SHOULD WE GO FOR A ONE- POINT
OR TWO- POINT CONVERSION?
Since 1994, when the NFL began allowing teams to go for a two- point conversion after a touchdown, it has become important for NFL coaches to determine whether to go for one or two points after a touchdown. The success rate for a one- point conversion is over 99%, so we will assume that there is a 100% chance that a one- point conversion will be successful. The success rate for two- point conversions is around 47%.1 On average, a onepoint conversion try earns one point and a two- point conversion attempt earns 0(.6) + 2(.47) = .94 points. So, on average, a one- point conversion earns more points but in some situations it is clear that going for two is the proper choice. For example, if a team scores a touchdown with thirty seconds to go and they were down by eight points before the touchdown, the team needs to go for two to tie the game. Most coaches have a “chart” that tells them whether they should go for one or two points based on the score of the game. The idea of the “chart” is believed to have originated with UCLA assistant coach Dick Vermeil during the early 1970s.2
The coach's decision should depend on the amount of time left in the game as well as the score. For example, if there is a lot of time remaining in the game, then if the team scores a touchdown and is down by eight points they may not want to choose a play (the two- point conversion) over a play with higher expected scoring (the one- point conversion). To determine how the optimal strategy depends on the score of the game and time remaining we need to use a sophisticated technique, dynamic programming, which allows us to work backward from the end of the game to
1 Schatz, Football Prospectus.
2 Vermeil later became a successful NFL coach and NFL TV commentator. Sackrowitz's
“Refining the Point(s)- After- Touchdown Scenario” appears to be the first mathematical study
of the one- or two- point conversion decision.