When the Pittsburgh Steelers score their first touchdown on Thursday against the Carolina Panthers, coach Mike Tomlin will raise a single finger and send Chris Boswell out for the extra point. He probably shouldn’t. Neither should Ron Rivera’s Panthers, who have the most devastating goal-line runner in the league, when they find the end zone.

The Steelers and Panthers are among several teams that should consider flipping their post-touchdown mindset and making a two-point attempt their default option during the first three quarters or so (when football games are about point maximization).

It sounds crazy, but the math is actually pretty simple. Since the NFL pushed back the extra point from the 2-yard line to the 15-yard line in 2015, kickers have converted on 94 percent of PAT attempts. Using the 47.7 percent two-point conversion rate since 2001, two-point attempts have a higher point expectancy (.954) than PAT attempts (.94) right from the jump. It’s close enough that for some teams — like the Baltimore Ravens, who employ Justin Tucker — the conventional wisdom makes more sense. But it’s clear that there are some teams that would benefit from going for two most of the time.

No team seems to be willing to dive in on the logic just yet, though keep an eye on the Cleveland Browns, who went for two after all three of their touchdowns under Gregg Williams last week. Coaches are, however, opting for the two-point attempt more often than before. From 2015 to 2017, two-point plays were attempted following 7.4 percent of touchdowns. In 2018, it’s up to 10.2 percent.

Let’s revisit to the Steelers and Panthers. Why should they be going for two? While it’s easy to see that some teams should make going for two their Plan A, it’s quite difficult to identify them. The problem is that no team this year, or any year really, has a large sample of two-point conversion attempts to get a good read on their skill in the situation. But that wasn’t going to stop us.

For every team, we came up with a point expectation when going for two and when kicking a PAT. Teams with a higher differential are more likely better off going for two early in games, while teams below it are advised to keep kicking the PAT. (For a full explanation on how we did the math, click here.)

Point expectancy on two-point and PAT attempts for every team. The break even line is shown in orange: teams above that line might want to consider making a two-point attempt their default choice following a touchdown. pic.twitter.com/XMUufWuKSB

— Seth Walder (@SethWalder) November 8, 2018

So let’s analyze why a few of the teams ought to at least consider going for two early on in games.

## Go for two

We would expect Boswell an average PAT kicker going forward, but the Steelers’ offense is also more likely than most to convert two-point attempts. That’s based both on their success going for two this season and the historical success of two-point conversions since 2001. In a decision this close, a little information can nudge the needle one way or another. Pittsburgh has the offensive assets to succeed with James Conner in the backfield and two talented receivers in Antonio Brown and JuJu Smith-Schuster.

Tomlin has actually flirted with going for two at unconventional times before, so it’s not totally crazy to think he would be open to the idea. Don’t be surprised to see the Steelers line their offense up at the 2-yard line after a score on Thursday night at some point.

Pittsburgh’s opponent on Thursday night also falls into this bucket of teams. Something that’s not considered here but might be a critical piece to this calculation: Cam Newton. Running plays on two-point attempts actually convert at around a 60 percent clip, and that’s true whether it’s a running back or quarterback running the ball. Though there’s no extra advantage by having a QB run on a two-point play that we can “see” in the numbers, presumably the ability to use someone like Newton would allow Rivera to call more running plays and open up the option.

With this offense and Sean McVay calling the plays, the Rams seem like a clear choice to give this strategy a shot. But it might not be that simple. Though going for two might increase point expectancy, it also increases the variance. So while this might be the right strategy when Los Angeles plays the Kansas City Chiefs in a couple of weeks in what should be a closely contested game, against a lesser opponent, where an easy win is expected, the last thing the Rams want is variance.

In other words, like all coaching situations, the context matters. And your opponent is a big part of that context.

Like with Newton, Andrew Luck‘s running ability adds a different dimension near the goal line. Though to be fair, the Colts might not want to risk a ton of contact to their quarterback at this point, after he missed all of last season with a shoulder injury. Still, coach Frank Reich is a former Doug Pederson assistant, so he has seen aggressive play pay off.

If you’re going to draft a running back with the second overall pick, you better think he gets you to at least an average two-point conversion rate. That would be enough to justify keeping below-average kicker Aldrick Rosas on the sideline and letting Saquon Barkley carry the ball.

The Eagles are perhaps the most likely team on this list to actually attempt the strategy. Pederson has shown before he’s willing to fight for extra expected points with his fourth-down decision-making, so this would be a next step.

This was such an easy call when Caleb Sturgis, an 88 percent PAT kicker, was still on the roster. But even after cutting him earlier this week, coach Anthony Lynn ought to strongly think about just letting Melvin Gordon run two-point plays all the time.

Was Gregg Williams’ two-point strategy in his first game as the interim head coach just a variance play, or could it be a lasting strategy? The Browns’ kicking woes might make it a viable one, and Baker Mayfield and some versatile running backs give Cleveland some options.

In addition to Drew Brees and Alvin Kamara, the Saints also have Taysom Hill, who could be a weapon on the 2-yard line. Hill adds the running QB dimension we mentioned earlier. In a world where going for two catches on and teams are trying two-point conversions as their default option, would players like Hill find more jobs available as two-point specialists? It at least seems feasible.

Gang Green’s expected two-point success might be below average, but that doesn’t matter with a kicker like Jason Myers. It’s hard to believe, but the Jets’ kicker has only made 88 percent of his PATs in his career. Even an anemic offense ought to have a higher point expectancy than that.

## Understanding the uncertainty

Now here’s the part of that expected-points plot that we didn’t tell you about. If we were to show error bars for the two-point expectancy, you would see massive amounts of uncertainty that would literally fly off the screen. That’s the nature of small samples. The Steelers’ logo on the plot above could easily be higher, lower, farther left or farther right if we had more information. But what we can tell you is that there is a 69 percent chance the Steelers’ true spot on that plot is above the break-even line, allowing us to confidently say that it is most likely worth it for Pittsburgh to make going for two its default choice.

Every team listed above has greater than a 50 percent chance of being above the break-even line. The Rams lead the way with a 70 percent chance.

Given the uncertainty, is there any other information we can throw into the equation to help us sort it out? Maybe. If we make a large but seemingly common sense assumption that better offensive teams in general have a better chance at converting two-point attempts (and we’re not sure they do), it might be worth comparing offensive FPI to expected PAT rates.

Now in this case, these two variables are not on the same scale, and we don’t know where exactly the break-even line or curve should be drawn. What we do know is that zero is the average offensive FPI, and 0.94 is the average PAT rate, so those at least give us some landmarks that we could draw some inferences from. If FPI perfectly correlated with expected two-point success (again, a huge assumption), then teams in the top-left quadrant would be advised to go for it. But really this is just a check from our first set of conclusions.

When we add FPI into the equation, teams like the Jets or Browns might think twice about actually attempting this strategy (though really, neither of them have much to lose). And additionally, teams like the Chiefs and New England Patriots might be better off going for two than our first plot suggested.

Comparing PAT rates to offensive FPI. Note that the the two axes are on completely different scales. If offensive ability directly translated to 2-point conversion success, at least teams in the top-left quadrant might consider making 2-pt default choice. Big assumption, though. pic.twitter.com/UGfIzyg9Xd

— Seth Walder (@SethWalder) November 8, 2018

Keep in mind that this concept of going for two as a default option is only for the earlier stages of games, when teams are trying to score as many points as possible. By the time the fourth quarter rolls around, the strategy naturally shifts.

Of course, all this information cuts both ways. It’s a close enough call that for some teams, all this does is confirm they should just keep doing what they’re doing.

## Stick to one

Though Justin Tucker missed a high-profile PAT earlier this season, he has still only missed one. And as a result, no team has a better point expectancy from PATs than the Ravens. Combine that with a below-average two-point expectancy and an average offense, and Baltimore is the perfect candidate to stick with the status quo.

Denver is in basically the exact same boat as Baltimore, with almost as proficient of a kicker in Brandon McManus. Given the offense, there’s little reason to suspect their two-point conversion expectancy to be above average.

## The deeper math behind the strategy

Using two-point rates since 2001 and individual teams’ success on two-point attempts this season, we were able to find a Bayesian estimate for those teams’ chances going forward. We begin by expecting all teams to have an average chance of converting two-point attempts, but if a team goes 3-for-3 on their two-point conversion attempts in 2018, we update our expectation for that team’s ability to execute two-point plays going forward. That update is based on past teams’ performances in this area. Of course, the movement is slight, but in a calculation this close, it can be significant.

We then multiplied the expected two-point rates by two (you do get two points for succeeding, after all) to get a point expectancy for two-point plays. Then we did the same thing with kickers, using their career PAT rates (since 2015) to find a Bayesian estimate for their expected rate going forward, and compared that to the two-point point expectancy.

New Chargers kicker Mike Badgley, for example, is 7-for-7 in PATs in his career. It would be unreasonable to expect him to be perfect going forward, and in fact, his expected PAT rate is just above average in that small of a sample.

Generally speaking, the more two-point attempts we see from an offense or PAT attempts we see from a kicker, the more confident our expectation is.

Lastly, using the range of plausible values for our Bayesian expected two-point and PAT conversion rates, we were able to estimate the probability that the team would have a higher point return by going for two than kicking a PAT. So if we see the Steelers or Panthers line up for a two-point conversion at an unconventional time early in the game on Thursday night, don’t question it. Tomlin and Rivera are just going by the book.