meaningless. It is not relevant whether the kicking team answers with a field goal or a touchdown because either one results in a victory.

Now what is the probability that the kicking team holds the receiving team on the opening drive without points and responds with a score to end the game? Based on the current empirical evidence over the last decade the kicking team wins 39% of the games. Assuming a 50% - 50% split between the first possession and later possessions there is a 19.5% chance that the kicking team wins on their opening possession after holding the receiving team scoreless. Note that this percentage includes any turnovers that may directly result in a touchdown on the opening possession for the receiving team (interception or fumble run back for a touchdown). Similar to the previous paragraph the percentage distinguishing whether the kicking team kicks a field goal or scores a touchdown is immaterial as the base percentage is all that matters for the comparison because either results in victory.

Finally what is the probability that the receiving team wins when neither team scores on the first two drives of the overtime period? Based on empirical evidence from the last decade the receiving team has an overall winning percentage of 24% after the first possession. The kicking team has a winning percentage of 19.5% based on the aforementioned 50% - 50% split from the above paragraph. Therefore, the extrapolated occurrence percentages for the new system based on current empirical data would be:

Assume that Team A wins the coin flip and elects to receive –

Team A scores a touchdown, Team B receives no possession, Team A wins; (9.25%)
Team A kicks a field goal, Team B does not score, Team A wins; (16.65%)
Team A kicks a field goal, Team B kicks a field goal, Team B wins; (5.55%)
Team A kicks a field goal, Team B scores a touchdown, Team B wins; (5.55%)
Team A does not score, Team B does not score, game continues as sudden death; (Team A wins = 24%; Team B wins = 19.5%)
Team A does not score, Team B kicks a field goal, Team B wins; (9.75%)
Team A does not score, Team B scores a touchdown, Team B wins; (9.75%)

So when moving beyond theoretical percentages to estimated occurrence percentages the two new conditions create an environment where the receiving team wins 49.9% of the time with 9.25% of the games ending without the opposing offense getting a possession and the kicking team wins 50.1% of the time. The new system proposed in the above analysis appears to be extremely fair. However, clearly with results so close to 50% - 50% some may find such a conclusion fishy. In the analysis only two of the numerical assumptions are challengeable in that it is appropriate to use different values: the percentage split between the receiving team concluding the game on the opening possession with a field goal vs. a touchdown in the current system and the probability of the kicking team answering with a score after the receiving team kicks a field goal on the opening possession.

Assume that an individual believes the 75% - 25% split assigned favors touchdowns too much and it is changed to 85% - 15%, how does that change the final percentage of victory? A 15% touchdown split lowers the instant victory percentage to 5.55% and changes the total probability victory for a field goal with a stop to 18.87%. Thus this change drops the total probability of victory for the receiving team from 49.9% to 48.42%, a rather miniscule change. Overall it seems unreasonable to assume a field goal – touchdown percentage split higher than the one assumed in the original analysis.

Next assume that an individual believes the 60% - 40% split assigned for the kicking team’s response after a field goal on the opening drive is too high and it is changed to 70% - 30%, how does that change the final percentage of victory (assuming the original 75% - 25% split)? Under the new percentage split Team A now has a probability of winning with a field goal with no response of 19.425% and a total winning percentage of 52.675%. The change in winning percentage is 2.775%, which is higher than the change associated with altering the field goal – touchdown split. Such an outcome is understandable as long as the field goal – touchdown split favors field goals by more than 50% because the response split focuses on what happens after the receiving team kicks a field goal. Overall any reasonable assumption for either of these two splits creates a boundary condition probability of victory for the receiving team of 48% - 53%.

In the end whether or not the overtime system used by the NFL needs reform is probably still up for debate based on personal preference. However, if reform comes it needs to be effective reform that ensures a balance between dragging out the game and fairness. If these two elements cannot be attained in a given reform strategy, that strategy is not worth pursuing. The system proposed here seems to fulfill those two elements, but may have a problem with some pundits due to the trading field goals results in a winner scenario.