The Packers should have gone for it on 4th and goal

The Green Bay Packers were defeated by the Tampa Bay Buccaneers last night. The Packers trailed 31-23 when it was fourth down and goal with 2:22 to go in the fourth quarter. The Packers decided to kick a field goal instead of trying for a touchdown. The decision was universally criticized. Without crunching the numbers, I knew it would be better to go for it and attempt to get a touchdown, even though either decision was a longshot. The Packers lost 31-26.

Since the game ended, I crunched the numbers.

Here is how I approached the decision. First, the Packers needed a series of events to occur, with all or nearly all events working in their favor to win. Computing the probability of the intersection of multiple events occurring is likely to be a small number. I examined the pathways to winning below. There were some fluke ways to win that I left out because those probabilities were negligible. My calculations are in this spreadsheet.

Decision #1: Go for it on fourth down. There are two ways to win in this scenario.

1. Score a touchdown.
2. Make the two point conversion to tie the game.
3. Stop the Buccaneers defensively (a TB field goal means the Packers lose).
4. Win by scoring within regulation or in overtime if time expires.

I estimate that the Packers had a probability of 0.6 of scoring a touchdown based on Aaron Rodgers’s pass completion numbers. Teams have a probability of 0.48 of getting the two point conversion. Teams have a probability of 0.68 of stopping their opponent from scoring on a possession. There was not much time on the clock, so this may have been an underestimate. However, both teams had multiple time out to stop the clock, and there had not yet been the two minute warning. Winning in overtime for two evenly matched teams is 50-50. Winning within regulation with very little time left has a small probability (say, 0.03). Putting this together, I estimate that the Packers had a win probability of 0.104.

Decision #2: Make a field goal attempt. There are also two ways to win in this scenario:

1. Make the field goal.
2. Stop the Buccaneers defensively while leaving enough time on the clock to score.
3. Win by scoring a touchdown within regulation.

or

1. Miss the field goal.
2. Stop the Buccaneers defensively while leaving enough time on the clock to score.
3. Score a touchdown within regulation, make the two point conversion to tie, and win in overtime (see Decision #1).

I estimate that the Packers had a probability of 0.96 of scoring a field goal. Teams normally have a probability of 0.68 of stopping their opponent from scoring, but I lowered that to 0.5 here because it needed to happen in such a way that the Packers had enough time for one last drive. That is likely an optimistic estimate. I estimate that the Packers could score a touchdown with a probability of 0.15 with the remaining time (Rodgers had an MVP worthy season). The second way to win involved missing the field goal and tying the game in regulation with a last second touchdown and later winning in overtime. Putting this together, I estimate that the Packers had a probability of 0.076. I believe this is optimistic.

Takeaways

1. Going for a touchdown increasing the win probability by about 3% compared to kicking a field goal. It’s not a huge different, but it’s also not insignificant.
2. Either way, the Packers were unlikely to win. So while the decision was bad, it wasn’t a decision that likely cost the Packers the game.
3. Kicking the field goal (Decision #2) could make sense with high confidence in a defensive stop or scoring a TD with time expiring. For the best defensive team in the NFL, decision #2 might be the better option. If Tampa Bay had, say, the worst defense in the country, especially if their secondary was weak, Decision #2 would be more attractive.
4. The Packers had two bad choices.