The NFL is apparently considering a proposal to revise the point after touchdown (PAT), also known as the extra point, when a team can snap the ball from the opponent’s three yard line and either kick the ball through the uprights for one point or attempt to get the ball across the goal line for two points. The leading proposal for a change, it seems, is to move the ball from the 3 yard line back to the 26 yard line, for kicks only, which would change the kick from a 19 yard “gimme” to a less makeable 43 yard kick. Mike Pesca, writing at Slate, explains why: there is no drama as almost no kickers miss.
A total of 1,267 extra points were attempted in the NFL last year, and 1,262 of those were made. The year before that: 1,235 attempted, 1,229 made. Last year, 27 [out of 32] full-time kickers did not miss one extra point.
How might that change the game? A quick check of 2013 statistics on PATs and field goals suggests that we would see a shift away from teams almost always going for the one point kick to instead usually trying to earn two points from scrimmage. Why?
As undergraduate economics majors should be able to explain, coaches can maximize the number of points their team will score in a season by calculating the expected value of the one point kick versus the two point play from scrimmage and select the option that is higher. If we use the 2013 NFL season’s statistics as a basis for calculating a typical NFL team’s expected value for each option in 2014 we obtain the following.
1 point kick: 1 * 0.996 = 0.996 points per kick
2 point play from scrimmage:  2 * 0.478 = 0.956 points per
A team that scored 100 touchdowns in 2014 and kicked 100 PATs could expect to score 700 points (600 + 99.7 for the PATs) while that same team could expect to score 696 points if it went for the two point play from scrimmage every time (600 + 95.6 points).
What is the expected value of a 2014 PAT kick if the proposed rule were adopted? I was unable to easily locate data on 43 yard kicks in 2013, but data on kicks from 40-49 yards are available here. It turns out that 240 of the 290 NFL field goals attempted between 40 and 49 yards were successful (83%).
1 point 43 yard PAT kick: 1 * 0.828 = 0.828 points per kick
That is, the proposed rule would make the expected value of the one point kick lower than the expected value of the two point play from scrimmage. Over the course of a season in which 100 TDs were scored a team that kicked all of its PATs could expect to score 683 points (600 + 82.8). Thus, we can anticipate a shift toward plays from scrimmage if the NFL adopts the proposed rule change.
Two Alternative Proposals
Apparently the NFL is considering the new policy because it wants to make the PAT more exciting. A shift away from kicks toward plays from scrimmage should have that effect. From that perspective, the proposed policy looks like a winner. But why not consider two alternatives: one that introduces chance (a coin toss option) and a second that engages the home crowd (a 12th man option).
The Coin Toss Option
This isn’t a real proposal, but instead a teaser that helps me setup my real proposal. So bear with me, because you need to follow this to really understand the 12th Man Option. The Coin Toss Option relies upon the fact that we can identify the yard line upon which to place the ball for kicking a PAT that sets the expected value for a 1 point PAT equal to the expected value of a 2 point play from scrimmage. All we need to do is determine the yard line from which NFL kickers make 95.6% of their kicks. While I do not have that data, the folks in NFL’s New York offices sure do.
If the league adopted a new rule that placed the ball at the yard line from which kickers averaged a 95.6% field goal success rate then a coach could not choose the best option for scoring the most points during the season: it would literally be a coin toss. So, to add some excitement to the game, after each touchdown the referee could pull that coin out of his pocket, toss it in the air, and if it lands Heads then the team has to kick a one point PAT from the yard line that yielded 95.6% success, but if lands Tails the team would need to run a two point PAT from the three yard line. Sure, the coin toss is arbitrary, but the outcome would be more interesting than the current situation.
However, there is an event better option for taking advantage of the fact that we can set the expected value of the options equal. It would get the crowd involved in the game, which is important given leagues’ desire to provide a unique game day experience in response to the increasing number of fans who choose to watch games at home or in bars on big screen TVs rather than at the ballpark (e.g., see here and here). I call it the 12th Man Option. How might this work?
The 12th Man Option
Last season the 12th man (aka, the crowd in the stadium) in Seattle drew attention for setting crowd noise records (measured in decibels). The NFL could require all teams to install the same decibel measuring device in all 32 stadiums and then let the crowd decide whether each team that scores gets to try a one point kick from the yard line that yields a 95.6% success rate or a two point play from the three yard line for its PAT. After a touchdown the stadium scoreboards would prompt the crowd to prepare to cheer loudly in support of the Kick or the Play from Scrimmage. Then the two options would be displayed, in sequence, on the scoreboard, for say 10 seconds, and the team that had just scored would have to pursue the option that drew the loudest noise.
The 12th Man Option would stir incredible debate among NFL fans as those in attendance could actually claim credit for victories, and following losses those who did not attend could cast blame on their friends who did. The facts of the matter would be that the choice between the two options is a genuine toss-up, thus granting favor to neither side, but as anyone who has listened to a few minutes of fans discussing their favorites sports teams can attest, facts have little to do with the debate that fans enjoy. And given a chance to believe that she can have an impact on the game, what superfan would elect to watch on a big TV?
 The reader might reasonably object that the coach ought to be maximizing the number of games won, not the number of points scored, and that is definitely true. Regrettably, such an analysis quickly becomes fabulously complex, and further would require data well beyond what I can readily put my hands on. For these reasons I ignore that complexity.
 The value 0.996 is the proportion of made kicks in 2013 (1,229 / 1,235 = 0.996), and the value 1 is the number of points scored for a kicked PAT.
 The value 0.478 is the proportion of successful PAT plays from scrimmage during 2013 ( 33 / 69 = 0.478; data obtained here), and the value 2 is the number of points scored for a successful PAT from scrimmage.