Payoffs of two-point conversions in football
National Football League (NFL) fans may have noticed a rule change during preseason games last month. In an effort to make the game more interesting, the NFL lengthened point after touchdown (PAT) kicks from 20 yards to 33 yards. To give some background, points can be scored in the following ways: touchdown (6), field goal (3), safety (2), PAT kick (1), or two-point conversion after a touchdown (2). For both the PAT kick and two-point conversion, the ball is usually placed two yards away from the end zone. Teams then choose to kick the ball 20 yards through the upright goalposts – a foolproof play for professional kickers – or run/pass the ball to advance it 2 yards into the end zone. Unlike the soccer penalty kick discussed in lecture, the defense does not have to guess whether the offense will attempt the PAT or a conversion; with the exception of trick plays, there are obvious differences in setup.
In the past, teams have almost exclusively opted for the PAT unless they are losing by two points. NFL kickers are successful for 99.6% of PAT kicks, while only 50.5% of two-point plays are converted. It is interesting to note that based of these statistics, the two-point conversion has a higher payoff in terms of “expected points,” albeit by a small fraction. By multiplying the success rate by the number of potential points for each play, PATs have a payoff of 0.996 while conversions have a payoff of 1.01. At the time when a 43-yard PAT was discussed, Business Insider used data from previous seasons to predict that only 78.3% of longer kicks would be successful. Ultimately, 94.3% of the 33-yard PATs were made during the preseason games, according to the USA Today article, a small deviation from the norm.
As discussed in lecture, human nature can influence decision making. Even though two-point conversions have a mathematical advantage, they are riskier than PAT kicks. The NFL will continue to use 20-yard PATs during the regular season and playoffs. Finally, the USA Today article includes suggestions for more effective solutions that encourage teams to attempt 2-point conversions, including narrower goalposts which would supposedly decrease efficiency.
Links:
http://www.businessinsider.com/new-nfl-extra-point-rule-2014-3
http://ftw.usatoday.com/2014/08/nfl-extra-points-debate-distance-33-yards-conversion-rate