There’s a post today over at Grantland about the NFL’s attempts to engineer a more interesting extra point. Given that the current success rate hovers right around 99%, the kick is currently a formality.

For this preseason the NFL is experimenting with moving the spot of the PAT back to the 15-yard line. So instead of a 19-yard kick, it’s now a 32-yard kick. The change in distance should result in about 90% of PAT’s being converted. So misses will happen just often enough to, what, keep viewers from going to the bathroom until after the play? Make the game more unpredictable by affecting potential outcomes? Force Vegas to reconfigure odds and point spreads? Something.

A myriad of suggestions for ‘fixing’ the extra point is just a Google search away. Here’s mine (unsolicited, I know): Make the PAT a 2-point play and move it back even farther.

The idea here is to make the current 2-point play and the PAT mathematically identical. To do that, just perform an expected value (EV) calculation. That’s simply the value of something multiplied by the probability of it happening.

So if there is a 5% chance your scratch-off lottery ticket is going to pay you $5.00, then its expected value is $.25 (or .05 x 5.00). This is why you should almost never play the lottery as the ticket probably cost at least a $1. So you just voluntarily taxed yourself 75 cents.

Good job.

It turns out that under current rules the PAT and going for 2 are already extremely close in value. The EV of an extra point is about .99 points (there’s a 99% chance you get 1 point, so .99 x 1). It’s essentially 1 point. Two point conversions are successful about 47.5% of the time. So they are worth .95 points (or .475 x 2).

Moving the kick back to the 32 is actually making the 2-point play more attractive. NFL kickers make 32-yard field goals 89.4% of the time. So kicking the extra point is now worth only .894 points.

If you made it out of the third grade you should be able to figure out that .894 < .95 and that, as long as that’s the case (forever), you should go for 2. So the NFL really created an imbalance. To get back to where the two events are roughly equivalent, the NFL can make the PAT worth two points and move it back to somewhere around a 53-55 yard kick. That’s about the range that kickers are currently making 50% of their kicks (I can’t find the actual table for kicks > 50 yards, but you can eyeball it in this graph).

So the choice now facing coaches becomes: Do I go for 2 from the 2-yard line (the current 2-point play), or do I attempt a 53-yard kick that’s also worth 2 points? Mathematically, the two choices have the same expected value (and both still really, really close to the near-1-point currently gained; you could obviously adjust the kick annually if kickers continue improving accuracy from distance). The difference is that you have much more variability in actual outcomes.

Expected value calculations work for a large number of instances. If you play just one scratch-off ticket and it pays out $100, you probably think math is stupid because you made way more than 25 cents (keep playin’, my man, then get back to us).

For football there is a small enough number of events per game (here touchdowns) to make it interesting. Think of it this way: under current rules if two teams each have 3 TDs, then the score is almost certainly going to be 21-21. But if coaches now face the choice between two events that are pretty close to 50-50 (going for 2 or kicking a 2-point 50-yard PAT), then things can get far less even. And quickly.

Here are the possible scores for each team after 3 TDs (with the possible conversion sequences):

18 – MISS MISS MISS
20 – MAKE MISS MISS
20 – MISS MAKE MISS
20 – MISS MISS MAKE
22 – MAKE MAKE MISS
22 – MAKE MISS MAKE
22 – MISS MAKE MAKE
24 – MAKE MAKE MAKE

So instead of 21-21, you might end up with two teams having both scored three touchdowns but a total score of 24-18.

That might seem radical and be an affront to some sense of fairness we have about sports. If you score the same number of TDs as your opponent you should be tied, or you should only be trailing if you somehow failed at the near-automatic extra point in which case you deserve to be behind.

The thing is we’ve already seen the asymmetries of multiple 50-50 events contributing to the outcome of a game. And we’ve seen it on the biggest stage possible: Super Bowl XXXVIII.

With his team trailing 21-16, Carolina Panthers coach John Fox decided to go for 2. He failed. When the Panthers scored the next TD, Fox again decided to go for 2. And he failed again.

So instead of just kicking extra points and leading 24-21, Fox and the Panthers were only up 22-21.

When New England scored the next touchdown, they went for 2 and converted. So they were then leading by a full 7 points (TD and PAT), 29-22.

The Panthers scored again, but being down only 7 points, they kicked the PAT. That set up the Patriots to kick a game winning field goal with just a couple of seconds left in the game.

Sidenote, it’s baffling that in all of the postgame analysis there was almost no mention of Fox going for 2, his subsequent chasing the missed points, and it costing Carolina. If Fox never goes for 2 in the first place, the scores before New England gets the ball for its final drive, in all probability, go something like:

NE – CAR
21 – 17
21 – 24
28 – 24 (the Patriots almost certainly do not go for two here)
28 – 31

The Patriots would have needed a field goal to tie the game, not win it. Who knows what would have happened.

But the point remains, there was a spell over most of the 4th quarter in the Super Bowl where two coaches were playing with a 50-50 event; and it’d be hard to argue that it didn’t contribute to the outcome in a way that increased the excitement of the game. In fact it was kind of awesome.