## The Football Game Scenario

The football game was early in the fourth quarter on November 15, 2020. The home team Carolina Panthers were down 32-17 to the visiting Tampa Bay Buccaneers (Bucs). Hope came alive for the Panthers after quarterback Terry Bridgewater ran up the middle for a 3-yard touchdown. With over 11 minutes to play, the Panthers were down 32-23 and faced a key decision. Should the Panthers go for the near guarantee of the extra point kick and pull within 8 points? If so, the Panthers would next need a 2-point conversion after another touchdown to get even with the Bucs. Alternatively, the Panthers could try the 2-point conversion NOW to pull within a touchdown (and an extra point).

## The Basic 2-Point Conversion Scenarios

Traditional NFL rules tell coaches they should only try the riskier 2-point conversion when absolutely necessary to get a win or a tie. Here are some standard scenarios toward the end of the game:

**Down 1 point**: kick the extra point for the tie. If the other team will not have enough time for additional plays and the coach has a strong preference for going for the win, then go for the 2-point conversion. A coach may have a strong preference, if, for example, the team’s defense is exhausted and not likely to perform well in overtime.**Down 2 points**: go for the 2-point conversion. Whether the team comes away with one or zero points, the team will still need a field goal to win. Go for the tie now.**Down 3 or 4 points**: kick the extra point so the team can go for the win or the tie with a field goal on the next offensive possession.**Down 5 points**: go for 2 points so the team can get a tie with a field goal on the next possession. The team will still need a touchdown whether it comes away with one or zero points, so trying for the extra point is pointless.**Down 6-8 points**: kick the extra point as the team will need a touchdown to tie or win no matter what. When down 7 or 8 points, the extra point has the added bonus of positioning the team for a win or a tie without resorting to a 2-point try on the next touchdown score.

Note that these scenarios do not take into consideration the potential for the other team to score. As a result, these scenarios are most useful toward the end of the game. They can also be useful when the coach is “relatively” confident that the defense will stop the other team from scoring any more points.

## The More Tricky 2-Point Conversion Scenario

The 9-point deficit after scoring a touchdown begins the trickier scenarios. If the Panthers kick the extra point, the team stills need a touchdown and a 2-point conversion to tie. In the past, the decision was easy: bank the “sure” extra point now and worry about getting the 2-point conversion later. According to the sports announcers, modern “football analytics” recommend going for 2 points right away. Apparently, the goal is information discovery. The coach gets to find out now instead of later whether the odds of winning remain promising. However, I disagree with this approach. The 2-point conversion is not a neutral prize sitting behind curtains awaiting discovery. The announcers made a good point: the decision is complicated by the costs potentially incurred by sports psychology.

If a team pulls within 8 points on a successful extra point, the entire team gets an extra boost of hope. The game remains within reach. The defense stays focused on preventing further scoring as the biggest chance to win the game. Upon receiving the ball again, the offense can focus on a single mission: use the time available to get one more touchdown.

If the team fails the 2-point conversion, it faces the daunting task of scoring twice to avoid losing. This scenario creates a higher hurdle to overcome for sports psychology. If the defense doubts its offense can score twice, it may not play quite as hard. The defense will more likely become aware of its exhaustion. Upon receiving the ball with two scores to go, the offense needs to hurry more. It will be more prone to mistakes. The opposing defense gets the advantage of a lower bar of performance. The defense just needs to slow the offense down as much as possible.

In other words, the football analytics do not seem to take into account the high cost of failing to convert the riskier 2-point conversion. Depending on the team and the specific game scenario, those potential costs can be too high to risk. Ironically, in this case, more information is bad, not good.

Putting the fuzziness of sports psychology aside, the slightly less fuzzy world of assessing odds provides another way of understanding the likely wisdom of kicking the extra point now and worrying about the 2-point conversion later.

## Quantifying the Cost of Failing A 2-Point Conversion

The odds for the different scoring options are also important considerations. In today’s NFL, the extra point is harder to convert. Starting with the 2015 season, the NFL moved the line for the kick from the 2 to the 15-yard line. The odds of making an extra point fell from near certainty (26 of 32 teams made 100% of their extra points in the 2014 season) to somewhere around 94%. The worst team in the 2019 season only made 85% of its extra points.

The odds of making a 2-point conversion these days is reportedly just under 50%, but the range of actual outcomes in 2019 was extremely wide. Excluding the teams with 0% success (in some cases these teams did not attempt any 2-point conversions), the success rates ranged from 17% to 100%. Depending on the team, the 2-point conversion can be quite speculative. The Panthers only made 25% of their 2-point conversions in 2019. Before this game at hand, the Panthers had a 100% conversion rate.

For argument’s sake, I assume the Panthers had a 70% chance of making the 2-point conversion. The Panthers converted 90% of extra points to-date. So the “expected value” of a 2-point conversion is 1.4 (0.7 * 2). The expected value of an extra point is 0.9 (0.9 * 1). These values suggest that the Panthers should always go for the 2-point conversion. Since the team kicked 19 extra points to-date, I assume that the Panthers consider the odds of making the 2-point conversion to be too low to replace kicking extra points. Even so, this expected value does not take into consideration the cost of failure. With the above odds, the cost of failure must be lower than “-2.5” to advantage the 2-point conversion. (If x is the cost of failure, then the two options are equivalent when 0.9 * .1 + 0.1 * x = 0.7 * 2 + 0.3 * x).

What does -2.5 mean in this context? This value can represent a proxy for measuring the impact of missing either the extra point or the 2-point conversion. Either miss presents the team with a 9-point deficit at the subsequent kick-off. In addition to the touchdown the team needs in either case, a lack of extra points means the team must score one more time after the touchdown.

For simplicity, assume the coach decides the odds of scoring an extra field goal is 30% and an extra touchdown (with the extra point) is 10%. The expected value of this scenario is 0.3*3 + 0.1*7 + 0.6*0 = 1.6. This value is too low to compensate for (zero out) the -2.5 cost of failing to convert. The coach needs, for example, to conclude that the odds for the extra field goal are 60% and the touchdown 10%. The expected value for this assessment of probabilities is exactly +2.5.

These odds of course require a lot of optimism. For the Panthers facing one of the toughest defenses in the NFL, these odds sit precariously at the extremes of optimism. Note well that these stylized assessments do not even include the cost incurred for the lower odds of scoring the first required touchdown when the offense is rushed and the coaching staff is thinking through more game scenarios.

## Conclusion: Kick the Extra Point Now

Putting everything together, I recommend that a team just kicks the extra point when facing a 9-point deficit after scoring a touchdown. Bring the deficit to 8 points and live to think through one more offensive series. In this case, postpone going for the 2-point conversion until it is necessary to tie the game.

So what happened in the actual game? The Panthers followed the football analytics but failed to convert the 2-point conversion. The team went on to lose the game 46-23. The Panthers did not score again even as the Bucs continued to pile up points.