The Situation
Down 20-27, Washington QB Kirk Cousins completes a TD pass to WR Santana Moss, pulling the team within 1 point. There are 18 seconds left in the game, so whatever happens here is highly likely to be the final outcome of regulation. Coach Shanahan decides to go for a 2 point conversion. Was this the right move?
This is a relatively simple situation to analyze since there are only a couple of possibilities.
If Washington goes for the PAT, they will go to overtime 98% of the time historically. That's close enough to 100% for our purposes. In overtime, there is nominally a 50/50 chance of winning the game.
If Washington goes for the 2PAT, they will convert and win the game x% of the time and lose the game 100-x% of the time. What is x actually?
Converting a 2 Point Conversion
Nominally speaking, if a 2 point conversion succeeds 50% of the time, it becomes right to go for it. There are a few other intangible factors involved, but if we purely look at the numbers, we want it to be greater than 50% to go for it.
Historically, according to Advanced NFL Stats, a normal 2 point conversion is 47.1% chance to convert, which would indicate the correct decision is to go for 1. However, deeper in the article, they note runs have closer to a 60% success rate, rather than passes which have a 43.4% success rate.
Maybe the issue wasn't with going for 2, but with the play call itself?
Other Factors
What other factors would change our decision. If Shanahan goes for 1, he's playing for overtime. So, the better a team's offense is, or the better a team's defense is, how does that change the situation?
How good is your team?
If a team is expected to lose the game, going to overtime is, in general, a bad idea. The reason it's a bad idea has to do with the concept of regression to the mean. Basically the concept is the more trials or chances you get, the more likely the outcome will be closer to the average outcome. If your team is worse than the other team, it is better to take the chance of winning the game on 1 play, where "anything can happen", rather than going to overtime where it's much more likely the worse team will lose.
How good is your defense?
How good is your team can take a couple of different forms though. Relatively speaking, if your defense is better than the other team's offensive, then it's probably better to kick the PAT and go to overtime, since a defensive stop keeps you in the game. However if your defense is much worse, then it's better to go for the 2 point conversion now, when your defensive ineptitude doesn't come into play.
How good is your offense?
The statistics show running is more successful than passing on the 2 point conversion, even though passing is attempted more often. That's for the average team however If your team is above average in these offensive categories, it would indicate you should go for two more often. Your quarterback's ability also should be a factor. A better quarterback forces the defense to play against the pass, which can open up the run game.
What if both your offense and defense are below average?
In this case, it's very possible that BOTH decisions can have a negative expected win probability. If your team is that bad, you might be an underdog going into overtime. You might also be less than 50% to convert a 2 point conversion. Many people argue it's less than 50/50 to make the 2PAT, so they should play for overtime. However, overtime might be an even worse proposition.
Do you have momentum?
Momentum is a debated topic as to whether it actually exists in sports or not. If it doesn't exist, then it doesn't matter in our decision. However, if it does exist, all the momentum is on the side of Washington, so that would indicate they should go for two. What coaches and pundits say about losing momentum if you miss the 2 point conversion doesn't matter, since there's very little time left on the clock.
Conclusion
If you think you can get 2 yards when it counts more than 50% of the time, it's right to go for two. If your defense is horrible, you should go for two. Running is typically better than passing, and momentum, if it exists, is actually on your side.
In this specific case, I like the decision to go for 2, but not necessarily the play call in this case.
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