## Down 14, Scoring a Touchdown, and then Going For 2

The math has been clear for so long, and been presented by so many writers, that this topic is essentially beating a dead horse. Late in games, it has always made sense for a team, after scoring a touchdown to cut a lead from 14 to 8 points, should go for two. The trailing team gets two bites at the apple: if it converts, a touchdown now wins the game. If the team fails, they get a second chance to erase that mistake. Only if the odds of missing *both* attempts were higher than the odds of making the first attempt would this strategy fail to make sense.

Yet it never happens. In fact, Brian Billick with the 2001 Ravens was the last coach to go for 2 late in a game after scoring a touchdown to cut the lead to 8 points.

More astonishingly, just once since the 2-point conversion rule was introduced in 1994, has a team ever been trailing by 14 points, scored a touchdown, and then converted a 2-point attempt. Once! And it came by none other than Bill Belichick as coach of the 1994 Cleveland Browns.

Trailing 20-6 in the 4th quarter against the Denver Broncos, the Browns were in a tough spot. Starting quarterback Vinny Testaverde was out with a concussion, leaving Mark Rypien as the team’s hope for a comeback. After a Cleveland touchdown early in the fourth, Rypien hit Derrick Alexander to cut the lead to 20-14.

And that was it. That’s the last time a team ever cut a lead from 14 to 6 points. Which is mind-blowing. But I bring this up today not to rehash old talking points, but to consider the new extra point rule. This makes the math even clearer about going for it, and I think it will also lead to it finally happening. Let’s say a team has a 96% chance of converting an extra point. That means a team has a 92% chance of converting two straight extra points. Down 14, it’s no longer a given that two touchdowns tie the game: you still have to make sure your kicker doesn’t mess up.

Now, let’s say a team has a 38% chance of making a 2-point conversion. This, of course, is quite a bit lower than the roughly 50/50 proposition that going for 2 truly is, but let’s just use this as a base. If a team goes for 2 after scoring the first touchdown, they have a 38% chance of converting and making this the successful play. There is also a 38% chance that the team misses both times (i.e., the odds of two events with a 62% chance of happening occurring both times), and a 24% chance of ending tied after the second touchdown (this is the result of missing the first time, and converting the second).

So a 24% chance of being tied, a 38% chance of winning, and a 38% chance of losing. That’s the breakdown of results if a team has a 38% chance of converting a two-point conversion. Meanwhile, if the team just kicks the extra point, it has a 92% chance of being tied via hitting two extra points, although if the team misses the first kick, they will obviously go for two on the second one. So we’re more looking at a ~94% chance of being tied, and a ~6% chance of losing, with no upside. Is that enough to tip the scales to convince coaches to be more aggressive when scoring a touchdown to cut the lead to 8?

I think it might be. While the variance is obviously much larger in the first option, variance is neither inherently good nor inherently bad given the zero sum game nature of sports. If it helps your win probability, it hurts your opponent’s win probability, and vice-versa. Given that there is now a roughly six percent chance a team can trail by two touchdowns, score two touchdowns, and still be trailing, that may convince some coaches to finally make the right choice in this situation.

Also, I am here to help the unfortunate coach who does follow this advice, misses both two point conversions, and loses the game by two points. When asked why he did such a thing, here is what he should say:

Well, we really felt like the momentum was in our favor after we went down and drove for the score. I knew that if we cut the lead from 14 to 7, and then scored a touchdown in the final seconds, that I wanted us to for two there and to try to win the game. I always believe that yo have to coach not to lose, and if we got down there and could win the game on one play, I think it would have been worth it. Then, as I was thinking about it, I realized that going for 2 at the end would be pretty fun, but also more risky than it needed to be. If we just went for two after scoring the first touchdown, we at least give ourselves a chance to make it up on the second try. Obviously it didn’t work out that way but at least we gave ourselves a chance, rather than missing the two point attempt and having the game be over. So that was my thinking there. And now it’s on to Cincinnati.

• Not really that relevant to the overarching point, but if you’re going to be a pedant about XP rates declining, I feel the need to point out that a team having a 38% conversion rate doesn’t equate to a 38% chance of winning after two touchdowns; they’ll also need to hit that reduced-odds XP on the second touchdown, so it’s really a (0.38) * (0.96) or 36.5% chance of winning, (with the remaining 1.5% falling into the “tied” bucket).

Again, not relevant to the overall point given the massive disparity between the theoretical break-even of 38ish% and the observed success rate of 50ish%. It just shifts the break-even point up a tiny, barely-perceptible amount, (to levels still well below even the most pessimistic real-world projections).

• Dr__P

I would rather be generally right than exactly wrong.

• Ah, that is a fair point.

• Assuming OT is a 50/50 probability, I’m reading this as:

Going for 2 first:
Succeed 2 (.38) * Succeed 1 (.96) = .3648 (W)
Succeed 2 (.38) * Fail 1 (.04) * Win in OT (.5) = .0076 (W)
Succeed 2 (.38) * Fail 1 (.04) * Lose in OT (.5) = .0076 (L)
Fail 2 (.62) * Fail 2 (.62) = .3844 (L)
Fail 2 (.62) * Succeed 2 (.38) * Win in OT (.5) = .1178 (W)
Fail 2 (.62) * Succeed 2 (.38) * Lose in OT (.5) = .1178 (L)

Add up the Win scenarios and you get .4902.

Going for 1 first:
Succeed 1 (.96) * Succeed 1 (.96) * Win in OT (.5) = .4608 (W)
Succeed 1 (.96) * Succeed 1 (.96) * Lose in OT (.5) = .4608 (L)
Succeed 1 (.96) * Fail 1 (.04) = .0384 (L)
Fail 1 (.04) * Fail 2 (.62) = .0248 (L)
Fail 1 (.04) * Succeed 2 (.38) * Win in OT (.5) = .0076 (W)
Fail 1 (.04) * Succeed 2 (.38) * Lose in OT (.5) = .0076 (L)

Add up the win scenarios and you get .4684. So it’s a good idea even at these rates.

NFL teams are actually 30-64 in two-point conversions this season (.46875). That puts going for 2 first at a 58.4% chance of winning and going for 1 first at 47.0%.

• Andrew Healy

I like the conservative assumptions about the conversion rate and then seeing this, too, because the conversion rate varies by team. If you’re a good offense/bad defense team (think NO), maybe your chance of making the two is greater than 47% even and then you’re giving up even more than the 11.4% here.

Here’s why the mistake doesn’t get fixed soon, I think. The actual cost ends up being pretty low b/c you actually have to score the second touchdown and avoid the other team scoring, too. And it intuitively feels wrong even if Chase’s explanation for a coach is right on.

• Assuming OT is a 50/50 probability, I’m reading this as:

Going for 2 first:
Succeed 2 (.38) * Succeed 1 (.96) = .3648 (W)
Succeed 2 (.38) * Fail 1 (.04) * Win in OT (.5) = .0076 (W)
Succeed 2 (.38) * Fail 1 (.04) * Lose in OT (.5) = .0076 (L)
Fail 2 (.62) * Fail 2 (.62) = .3844 (L)
Fail 2 (.62) * Succeed 2 (.38) * Win in OT (.5) = .1178 (W)
Fail 2 (.62) * Succeed 2 (.38) * Lose in OT (.5) = .1178 (L)

Add up the Win scenarios and you get .4902.

Going for 1 first:
Succeed 1 (.96) * Succeed 1 (.96) * Win in OT (.5) = .4608 (W)
Succeed 1 (.96) * Succeed 1 (.96) * Lose in OT (.5) = .4608 (L)
Succeed 1 (.96) * Fail 1 (.04) = .0384 (L)
Fail 1 (.04) * Fail 2 (.62) = .0248 (L)
Fail 1 (.04) * Succeed 2 (.38) * Win in OT (.5) = .0076 (W)
Fail 1 (.04) * Succeed 2 (.38) * Lose in OT (.5) = .0076 (L)

Add up the win scenarios and you get .4684. So it’s a good idea even at these rates.

NFL teams are actually 30-64 in two-point conversions this season (.46875). That puts going for 2 first at a 58.4% chance of winning and going for 1 first at 47.0%.

• Josh Sanford

I very, very much want teams to go for it–that is my bias. However, I am sympathetic with the losing coach for this reason: if 2 point conversions are a 50/50 proposition, it doesn’t follow that teams that are down by 14 points get equal access to the half that is successful. There is probably not an even distribution of successful attempts across all teams, against all teams. Without access to the data, I would assume that the kind of team that gets down by 14 also misses a larger percentage of attempts. Or maybe success is correlated to yards per play in that specific game.

• Clint

Chase, what do you think of the Browns going for 2 in this situation to potentially go up 22-16?

This was his explanation: “You’re up four. You’re looking at how many possessions are left in the game. . . They hadn’t scored a touchdown . . . If you only go up five, two field goals beat you. If you’re up six and you kick a field goal, now you’re up nine.. . We discussed it. . Obviously knowing the end of the movie now, you’d kick it, but we felt comfortable with the decision. ”
http://www.pro-football-reference.com/boxscores/201510180cle.htm