When To Go For 2, For Real

“I can’t help but ask, one day many years later, when you find your previous awareness, cognition and choices are all wrong, will you keep going along the wrong path or reject yourself?” — Gu Li, a 9-dan Go champion, after losing to AlphaGo, Google’s nigh-unbeatable deep learning AI.

With 5:16 left in the third quarter of their wild-card playoff game in January, the New York Giants scored a touchdown to pull within 2 points of the Green Bay Packers. Despite having the opportunity to tie the game with a 2-point conversion, the Giants proceeded to kick an extra point. Yet, rather than criticize the decision for materially damaging the Giants’ chances of advancing in the playoffs, commentator Troy Aikman praised the move, explaining that “the chart would say go for 2 and try to tie it up,” but “there’s a lot of time left in this game.”

Despite the revolution taking place in basketball, despite Theo Epstein ending the two greatest curses in sports, despite AlphaGo going 60-0 against top human players, despite all evidence to the contrary, football stubbornly clings to the notion that experience always trumps analysis. Although NFL coaches have a level of expertise about the game of football that most of us will never approach, it’s hard to give them the benefit of the doubt when they’ve collectively demonstrated an inability to master basic tactical decisions — like when you should go for 2 points when your team is down 2 points (spoiler: pretty much always).

Which is not to say their resistance to change is entirely unfounded. I see the value in being cautious about adopting new strategies and generally think the burden should be on the purveyors of new techniques and tactics not only to find rigorous, workable proposals, but also to explain them compellingly — for coaches, players, decision-makers and the sports-viewing public.

In that spirit, let’s try to figure out when you should go for 2. For real.

Finding the right question

Let’s say you’re skeptical about WPA and EPA and OSHA and RADAR and WAROZ and other collections of capital letters that tell you what to do. I get that — I can be skeptical myself. So before we stick a model on it, let’s try to reason our way through the question.

The math would be more complicated if the NFL hadn’t moved the extra point back to the 15-yard line. But now going for 1 and going for 2 yield more or less the same number of points, on average, once you factor in how likely each is to succeed. If you go for 1 point, you’ll likely succeed around 95 percent of the time; if you go for 2 points, you’ll cash in roughly half as often, with twice the prize. But the fact that these have equal expected values (~0.95 points) doesn’t mean a coach should be indifferent between the two — and it certainly doesn’t mean he should take the “low risk” option by default (as coaches still seem wont to do). It means the decision ultimately turns on one simple question:

Which would improve our chances of winning more, the first point or the second point?

The beauty is that you don’t even need to figure out an exact value for each option — you only need to know which is more valuable. If the second point would improve your chances of winning more than the first one, then “risking” the first point to go for 2 improves your chances of winning overall.

Since scoring in the NFL comes mostly in chunks of 3 and 7, different point margins have different, non-uniform implications for winning chances. For example, the other team is generally far more likely to score 3 more points (from a field goal) than it is 2 more points (from a safety), so being up 3 points is significantly better than being up 2. Being up 2 points, though, is only slightly better than being up 1 (since you’d lose the lead on a field goal either way). The good news is that the relative importance of each point is fairly intuitive.

Each potential lead has different implications and benefits, like putting the leading team up a field goal or a touchdown. The marginal value of a point is just the difference between neighboring scenarios (like the value of being up 3 points instead of 2). Let’s imagine that there are 10 minutes left in a game. Think about each scenario and what it gives you, and you can probably estimate the marginal value of points pretty well. I tried this myself: First, I came up with a basic list of benefits that each additional point of a lead gets you. Then I guessed the relative importance of each (for a game with 10 minutes left). Then I checked my guesses against the marginal value for each point, as suggested by ESPN’s expected win percentage model:

I won’t subject you to my guesses, but the model matched up fairly well. The most counterintuitive one to me is that the difference between being up 7 and being up 8 (3.3 percentage points) is virtually the same as the difference between being up 8 and being up 9 (2.9 percentage points). Thus the “two score” threshold doesn’t seem to be as important as I would have thought, even that late in the game.

Note that as the leading team’s advantage increases, the marginal value of each point tends to get smaller — this illustrates why teams that are ahead by a lot should tend to go for 1 (because extending your lead gets less and less valuable the bigger it is) and teams that are behind by a lot should tend to go for 2 (because cutting your deficit gets more and more valuable the smaller it is).

Those changes to a team’s win probability are all that’s needed to construct a rudimentary “Go or No” chart (for 10 minutes left). What matters is whether a point is more or less valuable than its neighbors. So for a team up 5 points, the question is whether the next advantage (“5 to 6: Puts you up two field goals” in the table above) is more or less valuable than the one after that, (“6 to 7: Puts you up a touchdown”). Make that comparison for each point margin from -15 to +14, and voila:

For any particular point margin, if the two options have a similar shade, that means there’s not much difference between them. But if one is shaded significantly darker, it means that that point has significantly more value, and you should probably pick the corresponding strategy.

We’re going to go a lot further with this, but even this first cut of analysis reveals a couple of important cases where the conventional wisdom is wrong. In particular:

• If you’re down 8 points after scoring a touchdown (with 10 minutes left), you should go for 2, because the difference between being down 7 points (if you make the extra point) and being down 6 points (if you convert the 2) is greater than the difference between being down 7 points and being down 8 points (if you miss the 2-point conversion). Note that this is backed up by the numbers but should also be apparent intuitively.
• If you’re down 4 points after scoring a touchdown (with 10 minutes left), you should go for 2, because being down 2 points instead of 3 helps you more than being down 4 points instead of 3 hurts you. This one is a bit more counterintuitive, but if you think ahead, the second point means a future field goal could win the game (and if you don’t convert, you just have to adjust to go for winning touchdowns instead of tying field goals).

Failing to go for 2 in these situations turns out to be two of the most common, costly and clear-cut mistakes that even the best coaches make virtually every time.

Finding all the answers

Now, that’s just a snapshot of what coaches should do with 10 minutes to go in the fourth quarter. The particular values of different point spreads shift quite a bit depending on how much time remains. When there isn’t much time remaining, being up 1 point instead of 0 is way, way more valuable than being up 2 points instead of 1; but very early in the game, when there are likely many scores to come, even that difference is fairly small. Which is to say, earlier in the game, points are significantly more fungible.

So coming up with a complete guide to 2-point conversions merely involves repeating the process above, but for every possible combination of point spread and time remaining. For this, we’re going to let ESPN/Brian Burke’s expected wins model do the heavy lifting. Moreover, since all of this is based on league averages and no coach likes to think of his team as average, we need to compute all the scenarios for different types of teams, based on how good (or bad) they are at 2-point conversions. (Scenarios within scenarios!)

Bleep-bloop-bleep — that was easy. Now let’s combine all of that into one chart:

In the chart above, orange means go for 2, purple means kick the extra point. Each vertical line within each mini-chart represents a range from a terrible 2-point conversion team (40 percent conversion rate) at the bottom to an amazing one (55 percent) at the top. That range is pretty wide and should cover most knowable matchup advantages, like facing a particularly good defense, having injured players, it being windy, your team being an underdog, etc. (We’ll disregard how these excuses seem to lead every coach to make the same decisions every time.)

But enough about how to read the chart — here are some of the main things that popped out at me:

• When a team is down 2, it should go for 2 — pretty much any time, but especially in the third quarter and beyond.
• As previously noted, being down 8 and being down 4 in the fourth quarter are clear “go” situations. Yet no coach has gone for 2 in either of these spots in the past two years. The NFL’s extra point rule change practically begged coaches to go for 2 more often, and not one has tried to pluck even a single one of the lowest hanging fruit.
• Cases like going for 2 when up 5 or 8 early (aiming to go up 7 or 10) show small but fairly clear advantages. They may not be super costly, but mistakes are mistakes.
• When down 9 points late-ish, there’s a case that you should go for 2, because being down 8, you would have to go for 2 to draw even eventually anyway, and it’s better to know whether you converted your attempt earlier so you can make tactical adjustments. Although this logic seems sound, the data doesn’t suggest the effect is very significant (if it exists at all).

One special case: when a team scores a touchdown late to narrow the score to 1 point and then a coach has to decide whether to go for an extra point and the tie or 2 points and the win. Amazingly, this is the one situation in which coaches have broken with orthodoxy and gone for 2 occasionally — even though the chart suggests that it often isn’t justified.

Whether to “go for the win” or not in this situation is intrinsically a pretty even decision — the difference between being up 1 and tied is the same as the difference between being down 1 and tied — and depends largely on how good your 2-point conversion unit is (note the tall lines in the -1 box). But toward the end of the game, remaining time becomes an extremely important factor. In particular, when your opponent is likely to get another possession and your team is not, going for 2 becomes something a coach probably shouldn’t do. This is because if the other team goes down 1, it may end up driving for a game-winning field goal with nothing to lose. Because the opponent is likely to take a lot of risks, go for it on fourth down, etc., those drives have a disproportionately high success rate. In this case, playing for the tie to get into overtime becomes the far better strategy.

Passing judgment

Out of 1,897 post-touchdown decisions in the last two years (including the playoffs), coaches should have attempted to go for 2 approximately 690 times, of which they only did 107. Overall, coaches made 607 “mistakes” (either by kicking when they should have gone for 2 or vice versa), although the vast majority weren’t very costly one way or the other. They made 127 decisions that were “clear-cut” mistakes — meaning that they’d be mistakes for virtually any team, regardless of whether it was terrible (40 percent) or excellent (55 percent) at conversions. And 124 of those were failing to go for 2 when the situation clearly warranted it. Here are the “clear-cut” decisions that coaches got wrong most often, along with the average amount those mistakes cost their team:

The most common and significant mistakes by far are failing to go for 2 when down 4, 8 or 11 late in the game: Of 81 such clear-cut decisions, coaches got it right a combined zero times. They also kicked the extra point down 2 in the third quarter five times, when they clearly shouldn’t have, and once in the fourth(!) for good measure.

There is no excuse for professional coaches to make such simple mistakes. If you’re a coach, you should be doing this analysis yourself — or doing it better. If you’re still kicking extra points 14 times more often than going for 2, you’re not doing your job. If you’re in the sports media and you haven’t mastered this material, and won’t hold coaches accountable for not doing their jobs, then you’re not doing your job either.

CORRECTION (Feb. 4, 10:11 p.m.): An earlier version of this article contained a table that inaccurately listed “one” as the better option when up 7 points after a touchdown. Since the difference between going for 1 and going for 2 in that scenario was less than 0.5 percent, it should have said “same.”

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