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NFL Coaches Are Getting Away With Crimes Against Middle-School Math

The NFL divisional playoff action once again demonstrated that NFL coaches are terrible at basic win-maximizing tactical decisions. In particular, there were two glaring spots where teams failed to go for two despite it being a fairly straightforward decision.

In the wake of Green Bay’s loss to Arizona — in which the Packers conceded a relatively routine winning touchdown on the first drive of overtime after spectacularly driving the length of the field (and then some) to tie the game in regulation — debate rages about whether the NFL needs to guarantee that both teams get a possession in OT. Whatever you think of the overtime rules, they are what they are, and under those rules, the Packers abandoned their best chance of winning by kicking the game-tying extra point at the end of regulation instead of going for it.

Much more quiet, but no less frustrating, was the call after Kansas City — which never seemed like much of a threat to New England — scored a touchdown with 1:13 left in the game that cut its deficit to 8. No one outside of sports nerd Twitter raised an eyebrow as the Chiefs kicked the extra point to draw within 7, and after they failed to recover their attempted onside kick, it’s likely that no one will ever care. But failing to go for two in this exact situation is one of the clearest and easiest-to-demonstrate mistakes in all of football, and how coaches continue to make this error virtually 100 percent of the time is a melancholy mystery.

Look, “advanced” stats can be opaque. In midfield situations, whether to punt or go for it on fourth down, for example, takes some confidence in expected points and expected win models that are statistically somewhat complicated and can sometimes get things a little wrong. Although I think those models are pretty good (or are at least good enough for most of the types of decisions they’re used to analyze), I can see how someone might find them foreign or overly abstracted. And yes, the statsy crowd can be preachy and overconfident. We probably don’t know as much as we think we do, and we often aren’t very good at explaining ourselves to skeptics.1

But some decisions — like the ones faced by Green Bay and Kansas City — aren’t that complicated. Analyzing them requires no advanced statistical techniques, and solving them requires no more than grade-school-level math and an eye on win maximization.

First up: How Green Bay broke my spirit

Aaron Rodgers got utterly jobbed. To recap — not because you aren’t familiar, but because it’s not possible to relive this too much or too soon — at one point, the Packers’ last drive looked like this:

Just 54 seconds of game time later — after Rodgers pulled the requisite pair of canonizing miracles out of his backside — all the Packers needed to win the game and knock off the second-seeded Cardinals was 2 more yards.

As the game went to commercial, I hoped against hope that Mike McCarthy would do the right thing and let that game live or die on Rodgers’s ability rather than try to send the game to overtime, on the road, against a superior opponent.

Was I being emotional about what I’d just witnessed? Sure. Even if the Packers ended up winning, it was depriving Rodgers — my sometimes muse — of the opportunity to complete what would have been probably the greatest drive in NFL history. But I also felt the passion of conviction — that this was the right choice — and the desperate hope that the professional NFL decision-maker would have arrived at the same conclusion.

In the first season of “Survivor,” the three final contestants were Richard Hatch, Kelly Wiglesworth and Rudy Boesch. Rudy was everyone’s favorite elderly curmudgeon. There would be one more challenge, and the winner would get an automatic berth in the final and the ability to vote off either of the two remaining opponents. Functionally, this meant they could choose their own opponent in the jury vote, in which eliminated contestants would choose the overall winner. Richard had a long-standing alliance with Rudy and was faced with an interesting strategic conundrum. If he won the final challenge and took Rudy with him, he would likely lose the voting to the lovable old homophobe. But if he betrayed Rudy, all that Rudy love would likely turn into Richard hate, and he would likely lose the jury vote to Kelly.

The “Survivor” forums were abuzz with strategic discussions,2 and people saw this conundrum coming weeks before it came to fruition. The solution to Richard’s problem — indeed, his only option if he wanted to win — would be to lose his final challenge intentionally. Then if the third player (ultimately Kelly) won, she would be forced to eliminate Rudy herself. (If Rudy won, none of this was likely to matter, as he seemed likely to win the final vote regardless of who his opponent was.) The “will he or won’t he?” suspense when it came down to the final four was amazing. On the one hand, the logic was sound and it was clearly the right choice, but on the other hand, it’s asking a lot to expect someone to see past the seemingly lower-risk play of winning the challenge and guaranteeing his spot in the final two.

After whittling the field down to the final three, the anticipated situation finally came to be. The final challenge was called “hands on an idol” — each contestant had to stand on a small log while keeping one hand on a pole, and the last one to break contact would win. At first it looked like Richard was going to play the game straight-up. Hours passed (or so the show told us). Jeff Probst offered an orange to any contestant who wanted to join him. And then, finally, it happened:



With a twinkle in his eye, Richard wished the others luck and let go. It was one of the most satisfying moments of my televiewing life. It filled me with optimism that, yes, human beings are smart and capable creatures. Hatch went on to be the inaugural “Survivor” winner, claiming his $1 million prize (in addition to jail time for failing to pay taxes on it).

The opportunity for the Packers to cap off that already legendary drive with a counterintuitive but mathematically sound two-point attempt — whether successful or not — had the potential to be another such reason-affirming moment for me. But alas:

Now, don’t get me wrong: That the Packers should have gone for two wasn’t obvious. But just because it wasn’t obvious doesn’t mean the call was difficult. This requires no advanced math and could literally be on a middle school homework assignment.

The question is: Which is greater, the chances of (1) Aaron Rodgers converting that 2-point conversion, or the chances that the Packers (2) make the extra point and (3) win in overtime? To make this comparison, we need to know or estimate three numbers.

Let’s start by looking at league averages:

  1. Two-point conversion success rate: Since 2001,3 teams have converted 47.2 percent of their 2-point tries from the 2-yard line (431 of 913).
  2. Extra point success rate: Since the inception of the longer extra point this season, NFL kickers have made 94.3 percent of their attempts from the 15-yard line (1,131 of 1,199).
  3. Expected winning percentage in overtime: Since 2001, the away team has won in overtime 45.5 percent of the time (110 of 242 overtimes that produced a winner).

With these numbers (which used only division), we can find our chances of winning for each option using — wait for it — multiplication.

  • Go for two: With no time left, this is exactly equal to the estimated 2-point success rate: 47.2 percent.
  • Send to overtime: Chances of making extra point multiplied by chances of winning in overtime. 94.3 percent * 45.5 percent = 42.9 percent.

There, we already have a baseline 4.3 percentage point advantage to going for two for a typical road team in the Packers’ position, using nothing but grade-school mathematics.

But those are just baselines, right? Everyone from coaches to media to fans will tell you that averages miss the hundreds of situation-specific factors at play. This is a technically true but often misleading rejoinder — and one that’s almost always used only to defend the status quo.

But in the spirit of accuracy and transparency, I’ve tried to refine the assumptions that go into that calculation above.

  1. Two-point conversion success rate: Adjusting for team strength and refining the data to the most comparable situations boosts our estimate to 48.8 percent.
  2. Extra point success rate: Adjusting for league trends and kicker Mason Crosby’s skill raises our estimate to 95.9 percent.
  3. Expected winning percentage in overtime: Adjusting for the overtime rules changes and playoff dynamics lowers our estimate to 42.6 percent.

If you would like a little more detail about how I arrived at those estimates, here is a longish footnote.4

So here’s where we stand under our revised assumptions:

  • Go for two: Equals estimated 2-point success rate: 48.8 percent.
  • Send to overtime: Chances of making extra point multiplied by chances of winning in overtime. 95.9 percent * 42.6 percent = 40.9 percent.

Naturally, these educated guess assumptions could be off in various respects, but that 8 percentage point gap is hard to overcome. When people who argue that there’s too much uncertainty to buck the status quo actually list the variables they have in mind (unfortunately, they often don’t), they tend to overestimate the amount that situation-specific variables affect the balance of probabilities. And the variables cited often don’t even cut the way they think they do. For example: In this case, an oft-cited factor is that the Packers’ receiving corps was weakened by injuries, including the loss of Randall Cobb earlier in the game. But, as I discussed in the footnotes, anything that makes the Packers weaker relative to the Cardinals is likely to hurt their chances in overtime more than their chances of converting the 2-point try.

Thus, our best (and perhaps slightly conservative) estimate is that the Packers cost themselves about 7.9 percent of a win by kicking rather than going for two, and this whole thing could have been avoided if NFL coaches took the time to sit down and learn some basic percentages.

Kansas City fails to butter its toast

In Kansas City, we fast-forward past the long, grueling slog down the field that Andy Reid perpetrated on Chiefs fans. That was painful to watch, but it was a problem of tactics and execution, not arithmetic. Reid went so far as to say that right up until the onside kick, things went exactly as planned. Except the plan went off-rail one play before, when the Chiefs kicked the extra point — an error that is in some ways even more frustrating than the Packers’ because it’s so so simple and has been clear for so long: If you are down 14 and score a touchdown late in the game — where you are very likely to have only one more scoring opportunity, at most — you should go for two.5

This doesn’t require any modeling, it requires just a little thought and a little more grade-school math.

In a situation like the Chiefs’ — where there was only 1:13 remaining — it doesn’t matter that their chances of recovering an onside kick and scoring another touchdown are very, very small. We don’t forgo safety checks on airplanes because the odds of a crash are small, and you shouldn’t ignore basic win maximization just because it will only earn you the occasional extra win.

The key is to assume you get the second touchdown (and in K.C.’s case, recover the onside kick, but the logic is the same when you have time to kick off and go for a defensive stop) — because if you don’t, it doesn’t matter what you do now, you lose. Once that little leap is taken, this all flows from a little multiplication.

If you kick an extra point, you are essentially playing to make two extra points and win in overtime.6

As above, let’s use league averages. Assume a 94.3 percent chance of making each extra point and a 45.5 percent chance of winning on the road in in overtime.

  • Your chances of winning this way are 94.3 percent * 94.3 percent * 45.5 percent = 40.4 percent.7 Add in the small chance that you’ll miss the extra point but then make up for it with a successful 2-point attempt, and your overall chances of winning with this strategy are 41.7 percent (of the times that you get the second touchdown).

Now, if you go for two and make it (which you should about 47.2 percent of the time), you can win by kicking an extra point (94.3 percent) after your second TD, or (much less frequently) by missing your extra point but still winning in overtime. If you go for two and don’t make it (which will happen 52.8 percent of the time), you can still win by going for two again (47.2 percent) and making it and then winning in overtime.

  • Chances of making 2-point conversion and XP: 44.5 percent
  • Chances of making 2-point conversion, missing XP and winning in OT anyway: 1.2 percent
  • Chances of missing 2-point conversion, making second attempt and winning in OT anyway: 11.3 percent
  • Combined chances of winning: 57.1 percent (of the times that you get the second touchdown)

I won’t bother going into detail trying to find perfect assumptions as I did above, because this calculation isn’t close enough for them to be necessary. Even if you assume a 50 percent chance of winning in overtime and a 100 percent chance of making your extra points, you still only need around a 38.5 percent chance of making each 2-point conversion (which would be absolutely terrible) to make going for it the better play.

Despite its obvious correctness, this is pretty much never done in the NFL. The only case of a coach going for two after a touchdown brought the team within 8 points in the fourth quarter since 2001 was Brian Billick with the Baltimore Ravens in 2001. Further back is murkier, though according to Football Perspective, the only time a team trailing by 14 has ever scored a touchdown and a two-point conversion to cut the deficit to six in the modern era was the 1994 Cleveland Browns — coached by none other than Bill Belichick.

And finally

Another year, another year with NFL coaches not doing their jobs and not being taken to task for it. By now, coaches have no excuse for not having mastered basic decisions like these.

People say coaches are afraid of media criticism. But they’re professionals, among the handful of elite who are capable of doing what they do. If a coach cares what the media thinks, let him explain his logic.

I recall when the current replay system was implemented, there was concern that people wouldn’t be able to understand what it meant that there had to be “indisputable evidence” to overturn the ruling on the field — even though burdens of proof have been an essential part of our judicial system since this country’s founding.

It took a little while, but the refs, and then the media, and eventually fans all came around, and now you can go to your local dive bar and hear arguments in the form of, “It looked like a catch to me, but there obviously isn’t indisputable evidence to overturn the call. Sucka.”

It’s time to do the same with arithmetic.


  1. Side note: In my opinion, the term “analytics” is one of the worst things to happen to serious sports analysis, as it created an artificial barrier between traditionally informed methods and data-informed methods. Either way, the goal is to understand the dynamics of a sport to figure out where winning comes from. Some analysts study film, some build statistical models — each method has strengths and weaknesses.

  2. Remember, this was all relatively new back then. “Survivor” strategy has since come a long way.

  3. As far back as the play-by-play data set I’m using goes.

  4. OK, here’s a little nitty-gritty:

    1. Two-point conversion success rate

    First off, if you believe in momentum or destiny, the fact that Rodgers obviously had miracle mode switched on suggests that his chances of making that conversion were likely closer to 1,000 percent than to 47 percent. (It’s fun watching old-fashioned football types having to choose between old-fashioned concepts like momentum and old-fashioned strategies like playing for overtime!) But seriously, there are good reasons to think that 47.2 percent is low for Rodgers.

    For one, teams taking 2-point attempts tend to be slightly worse than average — which stems from the fact that teams take 2-point attempts more often when they are behind.

    Winning teams (teams who finished the season over .500) account for just 41.4 percent of all regular-season 2-point attempts since 2001 and converted exactly 50 percent of them (189 of 378). For comparison: Losing teams made up 46.2 percent of all attempts, converting 44.1 percent, and .500 teams made up 12.4 percent, converting 49.6 percent of them. Of course, being successful in 2-point attempts may ever-so-slightly improve their chances of being a winning team in the first place, but the numbers hold for winning teams playing other winning teams as well. In those cases, teams have converted 50.5 percent of the time (95 of 188). In the playoffs, teams have converted 53.5 percent (23 of 43) of attempts. Also, in the rarer but more neutral situation of fourth-and-goal from the 2 — which is slightly harder than a 2-point conversion because the average distance is greater than 2 yards, plus teams still must exercise some restraint for fear of losing field position on the turnover — teams are 41 of 79 (51.9 percent). Although Arizona had a better record than Green Bay, the trends suggest that team strength has more of an effect on its 2-point conversion chances than opponent strength. Even in cases where a team with nine to 11 wins makes an attempt against a 12-plus-win team, they have made 48.8 percent.

    (Of course, this is really a question of offensive and defensive goal-line strength, which is a pretty hard quality to isolate independently. In general, however, the dynamic is similar: Offensive strength tends to be more determinative than defensive strength. My suspicion is that this is because one-down two-yard defense is less similar to overall defense than one-down two-yard offense is to overall offense.)

    Finally, let’s look at some specifics: With Aaron Rodgers at quarterback, in the regular season and playoffs combined, Green Bay has converted 12 of 23 (52.2 percent) of its 2-point tries. This includes 12 of 21 (57.1 percent) when Rodgers throws and 0 of 2 otherwise. Meanwhile, Arizona’s opponents have converted 3 of 6 attempts (50.0 percent) during Bruce Arians’s reign.

    All things considered, I think it’s likely that the league average of 47.2 percent is low in this situation, though exactly how low may vary depending on other factors, such as the in-game loss of Randall Cobb. However, one important (though slightly more advanced) point to make here is that a wider skill gap between the Packers and Cardinals will virtually always favor going for two. This is because the gap has a bigger impact on the chances of winning overtime than it does on the conversion attempt. My suspicion is that the Packers’ chance of 2-point conversion success was probably above 50 percent, but to play it safe I’ll go with 48.8 percent (essentially the lowest of our higher indicators).

    1. Extra point success rate

    Kickers on the whole did a tiny bit worse on extra points than I expected this year. Since I have considerable faith in my kicking projections, I think it’s possible that this baseline reflects some bad luck and should be a little higher.

    More importantly, Crosby has been a slightly above-average kicker. In fact, this year he made all 36 of his extra points (though he missed two from the shorter distance last season) and has made 49 of 50 kicks from 33 yards during his career. However, he has missed kicks from similar and sometimes shorter distances: For his career he has made 95.3 percent (81 of 85) kicks from 29 to 33 yards (counting this year’s XPs). The rest of the league has made 93.6 percent over the same period.

    To be conservative, I’ll use a revised assumption of 95.9 percent — league average for such attempts plus how much better Crosby has been than league average over such distances.

    1. Expected winning percentage in overtime:

    The likelihood of a road team facing a stronger opponent in the playoffs winning in overtime is probably lower than the league average for road teams winning in overtime in general.

    First, the new overtime rule — giving the kicking team a possession even if it gives up a field goal on its opponent’s first possession — makes overtime results less random. That is, the team with the advantage should be more likely to win. So far, this has been reflected in the results: Since the new overtime system was adopted in 2012, the home team has won 58.2 percent (39 of 67) of the time in the regular season.

    Second, the playoffs aren’t the regular season. Home field in the playoffs is usually earned, as it was in this case by virtue of Arizona’s superior record. Again, although the number of cases is small, the results are in Iine with what we’d expect: The home team does even better in the playoffs, having won 68.8 percent (11 of 16) before the Arizona game.

    As for this particular situation, there are other reasons to be skeptical of the Packers’ chances in OT. Although they ran reasonably well against Arizona, they passed poorly — and passing is even more important in overtime. There are a couple of reasons for this: One, if you get the ball first and score a touchdown, you win. Another is that you may find yourself in desperate situations if your opponent gets the ball first and scores a field goal. Note that 101 of Green Bay’s 251 passing yards came on Rodgers’s two Hail Marys on that last drive. And it wasn’t even a great drive otherwise: Under normal circumstances, it would have ended in a punt from out of the Packers’ own end zone. (In other words, the Packers offense wasn’t suddenly rolling like the Seahawks in the second half against Carolina.)

    So let’s go with a conservative estimate of a 42.6 percent chance of a Packers victory in OT. That actually feels slightly high to me, but it’s apparently what the live markets thought, plus it’s right around how well away teams have done under the new rules (41.8 percent, above).

  5. Note this is a de minimis example. The principle should apply more broadly.

  6. You could also kick the extra point now and then go for two after your next touchdown, though if you are planning to go for two at some point, it is far more advantageous to do it now.

  7. Slight mismatch due to rounding. 40.4 is based on unrounded calculation.

Benjamin Morris is a former sportswriter for FiveThirtyEight.