Why Football Teams Don’t Go for Two Every Time
Editor’s Note: This is really just a very introductory lesson in how game theory applies to football, but I took a gamble that “Go for Two” would attract a better SEO crowd than “game theory.”
How many times have you heard someone suggest that NFL teams would be better off going for two after every touchdown? The theory goes kind of like this: if you can convert the two-pointer at better than 50%, over the long run, you’d average more points than simply taking the one.
Mathematically, that’s true. Actually, NFL teams convert on the kick around 99% of the time, so you can expect to get .99 points every time you take the one. At that rate, you don’t even need to convert the two pointer at better than 50%, you can convert exactly half the time and still come out ahead in the long run. Coincidentally, two-point conversation attempts last season in the NFL were successful 29 of 59 times, or exactly 50%. Mathematically speaking, last season in the NFL, teams averaged more points when they went for two than when they kicked the extra point.
It makes sense, right? You win games by scoring the most points, so you should stick to the strategy that will get you most points. Something economists are always yammering on about is expected outcomes, and using the math that I laid out above, the expected outcome of kicking for one is .99 points and the expected result of going for two is 1.00 points, so you should never kick it ever. Right?
This is where game theory comes into the equation. In case you’re not familiar with it, game theory is a part of economics that calculates expected outcomes (like we did in the last couple of paragraphs) of multiple players reacting to each other in the same game. It’s way more fun than predicting things in a vacuum.
Despite what you might think, one team is not playing football on its own. The point is not to score the most points possible, it’s to score more points than the other team. What these two-point enthusiasts fail to account for is how the opposing team will react to a two-point conversion on their next post-touchdown play. To say that you score more points going to two every time is true, but it completely forgets to account for how the other team will respond. When one team goes for two, it gives the opposing team the advantage of calling their next post-touchdown for them.
If you successfully convert a two-point attempt (which will happen about half the time), you can assume that your opponent will also go for two and match you about half the time. If you miss, the other team will take the point and convert about 99% of the time. In reality, going for two only gets you an advantage about 25% of the time. It leaves you tied about 25% of the time and puts you behind about half the time.
In case that didn’t make a ton of sense, there are three scenarios and I’ll spell each of them out, using hypothetical Teams A and B:
Scenario 1: Team A goes for two and converts. Now needing a conversion to pull equal, team B goes for two after their next touchdown and does not succeed. Since team A has a 50% chance of converting and Team B has a 50% chance of converting, this will happen about 25% of the time (.50 x .50). Team A leads by 2.
Scenario 2: Team A goes for two and converts. Now needing a conversion to pull equal, team B goes for two after their next touchdown and succeeds. Since team A has a 50% chance of converting and Team B has a 50% chance of converting, this will happen about 25% of the time (.50 x .50). Teams are tied.
Scenario 3: Team A goes for two and fails to convert. Team B now knows that they will pull into the lead by taking the almost guaranteed one point, so they kick and convert at an almost perfect 99% rate. This will happen about 50% of the time (.50 x .99). Team B leads by 1.
Of course there is also a fourth scenario when Team A fails to convert and Team B also goes for two and fails to convert, but any decently competent game theorist will recognize that strategy as ineffective and eliminate it.
Of course, a team that commits to the strategy of going for two might practice some plays and end up converting at a higher rate than 50%. there has to be a point where a team gets good enough to go for two every time, right? It looks like the magic number here is about 66%, or two-thirds of the time. Here are how the percentages break down in each scenario with Team A converting at 66% and team B converting at the standard 50%.
Scenario 1: .66 x .50 = 33% of the time, Team A leads by 2.
Scenario 2: .66 x .50 = 33% of the time, Teams A and B are tied.
Scenario 3: .33 x .99 = 33% of the time, Team B leads by 1.
If Team A can convert better than 2/3 of the time, they should go for it. Of course, this strategy doesn’t guarantee victory or anything, total touchdowns scored matters way more than what you do after them. Throw field goals in that mix too. This strategy deals exclusively with the decision to go for two to try to gain an edge on the opponent and how good you need to be to try.
Hope you enjoyed the math. I know I did.