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An example of a two-point conversion.

Let’s start with the obvious: your odds of winning when trailing by 15 in the 4th quarter are really, really low. From 1994, the first season the two-point attempt was introduced to the NFL, to 2011, 68 teams have entered the 4th quarter trailing by exactly 15 points. Only one of those teams won.

Over that same period, there have been 81 times when a team scored a 4th-quarter touchdown when trailing by 15 points, cutting the lead to 9 (pending the extra point or two-point conversion). Only 5 of those teams went on to win the game, with the most recent occurrence happening last year when the Dolphins were Tebowed.

So when trailing by 15 in the 4th quarter, even after scoring a touchdown, your odds of winning aren’t very good. But of those 81 teams that scored a fourth-quarter touchdown to cut the lead to 9, only nine of them went for two after the touchdown. While the time remaining could play a part in the decision, the fact is most of the other 72 teams made a strategic error in kicking the extra point when trailing by 9 points.

The last1 coach to recognize that going for two is the correct call? College football’s renegade, Steve Spurrier. In college football, the two-point conversion has been around since 1958, and in general, college football coaches are much more comfortable ‘going for 2’ than their NFL counterparts.2

The Ol' Ball Coach momentary forgets to go for two.

Against the 49ers on Sunday, with 6 minutes left in the final frame, Aaron Rodgers connected with James Jones to cut the lead to 30-21. At that point, attempting a two-point conversion is the obviously correct call, in an attempt to cut the lead to 7. I was disappointed but not surprised that Mike McCarthy decided to go for 1. But what did surprise me was seeing a number of smart people on twitter disagree with me that going for 2 is the right call. So I figured I’d devote a post to explaining why in this situation, it’s a no-brainer to go for two.

The counterargument goes something along the lines of “just take the points, that way it is a one-score game.” Essentially, people are afraid of missing the two-point attempt and trailing by 9 points. But it’s not a one-score game. Trailing by 8 isn’t a one-score game if you are going to fail on your two-point try. And there’s no reason to think your odds of converting a 2-point attempt are higher when trailing by 2 than by 9. Trailing by 8 is a 1.5-possiession game; half the time it is a 1-possession game, and half the time it is a 2-possesion game. To simply put your head in the sand and say “I don’t wanna know!!” may keep hope alive longer but it lowers your odds of winning.

There are many hypothetical scenarios where it would really matter to know whether you are going to be successful on your two-point conversion. Say you’re down 15 with 7 minutes to go and score a touchdown. You stop the other team, get the ball back, and drive to their 25. You’re out of timeouts and there are 3 minutes to go. It’s 4th and 10. At that point, wouldn’t your decision to go for it change if you were down by 9 instead of 8? Down 8, teams go for it because they consider it a one-score game. But if you’re going to miss the 2-point conversion, now you’d want to kick the field goal.

Knowledge is power. You need to get a two-point conversion at some point, and knowing whether you’re going to convert is important information. There is no reasonable reason not to go for 2 after your first touchdown. Yes, missing out on the two-point conversion earlier could be demoralizing. But what would you call missing out on a two-point conversion with 5 seconds left when trailing by 2?

There is a reason why coaches fail to go for 2 in this situation, and why smart fans also think it’s correct to take the safe points. It’s because they’re focused on keeping their hope alive as long as possible. As my friend Brian Burke once wrote, “coaches do not coach to maximize their team’s chances of winning. My theory is coaches are delaying elimination until the latest point in the game—that is, trying to “stay in the game” for as long as possible.”

By kicking the extra point, you (falsely) believe you’re staying in the game for longer. A missed two point conversion attempt with 8 seconds left means you had hope for 59 minutes and 52 seconds. Missing the two-point conversion earlier kills your hope, knowing that it’s now a two-score game. But the goal of a coach should be to maximize his team’s odds of winning, not to make his team’s players and fans feel warm and fuzzy. Missing the 2-point attempt at any point is going to drastically lower your team’s odds of winning. It’s true that if you score a touchdown to cut the lead to 9, and then miss the 2-point attempt, your odds of winning have decreased significantly. But it’s not the going for 2 early and failing that lowers your odds of winning, it’s simply missing the 2 point conversion that lowers your odds.

If you are going to convert the 2-point attempt, it doesn’t matter all that much whether you go for it early or late. If you’re going to miss it, going for it earlier significantly improves your odds of pulling off a miraculous comeback, precisely because you’re got almost no chance if you miss it late. If you are going to miss your two-point attempt, you’re in much worse shape finding that out with 1 minute left than with 7 minutes left. Knowledge is power, and coaches that pull a McCarthy are playing with a weaker hand. To state that you don’t want to go for 2 down by 9 because if you miss it is no longer a two-score game makes no sense, because if you are going to miss the 2-point conversion an 8-point lead is already a two-score game.

Note that how the Packers game unfolded presents a good example of why you want to go for two early. Green Bay kicked off to San Francisco, and eventually stopped the 49ers with just under 4 minutes to go. At that point, the Packers took their time driving down the field, reaching only the 49ers’ 45-yard line with 45 seconds to go. From there, Green Bay’s 4th down play was unsuccessful, but had the drive resulted in a score, there would have likely been only a few seconds remaining in the game. At that point, a missed two point conversion ends the game. Had the Packers gone for two and missed earlier, they would have played with more urgency on their final drive, and at least would have a chance for an onside kick and time to drive into field goal range for the win.

In college football, in overtime, each team gets one possession at the opponent’s 25-yard line. It is obvious that playing defense first is advantageous, and every college team elects to play defense first if they win the overtime coin toss. Knowing whether you need 3 or 7 points to win (or tie) is valuable information. We have exactly the same situation going on here, but the desire to keep hope alive prevents coaches from acting rationally.

  1. Technically, the last team to do this was the 2007 Jets. Trailing by 15 points with 3 seconds left, the Jets threw a touchdown as time expired, and then went for and converted a totally meaningless two-point conversion. []
  2. It’s worth noting that the American Football League had the 2-point conversion, and several teams there took advantage of the rule. In a 1965 game against the Oilers, the great Hank Stram recognized the benefit in going for two earlier rather than later. Trailing 35-20 late in the game, Hank Stram had the Chiefs go for two after a Len Dawson touchdown pass to Curtis McClinton. Kansas City converted, cutting the lead to 35-28. On their next drive, Dawson hit Otis Taylor for a 9-yard score, and Stram really upped the ante then. Calling a Pete Beathard run, the Chiefs converted and took a 36-35 lead with just over a minute to go. Unfortunately for Stram, the Chiefs went into an ultra-prevent defense, and allowed the Oilers to drive down and kick a game-winning field goal. []
  • Richie

    Going for 1, while down 9, makes a higher chance that the end of the game will be more exciting, but lowers the chance of a win. : )

    • How so? XP’s are as safe as it gets in the NFL. Say 99%? A two-point conversion is 50% at best.

      In other words, the team that kicks the XP is twice as likely to get the ball back down by one score than the team who attempts the conversion. Half those teams will be down 9 after it failed. For that reason alone, I can’t imagine WP would support going for 2 early.

      Keep in mind this is a game-tying situation either way. The goal is 2 TDs and a conversion on one of them. No coach will go for 2 twice, so this is basically an attempt to tie the game, and likely win it in OT. It’s not about winning directly.

      So if you want to tie your opponent, then you need to give yourself the best chance to be one play away from doing so. The early two-point attempt does not provide that. Because with that 50% chance of failure, chances are when you’re down 9 that you will not recover that onside kick and never will have had the ball down by one score. At least you can say you were one play away from the tie if you kick the XP.

      The coaching mistake I want to see corrected (which also came up in SF at GB) is when a coach kicks the XP in the second half (especially 4th QT) to give his team a 16-point lead. Screw that. Go for 2, push it to 17 (three scores), and crush the other team’s hopes. Even if you don’t get it, you’re sitll up 15, and as this post shows, in great shape to win regardless.

      • Chase Stuart

        What you seem to be ignoring is that your odds of winning the game after a missed 2pt attempt with six minutes left are better than your odds of winning the game after a missed 2pt attempt with 10 seconds left.

      • JCB

        “At least you can say you were one play away from the tie if you kick the XP.”

        This is exactly the problem that the author of the article exposed. You’re not helping your odds, all you’re doing is delaying the difficult conversion until a point where, if you miss it, you’re totally screwed. All so you could say “we were one play from tying it up”.

      • J

        Richie obviously didn’t read the article at all and blindly backing all the ignorant points that it exposed

        • J

          I meant Scott, not Richie

      • Greg T

        How can you not see the logic here??? What is WRONG with people?????????

  • Richie

    Going for 1, while down 9, makes a higher chance that the end of the game will be more exciting, but lowers the chance of a win. : )

    • Chase Stuart

      No doubt true.

  • Steven

    I’m generally in agreement, but I think you dismiss the “demoralizing” concern too quickly. If a demoralized team plays worse, it’s clearly better to have your team demoralized after failing on the last play of the game than to have your team demoralized with a nine-point gap and time left. I doubt that effect outweighs the informational advantage, and if they do get that onside kick or quick stop they need, that should moralize them right back up. But I’m sure psychology plays a role – in how players play, not just in how coaches make decisions – and it isn’t really captured in most of our models.

    • Richie

      Are you suggesting that the “demoralizing” factor carries over into the next game?

    • Chase Stuart

      Yeah, I’m with Richie. I don’t see how it can be better to have your team demoralized and down 2 with 10 seconds left than to have your team demoralized and down 9 with 7 minutes left.

      • JD

        I think what he’s trying to say is that a team down 8 with 3 minutes to play is less demoralized than a team down 9 with 3 minutes to play. Hence, the less demoralized team is theoretically playing harder (and better) than the one who feels the game is probably already over.

        • Greg T

          JD, I know you are speaking on behalf of someone else, but the philosophy below (whosever it is):
          Hence, the less demoralized team is theoretically playing harder (and better) than the one who feels the game is probably already over.

          Is INSANE!!! And the reason it’s INSANE is that they are not realizing that even if that team plays harder because they are still “in it” after going for one, if they THEN miss the 2 pt conversion with no time left, they have no OPTION to play harder or not!!!! At least by missing the 2pt conversion earlier, they have the OPTION to play or not play as hard as they want!!

          OPTIONS, people!! OPTIONSSSSSSSS!!!!!!!!!!!!!!!!!!!

          • Jeff

            Yes, Greg, but the team who is demoralized by failing to convert the 2pt conversion on the first TD will not have as a good of a chance of scoring a TD AND kicking a FG as the team who kicked the PAT, and since they were with in 1 score(albeit it, 8pts) were less demoralized and played with more of a purpose. The simply fact of the matter is that you have a better chance to win by being down 8 pts with 3 minutes left, than you do by being down 9 points with 3 minutes left to play. Therefore, go for the PAT on the first TD, and the 2 pt conversion on the 2nd TD. The odds of getting 2 possessions(TD and FG needed to overcome 9 point deficit) in the last 3 minutes are far less than the odds of getting 1 possession(TD with 2 pt conversion) in those same 3 minutes at the end of the game.

            • Greg

              OH MY GOD- you are a sick, diseased, deranged LUNATIC!!! What the HELL is WRONG with people????????

              Do you NOT understand that it MUST, I do not say this lightly, it MUSSSSSSST be agreed upon for sake of argument (in which case SOMETHING must be agreed upon) that the losing team has the EXACT SAME odds of a successful two point conversion whether they attempt it on the first touchdown or later. In other words- WHENEVER they attempt that 2 point conversion, they have the EXACT SAME chance of making it, REGARDLESS of when it is attempted.

              I will not continue speaking about this unless you (or ANYONE else who wants to discuss this matter) can agree to that. IT MUST BE AGREED ON before speaking intelligently about this debate AT ALL.

  • But it’s not a one-score game. Trailing by 8 isn’t a one-score game if you are going to fail on your two-point try. And there’s no reason to think your odds of converting a 2-point attempt are higher when trailing by 2 than by 9. Trailing by 8 is a 1.5-possiession game; half the time it is a 1-possession game, and half the time it is a 2-possesion game.

    It’s also not a one-possession game in that even if everything goes as planned, all you’ve done is tie the score. The tie keeps you alive, but still, you’ll have to score (at least) one more time to win. Maybe this distinction isn’t crucial in a 15-point game—the most you can hope to accomplish with your next two possessions is to tie the score (unless of course you go for two twice, but few coaches would even consider being that aggressive)—but it’s very relevant when the margin is, say, 10 or 11. A team facing fourth-and-short within striking distance of the end zone, down 11, will almost always take the field goal in order to “make it a one-possession game”, but the only way to truly make it a one-possession game is to score a touchdown.

    • Chase Stuart

      I give this comment a thumbs up.

  • Chase Stuart

    Good comment from the excellent Broncos-centered blog, Itsalloverfatman.com:

    “Kicking the extra point first is sort of like putting off being tested for a disease or opening a bill.”

    That’s exactly right. People don’t get tested for diseases all the time. I understand it, but that doesn’t make it rational or correct. Same thing here.

    • sn0mm1s

      It isn’t the same thing – it isn’t even close.

      Here is why kicking it, in theory, may be better than going for 2 – using the knowledge is power mantra (which isn’t supported in the actual game results).

      1) The leading team already has the huge advantage of being in the lead. Knowledge works both ways. The trailing team’s playcalling is simplified but so is the winning team’s. This benefits the winning team more because …. they are winning.

      2) Assuming playing correctly maximizes your winning potential, being down 8 would appear to benefit the trailing team more if they called the game as if they were down 2 possessions because the winning team would likely call the game as if it is a 1 possession game (both assuming worst case scenario). This would mean that the trailing team would be calling the game correctly more often than the winning team.

      However, as I posted below this doesn’t appear to play out in the scores (although it is impossible to tell how a game was called) *but* the knowledge is power crowd’s argument doesn’t work either because prior to the 2 pt conversion being down 9 was still better than being down 8 (and all cards are on the table at that point).

      • Chase Stuart

        Completely disagree, for two reasons. One, it benefits the trailing team more because the trailing team has a more diverse range of options. The leading team is focused on milking the clock for the most part, whether the leader is 7, 8, or 9. The variance in play-calling is much smaller for a team winning by 8 or by 9 than for a team trailing by 8 or 9. The trailing team goes into full hurry-up mode down 9, but can take a more relaxed pace down 8.

        It’s also worth noting that there is another benefit to missing early, which I didn’t want to include in the original post because it’s difficult to quantify. But a team winning by 9 is likely to be even more conservative than a team winning by 8. I suspect a team up by 9 with 6 minutes to go is more likely to go 3-and-out than a team up by 8 with 6 minutes to go. So that’s a benefit to going for 2.

        • sn0mm1s

          The problem is, neither theory is supported by the actual data (which I posted below). Being down 9 is better than being down 8 even when no 2pt conversion exists.

  • sn0mm1s

    There was a pretty long thread regarding this on FBGs at some point. You are simplifying the intelligent “kick it” crowd to a significant degree though. I don’t feel like posting a ludicrously long response but basically going for two appears to be the correct decision but *not* due to the reasons you list. The game logs suggest being down 9 is better than being down 8 regardless of whether or not a 2pt conversion is even available. Similarly being down 17 is better than being down 15 or 16 *regardless* of whether a 2pt conversion is available. IIRC being down 13 might have been better than being down 11 or 12. Do a parse of games prior to the 2pt conversion being adopted in the NFL. You will find that teams down 9 win more often than teams down 8. Similarly, teams down 17 win more often than those down 16 or 15. Why that is the case? I have no idea – but going for 2 isn’t the correct call because “knowledge” is power. Going for 2 appears to be the correct call because being down 7 or 9 is always better than being down 8.

    • Chase Stuart

      Being down 13 could *possibly* be better than being down 12, just because some coaches could become ultra conservative and try to go the TD+FG+FG+OT route vs. just the 2-TD route to win if down 12. I don’t see how your other examples would work, although I admit I haven’t seen the data you are referencing. I don’t think you can seriously argue that in today’s NFL, being down 9 is better than being down 8.

      I took a look at one thing you mentioned. Before 1994, there were 269 examples of a team scoring in the 4th quarter and, following the score, having a 9-point lead. They won 243 of those games (90.3%). There were 259 games when a team scored and then had an 8-point lead in the 4th quarter; they won 236 games, or 91.1%. So that does, ever so slightly, conform with your memory, which is that teams trailing by 9 in the 4th quarter won 9.7% of the time while teams trailing by 8 won only 8.9% of the time.

      It’s certainly possible that this is just due to sample size, but it’s also worth noting that the situations are more different than you might think. 146 of those teams had a 6-score lead and then kicked a FG to go up 9, or 54%. Meanwhile, only 66 of those teams were trailing by 5 and then kicked a FG to go up 8. So we’re looking at a different sample of games. In the 9-point lead games, most of the time it was a 6-point game and the team kicked a FG. In the 8-point lead situation, 72% of the time the team was leading by 1 and then scored a touchdown.

      It’s an interesting discussion, although not entirely on point in the modern NFL.

      • sn0mm1s

        To me it looked like you would rather be down some combination of multiples of 7s and 3s when the difference was only a point or two. Again, I don’t feel like doing a ton of PFR research and tabulating scores in the different eras but if my memory is somewhat close here is what you would rather be down by in the 4th quarter if you want to squeak out a win

        7 > 9 > 8 > 13 > 12 > 11 > 17 > 15 > 16.

        This led to an interesting situation that if you are down 23 in the 4th quarter and score you are better off not kicking the XP or going for two.

      • sn0mm1s

        The sample sizes I posted below aren’t really small each have 100+ games for each category in the 7/8/9 buckets.

      • If it is true that teams down by 9 win more often than teams down by 8 (and it wouldn’t surprise me if it is), I’d bet a big part of it is that teams down by 9 are forced by simple arithmatic to try to take the lead instead of being content with a tie. It’s similar to the point I made above—during a comeback attempt, coaches tend to overvalue tying the score at the expense of more aggressive play-calling aimed at taking the lead, which would presumably give them a better chance to win.

        So, if my theory is right, it’s not that teams are in a better position to win if they’re down by 9 instead of being down by 8; it’s that when a team is down by 9 their coach is essentially forced to make better strategic decisions.

        • sn0mm1s

          The problem is, the pattern holds when there is no two point conversion. In fact, without a 2 pt conversion, it is probably far more likely for teams to tie up the score when they are down 7 or 9 vs. 8. With no 2pt conversion being down 8 or 9 is still a two possession game. One would think that being down by less points, with the same # of possessions needed to go ahead in the game, would be advantageous – but it isn’t.

          • Ah, yes, I didn’t look closely enough at your numbers below. In that case, I’m stumped too.

          • Jeff

            Could it have something to do with the type of games that lead to these different spreads? Think of Team A down 40-49 and then think of Team B down 0-8. Team B is only down by 8 but who is more likely to pull it out? Probably Team A who has been able to put points on the board up to that point. Perhaps the 9 point spreads are more likely than the 8 point spreads in the much higher scoring games and thus lead to higher percentage of comebacks.

      • FWIW…the standard error of the difference between those two proportions is 2.5%, which makes it statistically significant from zero (p = .0018). If anything, it’s a large sample issue (higher Ns = easier to find significant differences) than a small sample issue (noise). Of course, as you noted below, this is totally agnostic re correlation/causation.

        • Chase Stuart

          Can you unpack exactly how you did that, Danny?

          I’m working on a post, and I’m pretty sure the effect is real. But I have yet to come up with a good conclusion why. I do agree that it’s not a sample size issue, but if you could show more of the math, that’d be helpful for me (and probably a few of the other readers!)

          • Ah, for f**k’s sake. My bad, Chase. I screwed up the decimal point for the difference between proportions by a tenth (brain fried). With the difference being o.8% (not 8.0%), the p-value is actually .975: soooooo not statistically significant. Of course, this means that there’s no statistical difference in win% between teams w/ a 9-point lead and an 8-point lead.

            As for the math, the standard error for a difference between proportions is

            sqrt{ p * ( 1 – p ) * [ (1/n1) + (1/n2) ] }

            where p is the pooled sample proportion, p = (p1 * n1 + p2 * n2) / (n1 + n2).

            So, with p1 = .903, n1 = 269, p2 = .911, and n2 = 259, the pooled sampled proportion is .907, which means the standard error of the difference is .025. With a difference in proportions of .008, your t-statistic (which might as well be a z-statistic at these sample sizes) is 0.32, which has a corresponding p-value of .975.

  • sn0mm1s

    This is from a post I made on FBGs website a while back – all of this is breakdown of teams winning% when down X points in the 4th quarter when 2pt conversion was *not* part of the rules. If knowledge is power is the only thing at play here being down 7, is preferable to being down 8, which is preferable to being down 9. That isn’t the case. When I first ran the results I didn’t realize the AFL had a 2pt conversion which is why there are two sets of data.

    I reran the filter from 1969-1993 (instead of inception to 1993).
    Down 9 97/26/0 = 21%
    Down 8 101/18/0 = 15%
    Down 7 445/117/21 = 22%

    And here are the results for NFL only from 1940-1993
    Down 9 114/29/0 = 20%
    Down 8 147/23/1 = 14%
    Down 7 617/157/44 = 22%

    • Chase Stuart

      Interesting. I suspect this is related to Why 13>14, but I think this is worth its own post. I’ll think about this and see what conclusions I can come up with next week. Thanks.

      • sn0mm1s

        Yeah, it seemed like being down multiples of 3 or 7 was better than not, and if you are down by multiples of 7 or 3 the least number of multiples of scores/possessions of 3 or 7 needed to tie was more important than the points.

        7 – multiple of 7, 1 possession
        9 – multiple of 3, 3 possessions
        8 – not combination of multiples
        13 – two 3s, one 7, 3 possessions
        12 – four 3s, 4 possessions
        11 – not a combination of multiples
        17 – two 7s, one 3, 3 possessions
        15 – five 3s, 5 possessions
        16 – not a combination of multiples

        I am sure it is some bizarre game theory issue based on how points are scored.

        • sn0mm1s

          My bad – I got ahead of myself here. Obviously, 16 = 3×3 + 7 – just noticed after rereading my posts. So for the pattern to hold it should be 17>16>15 but that, IIRC, isn’t the case.

          • sn0mm1s

            It might be a small sample size though so the difference isn’t very significant.

    • Richie

      I am curious about sample size possibilities here. Can you break down the 1969-1993 numbers into 5-year chunks, just to see if there might be a particular period in time where the 8-point deficit was particularly problematic?

      It’s really hard for me to see why there would be any inherent advantage to being down 9 over being down 8. The fact that the results show that there might be an advantage leads me to think that it has to do with the ensuing decisions. Things like the trailing team taking different risks at the different deficits.

      So it might also be interesting to see what the winning percentages are if you remove the games where the leading team scores after taking that 7/8/9 point lead. Or maybe just remove the times when it scores a TD. Just to see if the losing team is losing a lot of those 8-point deficit games because they threw a pick-6, or failed at the onside kick and gave up an easy TD, etc.

      • Chase Stuart

        I am nearly certain it is not an era issue.

        Keep in mind that correlation does not equal causation. I strongly suspect that being down 9 (relative to 8) is an effect, rather than a cause, of winning games. I also believe that this is not a sample size issue.

        I’m thinking this one over.

  • James Holzhauer

    Given current conversion rates, teams should also go for 2 after scoring when down 14, as they’re far more likely to make the first conversion, turning a tie into a win, than miss two attempts, turning the tie into a loss.

    • Chase Stuart

      Yes, that’s true. I almost included that in the post, but it’s a different discussion and I thought it might distract. But I’m with you.

  • Chase, two things. First, infinite kudos on finding a Spurrier image where fist-bumping is a metaphor for strategic decision-making. Second, it seems like most of the discussion here focuses on what’s optimal with enough time left for 2, 3, or maybe even 4 offensive possessions. With 6 minutes left, yeah, it makes sense to go for 2 when down 9 because there’s a reasonable expectation that enough time remains for the two possessions you need to overcome that deficit. But if you look at win probability holding everything constant except deficit and time remaining, you find that it makes sense to go for 1 the closer and closer you get to 0:00 (until time constraints overwhelm the situation).

    For calculating each of the following win probabilities, I’m assuming the team scores a TD with X time left, uses 3 timeouts on the ensuing defensive 3-and-out, and gets the ball back with X-minus-30-seconds left at their own 30-yard line:

    Score w/ 6:00 left, make XP: 12%
    Score w/ 6:00 left, miss 2pc: 11%
    Score w/ 6:00 left, make 2pc: 14%

    Score w/ 5:00 left, make XP: 10%
    Score w/ 5:00 left, miss 2pc: 11%
    Score w/ 5:00 left, make 2pc: 17%

    Score w/ 4:00 left, make XP: 12%
    Score w/ 4:00 left, miss 2pc: 8%
    Score w/ 4:00 left, make 2pc: 14%

    Score w/ 3:00 left, make XP: 19%
    Score w/ 3:00 left, miss 2pc: 5%
    Score w/ 3:00 left, make 2pc: 13%

    Score w/ 2:00 left, make XP: 12%
    Score w/ 2:00 left, miss 2pc: 5%
    Score w/ 2:00 left, make 2pc: 10%

    Score w/ 1:00 left, make XP: 4%
    Score w/ 1:00 left, miss 2pc: 2%
    Score w/ 1:00 left, make 2pc: 4%

    Now, obviously, that 19% WP when having the ball at your own 30 down 8 with 2:30 left is a small-sample-size theatre. However, I think it’s pretty clearly the general case that scoring at the 4:00 mark or later means you should go for the XP. Not because making the XP is better than missing the 2pc, but because the proportional benefit of making the XP over missing the 2pc is EQUAL TO OR GREATER THAN the proportional benefit of making the 2pc over missing the 2pc.

    You titled this piece, “…in the middle of the 4th quarter…” so I’m guessing the focus on a 6-minutes-left situation is an intentional distinction. I just wanted to bring this up because it seems like it’s getting lost in the ancillary discussion, “Well, teams down 9/8/7 win X percentage of the time.” The (completely valid) point you’re trying to make is a strategic one, so it’s worth noting that the strategy isn’t as sound once the game hits the 4:00 mark.

    • Chase Stuart

      We got sidetracked by the 9/8/7 thing because it’s an interesting quirk, and one I’m still working on. But putting that aside…

      I titled it “middle of the 4th quarter” because that’s when it’s obvious. But with 3 minutes left in the 4th quarter, it’s still the right play; it’s just less obviously so 🙂

      I’m not really following your logic. With all due respect to Brian (I assume that’s where you are pulling these #s from), who is a friend of the site, I don’t think his WP model has much applicability here. It’s a theoretical discussion, and one that is obvious enough to me that we don’t need to look at the data. And, as you hinted, the sample sizes here are going to be too small to be useful.

      You can’t argue that your odds of winning down 7 with 2:30 to go are worse than your odds of winning down 8 with 2:30 to go are. I enjoy the WP calculator as much as anyone, but I don’t think it has applicability here. And I do know Brian is on board with the tone of this post (although we haven’t discussed the specific change in utility as the minutes tick towards zero).

      Putting aside the most crazy of hypotheticals, for the most part, going for 2 early is better than waiting. The value is that you can gameplan the rest of the game better; as a result, yes, this becomes less valuable with 2 mins left than with 7 mins left. I mean, if you score a TD to cut the lead to 9 with 1:30 to go, you basically can only win the game by getting a 2pt conversion and winning in overtime. At that point, it really doesn’t matter which order you do it in (but I still don’t see an argument for kicking first; I just would be indifferent).

      • Heh. Well, according to the small sample theatre of WP w/ 2:30 left, the odds of winning when down 7 ARE better than winning when down 8. 🙂

        That said, I can get on board w/ your general theoretical point of not waiting to go for 2 earlier, if only I could get a better handle on the theoretical logic. Admittedly, as someone with the general affliction of appreciating theory more than application, this is embarrassing. I mean, I totally agree with the idea that coaches maximize self-preservation than win probability. So, is the gist of what you’re saying that it’s better to know you’ve missed the 2pc now than not knowing whether you’re going to miss the 2pc later; presumably because it better optimizes your strategy for the endgame remaining after your 2pc miss?

        • Chase Stuart

          Pretty much.

          I like the disease screening example because it works on multiple levels.

          If your results from the medical test — or from your 2pt conversion attempt — are good, then it doesn’t really matter whether you go early or wait till the end. It’s good news, after all, and sort of what you were banking on.

          If you decide to put off your screening, and you are going to get bad news, well, that’s not a wise move (from a rational person perspective). You basically prevented yourself from getting treatment right away.

          Well if you put off going for 2 and you are going to get bad news, it’s the same thing. If you miss the 2-pt conversion after the second touchdown, by definition, there is less time remaining. No matter what, if you are going to miss the 2pt conversion, a 15-point lead is a 3 score game. It’s better to find out that you need a 3rd score earlier rather than later. Again, we’re in some sense splitting hairs because maybe it only raises your chances of winning from 5% to 8%. But there’s no downside, which is why it’s a no brainer.

          The Packers were a good example. Had they known they were going to miss the 2-point conversion, they would have been more aggressive in the final minutes against SF. It’s simply a matter of knowing that you need to be more aggressive on offense (and defense) and hurry things up, rather than “milking” the clock. You also affect 4th down decisions (you may want to kick a FG in some circumstances knowing you need that third score).

          • Gotcha. Thanks for the clarification.

          • sn0mm1s

            The thing is, the disease acts the same either way and I don’t think the analogy holds when compared to an NFL defense. The entire premise of going for two first is based on the assumption that the trailing team gains a ton of knowledge and the leading team plays exactly the same whether they are up 7, 8, or 9. You might make the claim (and be correct) that teams do play the same when they are up 7, 8, or 9 – but that doesn’t mean they *should* play the same. It is basically the same argument but reversed for the team already in the lead.

            Similarly, you mentioned previously that being down 9 makes a team play hurry up offense and a team down 8 will play more relaxed. I am sure that is true – but that doesn’t mean it *should* be true. A team down 8 should play like they are down 2 possessions because they likely *are* down 2 possessions.

            But again, the 7/8/9 breakdown with no 2pt conversion doesn’t seem to support either theory. And, as much as I like playing with Brian’s WP calculator, it is based on real play by play data so if coaches routinely make the wrong decision it will be reflected in the calculator. It is making predictions on how games are being called not how they *should* be called.

  • Chase Stuart

    It’s not that the leading team plays exactly the same way — it’s that they play largely the same way. In any event, the trailing team certainly is more helped out by gaining the knowledge, which is all that matters.

    I think teams actually play more conservatively up 9, which is another reason to go for 2. If you miss it, you might get a benefit, i.e., teams are more likely to go 3-and-out.

    I’m with you on your second paragraph.

    Re: your third para, more on this next week. And I still maintain that there sample size isn’t large enough to really use Brian’s calculator for this.

  • Danish

    The Saints just scored a TD while down 15 and kicked the extra point. They were just inside the 4th quarter, so go ahead and add that to the list.

  • Ian S

    Main point that’s lost among all this, the aim is to win the game. An 8 pt deficit means a successful 2pts only forces overtime. A 9 pt deficit means that although you do have to score twice, you win if you do manage to achieve that.

  • Danish

    Saints just did it again although it was inside 2 minutes, so it probably doesn’t make a difference.

  • Paul Thomas

    Detroit just did it, too. In this case it hardly affected win probability since they absolutely had to recover an onside kick anyway. But it still made no sense. Better to KNOW you have virtually no chance so that you don’t end up getting players hurt in an exercise in futility.

  • Richie

    sn0mm1s, the point is that there are some diseases that can be treated early if they are discovered early. Wait too long and they will kill you.

    • sn0mm1s

      I understand the point – I just don’t agree that a leading team, if playing “correctly”, plays nearly the same being up 7,8 or 9. I think it is erroneous to say that the trailing teams gains a ton of knowledge which they then act on to maximize their chances of winning while the leading team for some reason thinks that knowing a team needs 2 possessions to win isn’t much different than needing 1 or unknown number of possessions and deems the info as more or less irrelevant. Regardless, as I have said repeatedly, the data doesn’t support either position and there is no way to prove either position because the only way to come close would be for teams to call games “correctly” and the reason the post was made in the first place is because of the assumption that they call games “incorrectly”.

  • Human psychology is real. It actually exists. It affects the world. Coaches go for one first because in their estimation the psychological impact of a failed attempt would hurt player morale, which changes player behavior, which changes the odds of winning. I know that this is annoying for stat heads because you lack metrics with which to measure such things. But to pretend that they don’t matter or can’t matter is to make a routine failure of empiricism: to believe that, if we lack the ability to measure something, it cannot be real.

    • Richie

      I agree that psychology is real. I believe that is why coaches choose to get the PAT first when down 15. Because they feel that this will keep their players in the game, and because it will make the fans feel like the game is still in question and because it may reduce the final deficit in defeat.

      However, I don’t believe that it will maximize win probability. Even if there may be some historical data to show that the PAT puts them in better position, I still don’t believe it (yet). I think there may be other issues at play.

    • Skins

      You are also ignoring any psychological effect (albeit a much tougher one to quantify) on the following game should a team down 8 score a TD as time expires (or close to it) and then miss the potentially game-tying 2-pt conversion.

  • Matt

    This is interesting from a game theory standpoint. There are two reasons why I don’t think you’ll see this catch on in the NFL though. One is that NFL coaches are so risk averse they make insurance actuaries look like the cast of Jackass. Two is that (I suspect) NFL coaches don’t have that many plays they are comfortable running for 2-pt conversions. Either because they don’t want to tip their hand for future games, or because they haven’t allocated the practice to it, it seems they would prefer to avoid going to 2 for as long as possible no matter the game situation.

    • Skins

      Great point I hadn’t thought about. If you only have 3 or 4 2-pt. conversion plays that you actually trust, perhaps you want to withhold revealing that play until it “mattered” (i.e would actually tie the game) as opposed to just bringing the game to a 7 pt deficit that may never be equalled (i.e a 15-pt deficit team scoring a Td and 2-pt. conversion, but never scoring again in the game)

  • Brandon

    I think the next post should be describing how teams down 14 should go for 2 if you they score in the middle of the 4th quarter. The book “Mathletics” works out the math behind that and it’s actually pretty genius. That will NEVER catch on in the NFL though, considering we can’t even get coaches to follow this, which is just completely logical and really requires no math to prove.

  • Andy

    Coaches in all sports choose conservative strategies and refuse to take sensible risk because they can more easily comprehend the extremely short-term impact of any decision versus the probability weighted impact on the game’s outcome.

    Of course the coach should go for two after the first TD. But they never do. In their minds, being down 9 feels so much worse than down 8, and being down 8 isn’t so much worse than being down 7 (as if the 2 pt conversion on the next TD was near automatic). But of course the idea is to win the game, not feel better after the next play.

  • Daliman

    With 5+ minutes left, I agree with you, but with 2 minutes or so left, like Detroit had last night is obviously a situation where you go for one, as your next possession is almost certainly your last, and if you get the onside kick, the opposing teams defense is now right back on the field after giving up a TD and is more likely tired.

  • sn0mm1s

    Chase, would it be easy for you to get a breakdown of the success rates of 2pt conversions when a team goes for 2 more than once in a game? Most of the models/theories assume that each 2pt conversion is an independent event (and usually around a 45% to be successful and a 55% to be unsuccessful). I am curious if a team that fails to convert their 1st attempt at a 2 pt conversion that they are more likely to fail their 2nd attempt and if they succeed in their 1st attempt they are more likely to succeed in a later attempt. Unfortunately, the sample size will likely be very small but it would be interesting to know.

  • Pranav

    I think one thing you are not considering is the detrimental effect on the team for the rest of the game if they miss the 2 point conversion. If a team misses the first two point conversion, they may play much worse knowing that they still need 2 more scores and will probably lose the game. You therefore have to weigh the knowledge of how many scores you have to gain vs. The potential detrimental play of the team. I would imagine that having the extra information does not greatly improve your chances of winning, but missing that early 2 point conversion would mentally remove many of the players.

    • sn0mm1s

      Well, it does make decisions more clear though.

      Scenario 1:
      Down 9 with 4 minutes left, you have the ball within field goal range on opponent’s 28 yard line, it’s 4th and 1 – the correct call is to kick the FG because you know you need at least 1 more possession.

      Scenario 2 – same thing but down 8. What is the correct call? In theory, it should be the same thing. In practice, I would guess that most coaches go for the 1st down.

  • Pranav

    That point has been made before, but what I am trying to say is that you simply can’t know which is better unless you can weigh those two factors against others. Otherwise, you cannot quantitatively prove that either strategy is better.

  • Richie


    In the article you said:

    But of those 81 teams that scored a fourth-quarter touchdown to cut the lead to 9, only nine of them went for two after the touchdown.

    You also said that 5 times out of 81, a team came from behind to win. But did you say how many of those 5 winners went for 2 when they were down by 15?

    • Chase Stuart

      None of those 5 went for two first.

  • “And there’s no reason to think your odds of converting a 2-point attempt are higher when trailing by 2 than by 9.”

    Is this a true statement? I am a sabremetrics fiend since day 1 with a math degree , but sometimes I do believe the human element must be factored in. Does the momentum of scoring two TD’s in the last 5 minutes against a now on its heels defense make a 2 point attempt’s success more probable? Or does being up by 9 instead of 8 make the opposing team more comfortable in running its normal offense as opposed to ultra conservative clock eating plays? There are many strategic and emotional variables to understand in this argument before I can put it in to the no-brainer category.

    • Richie

      It’s always possible that there are “human” factors involved that we can’t predict.

      But it’s sure hard for me to imagine a situation where a team going for the 2-point conversion while trailing by 9 is going to have any different of an effort than attempting a 2-point conversion while down 2.

      If anything, I would think that if the team is down 2, with the clock expired, that they will feel more pressure, because if they fail, the game is over. But if it’s trailing by 9 with 2 minutes left, they know that they still have 2 minutes for a miracle.

      Also, I would tend to think that passing the ball, catching the ball and kicking the ball would be more affected in this situation. More of an opportunity for you to tense up and make a bad pass, or not close your hands on the ball, etc. But in a running play, it’s much less psychological. Just blow your opponent off the ball, or just hang on tight and follow your blocker, etc.

  • ChrisV

    I’m pulling up an old thread here I know, but I just wanted to point out the fallacy in the argument that you need to kick the PAT because missing a 2PC will demoralise your players. Let’s assume for a sec that you’re always 50% to make a 2PC and that if you miss it, you always lose. Then if you go for it first time, your chance of game-tying is 50% * [chance of driving for a TD down 7]. If you go for it second time, your chance of game-tying is [chance of driving for a TD down 8] * 50%. This makes it obvious that the pertinent comparison is how your players feel down 7 versus how they feel down 8. How they feel down 9 isn’t very relevant as that provides very little of your winning chances.

    Imagine the success or failure of your 2PC is preordained. Imagine there’s a slip of paper in an envelope somewhere that says either “Succeeded” or “Failed”. When you go for two, you’ll open that envelope up and see whether you succeeded or not.

    If you assume it says “Succeeded”, what do you want to do? You’d want to open it early, right, because it will be better for your own team’s mentality and worse for the opposition’s if you are only down 7 instead of down 8.

    If you assume it says “Failed”, what do you want to do? Again, you want to open it early, because no matter how much it sucks and how demoralised you’ll be when you’re down 9 with 7 minutes to play, it’s a lot better than being down 2 with 10 seconds to play.

    This demonstrates that no matter what the result of the 2PC is going to be, you’d always like to know it early.

    Any legitimate argument to kick the PAT early is going to have to be an argument that you’re more likely to succeed at the late 2PC than the early one. I simply don’t buy that.

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  • Randy

    It is truly amazing that people refuse to understand this. I have had almost no luck in getting anyone (mostly otherwise intelligent) people to agree. I will add two comments. First, this is the same situation people argue against when a team down 8 points scores a TD and they say it is “too early to go for 2”. When they say that the best example they can give of what could happen it that you could be unsuccessful and the other team then scores a TD+PAT and now you are down 9 instead of 8. Same exact situation except when down 15 the other team has already scores the extra 7 before you score. Secondly, regarding the “demoralizing” argument. Basically they are grasping at straws at that point. But if you want to make that argument you must acknowledge both sides of it. If you do convert the 2-pt. conversion on the first TD and reduce the margin to 7 you have to acknowledge that the team should then be uplifted and play even harder than being down 8 because they KNOW that if they score another TD they will tie the game, rather than having a chance to tie it.

  • Tovia Behanu

    This scenario is more fun – this is a pure math question:

    You are up by 1 point and score a touchdown to go up by 7 with two minutes to go. Given everything is normal-average (typical stats, no unusual factors) for both you and your opponent, mathematically, should you go for the 1 point conversion or the 2 point conversion?

    The 1-point conversion rate is 95 percent
    The 2-point conversion rate is 55 percent

    We assume your opponent will get the ball back with 2 minutes go with average field position.

    So if you go for 1 and make it you are up by 8.
    If you go for 2 and make it you are up by 9.
    Miss either way and you are up by 7.

    We will also assume here, that if you do go up by 9, you will win.

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  • Statalyzer

    This is so obvious it’s amazing how most coaches and even fans will argue against it.

  • Statalyzer

    It’s even more obvious when down 18 instead of 15.

    Everyone goes for 1 to cut it to 11.

    Wouldn’t it be MUCH more important to know RIGHT AWAY if you need TD+TD or if FG+TD is ok?

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