Ravens guard, math scholar John Urschel analyzes extra-point rule change

As a math scholar, Ravens offensive guard John Urschel is accustomed to applying his knowledge and authoring complicated papers in academic journals.

A winner of the William V. Campbell Trophy given to the top scholar-athlete in the equivalent of the academic Heisman Trophy, Urschel has taught Vector Calculus Trigonometry to Penn State students.

And the 4.0 grade point average student had a paper published this year in the Journal of Computational Mathemetatics called “A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians.” A year ago, Urschel published a paper in the top math journal, Linear Algebra and Its Applications called “Spectra Bisection of Graphs and Connectedness.”

So, Urschel's analysis of the NFL moving back its extra-point to the 15-yard line is worth a perusal. Urschel, whose Twitter handle is @MathMeetsFBall, wrote a piece on The Players Tribune, where he's the advanced stats columnist, called "Math Meets Football: Is the New Extra Point a Game-Changer?"

With kickers making 99.5 percent of their extra points last season and missing just two field goals from 33 yards, many have predicted that the statistics won't change dramatically on extra points this season with the rule change.

Urschel predicted that extra points will fall to roughly a 92.8 percent success rate this season. And he posited that attempting the two-point conversion, which remains at the 2-yard line, is the better bet for NFL teams to follow.

"What does this mean?" Urschel wrote. "Little to nothing! But, won’t extra points be significantly harder now that they’re so much farther back? Won’t this incentivize coaches to go for two? No, and no. Good data on field goal success rate is somewhat hard to come by, unless you’re looking at ranges of field goals. Lucky for me, a few guys from MIT already did the heavy-lifting for me."

Leaning on the data for extra points and two-point conversions, Urschel came up with the following formulas to predict the probability of converting each one:

"It doesn’t take a probability theorist to know that the expected points (the sum of each possible point outcome times the likelihood of each occurring) of the two-point conversion is now higher than that of an extra point kick," Urschel wrote. "E(two-point conversion) = 2x.479 + 0x(1-.479) = .958 points E(extra point) = 1x.928 + 0x(1-.928) = .928 points

"It’s simple math, right? The expected points for two-point conversions is greater, so of course all 32 NFL teams are going to do away with extra points and go for two every time, right? Not so fast. Just because the expected points of one endeavor is greater than the other, doesn’t mean it is what coaches are going to do."

In Urschel's opinion, NFL coaches will remain fairly conservative in their philosophy and will still avoid going for two points despite the increased length of extra points.

"Because, as you might have surmised at some point, NFL coaches are risk averse," Urschel wrote. "Coaches like low variation, and a difference of .03 expected points per extra point is not nearly enough to deter them from the safer choice of going with a slightly longer kick (which has variance of .07) as opposed to the much riskier two-point conversion (which has variance .25). There may be some who embrace the new system and take advantage of this opportunity, but my guess is most won’t."