For those of you who don’t know Ravens guard John Urschel is one of the league’s smartest players. Urschel is a former winner of the William V. Campbell Trophy (equivalent of the academic Heisman Trophy). He has also taught Vector Calculus Trigonometry to Penn State students. The 4.0 graduate student from Penn State has decided to use a little math to determine the future of extra points. His results predict little change after the league decided to move the PAT’s back to the 15 yard line.
“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.”
The second year pro then provided the formulas he used to compute his answer.
“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.”
Urschel concluded that NFL coaches will still remain fairly conservative despite the rule change. Then again the formula does not account for Chip Kelly. He did sign Tim Tebow for a reason right? Only time will tell if Urschel’s prediction holds true.
“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.”
