This year, the NFL experimented with a new rule to make the “extra point” more appealing to the audience. This rule moved the extra point line to 25 yards instead of 2 yards from the endzone. The change decreased the likelihood of successful kicks from 99.6 % in the 2013 season to 94.3 % in this year’s preseason. We created a logistic regression model to map out the successful rate of extra point attempts based on the kicker’s distance to the endzone. Using this model, we compared our data with the successful rate of scoring a “2-point conversion” on the 2 yard line.
Since there is only a 2-yard distance where extra points are attempted, it is difficult to build a statistical model. We assume that the situational conditions of a field goal and an extra point attempt are similar. We combined data on field goal and extra-point in 2013 season and the extra-point in 2014 preseason. We choose Logistic Regression to model the relationship between yard line and scoring probability. The resulting model:
Log(P (x)/(1 − P (x))) = 3.93846 − 0.9906 * yard line
Our mean squared error is 0.022. The two coefficients are both statistically significant. The model fits data well until yard line reaches 40. However, teams rarely attempt to score field goal further than 40 yard line, we do not have enough data to make meaningful conclusion. The predicted success probability of 25 yard line is 81 %.
We assumed that the coach chooses either extra point attempt or two-point conversion based on the expected value that each option brings. Using our logistic regression model, we find that at 8 yard line, the probability is 95%. So if the extra point is at 8 yard line, it is equally desirable to choose between extra point and 2 point conversion.
We propose the further consideration of whether also moving back the line for the two-point conversion to the same yard line as the extra point attempt may be a feasible option since it retains the strategic benefit of being able to make either attempt on the fly. The touchdown data indicate that the probability of a one-play touchdown success decreases rapidly as yards from end zone increases. Consequently, moving the two-point conversion attempts back to even the 3- or 4-yard line would likely require increasing the point value from two to three to retain a comparable expected value for the play, and the requisite point value goes to four by the 5- or 6- yard line. However, this increase in the point differential over the extra-point kick may be something to embrace, for it opens up strategic possibilities of attempting the conversion for teams who are several points behind and could substantially benefit from such a point boost. Moving the conversion line back as well furthermore opens the possibility of compromising the kick and conversion placements by locating them both at the 6- or 7-yard line.
Mason Chow, ’16
Washington, D.C.
Thao Nguyen, ’15
Ho Chi Minh City, Vietnam
Dillon Pape, ’16
Houston, TX
Mathematics & Statistics
Sponsor: Tyler Skorczewski