Going For Two in the NFL: Right or Wrong?
Posted on June 28, 2007
Filed Under General
The National Football League’s 1994 decision to allow the two-point conversion helped to make the games more exciting by assuring that a team down by eight points could tie the game with one score. Under the previous rules, which only allowed the “extra point” after a touchdown, a team would need two scores to win. I often thought that teams were not taking advantage of the two point conversion early in games, and I decided to put that theory to the test.
Understanding the Principles
The basic point of a football game is to score more points than the other team. By definition, the more points a team scores, the greater the likelihood that the team will win the game. Thus, a team is generally correct to pursue situations in which it is more likely to score points than not; where they will achieve a positive “expected value.” Your expected value is the total benefit you expect to receive if you do the same thing over a statistically relevant number of times.
For example, your expected value of having “heads” turn up when flipping a coin is 50%. Of course, you may flip a coin 10 times, and see heads seven of ten times, or only three times out of ten. This is called “variance.” You’ll experience variance over a small sample size, but variance will be nearly irrelevant once your sample size is large enough.
Calculating Expected Value
In 2006, NFL teams scored 1181 touchdowns league wide according to NFL.com. Divided by 32 teams, we expect that each team will score about 37 TDs per season, or about 2.3 TDs per game. League wide, teams successfully convert the classic “field goal” style extra point about 96% of the time, again, based on statistics available from NFL.com.
A good, documented statistic detailing the success rate of the two point conversion in the NFL is surprisingly hard to find. I found two rates that seemed sufficiently credible, both on “official” NFL sites. The first estimate puts the rate at “below 45 percent . . . since 1994,” but provides no hard numbers. The second estimate puts the two point conversion success rate at 50.9% for teams in 2005, but is potentially faulty due to small sample size. I use both numbers below.
If our “average” team in the NFL only kicked for extra points after each of their touchdowns, those teams would expect to score 35.52 points over the course of the season, as shown:
37 (number of TDs) x 0.96 (extra point success rate) x 1 (available points) = 35.52 points
What would happen if a team went for two every time they scored a TD? Here is the application of both of our “success rate” numbers from above:
37 (number of TDs) x 0.45 (conversion success rate A) x 2 (available points) = 33.3 points
37 (number of TDs) x 0.509 (conversion success rate B) x 2 (available points) = 37.66 points
From a pure expected value calculation, a team that expects to convert a two point conversion over 50% of the time, as one might expect, should go for two. One that would not should kick the standard extra point.
Game Day Application
When it comes to game day application, however, it appears that going for two is likely not worth the additional variance, even if we assume that the 50.9% success rate is accurate. The potential benefit over an entire season is only 2.14 points:
37.66 (50.9% two-point conversion expected value) – 35.52 (extra point expected value) = 2.14
Spreading that additional point margin over 16 games leads to an expectation of only .13375 points per game, which would not even register on the scoreboard that only counts whole numbers. Teams are better off taking the more secure points by taking the standard extra point in most situations, barring circumstances where going for two might “balance the score” or allow the team to tie or win the game.