Going for Two Down 14

Nick Sirianni
Nick Sirianni
Photo: USA Today Sports Images

There is a classic problem in football analytics that was solved many years ago. When trailing by 14 points late in the game, it is almost always correct to go for two after your first touchdown. The logic follows that if you convert the two-point conversion, you will be able to win with a simple extra point on the second touchdown, and if you fail, you will still be able to tie with a two-point conversion on that second TD. All of this assumes that you get a stop and score a second time, which is of course required under all reasonable scenarios with few exceptions. Such was the case when the Eagles attempted a two-point conversion while trailing by eight points with 5:54 remaining in the game on Thursday night against the Tampa Bay Buccaneers. 

Prior to this decision, there were a couple of notable fourth downs in the fourth quarter that set up the scenario in question.

  • 12:43 remaining in the game and Eagles faced fourth-and-10 at the Bucs' 28-yard line trailing 28-14. Philadelphia opted to try a field goal, but Jake Elliott's 46-yard attempt was no good. There wasn’t much equity at stake here for the Eagles, but a custom simulation indicates the field goal attempt was slightly correct by about 0.5% Game-Winning Chance (GWC).
     
  • 9:04 remaining in the game and the Bucs faced fourth-and-3 at the Eagles’ 45-yard line leading 28-14. Tom Brady threw a deep pass to O.J. Howard that fell incomplete. Bruce Arians was questioned for his aggression, but we concur with the decision. Again, not much equity at stake for the Bucs as they were in a dominant game state, but we see it as essentially a pick-em decision with a very slight lean toward the first-down attempt.

When the Eagles decided to go for two with 5:54 remaining in the game, Troy Aikman could not conceal his skepticism bordering on disapproval. Sorry Troy, but even though it is rarely exercised, the value of this strategy has been settled for quite some time. Before we get into the proof, we should note that an extensive custom simulation by the EdjSports model shows the two-point conversion attempt to produce about 1.5% more wins on average for the Eagles in this situation. Since the Eagles were already huge underdogs at this point (~9.5% GWC), this was a very significant relative improvement of nearly 16%. The reason we can support this strategy with such confidence is that it can be represented in a straightforward decision tree. We will remove some of the outlier scenarios that involve more than two possessions as they are rare and present themselves under both winning parlays. 

There are four key factors that must be considered for the trailing team:

  • 2PAT success rate ("P")
  • 1PAT success rate ("K")
  • Game-winning chance at the start of overtime ("T")
  • "Stop and Score" ("S") 
    • This is the percentage of time the Eagles can stop the Bucs from scoring on the subsequent possession and then follow up with a touchdown.

2PAT Winning Parlay: 

(P x S x (K + ((1-K) x T)) + ((1-P) x S x P x T)

1PAT Winning Parlay:

(K x S x K x T) + ((1-K) x S x P x T)

It turns out the "stop and score" only affects the magnitude of the difference but will not flip the decision regarding 1PAT vs 2PAT. Here are some comparisons of how the 2PAT success rate and overtime GWC interact with overall GWC. Values of 15% and 35% for the "Stop and Score" were used for reference and a standard assumption of 95% for the 1PAT.

Assuming 15% "stop and score" and 95% 1PAT success:

2PAT Success Rate Overtime GWC 2PAT Overall GWC 1PAT Overall GWC
35% 40% 6.5% 5.5%
  50% 6.8% 6.9%
  60% 7.2% 8.3%
45% 40% 8.0% 5.6%
  50% 8.4% 6.9%
  60% 8.8% 8.3%
55% 40% 9.5% 5.6%
  50% 9.9% 7.0%
  60% 10.3% 8.4%
65% 40% 10.8% 5.6%
  50% 11.2% 7.0%
  60% 11.6% 8.4%

Assuming 35% "stop and score" and 95% 1PAT success:

2PAT Success Rate Overtime GWC 2PAT Overall GWC 1PAT Overall GWC
35% 40% 15.1% 12.9%
  50% 15.9% 16.1%
  60% 16.8% 19.3%
45% 40% 18.7% 13.0%
  50% 19.7% 16.2%
  60% 20.6% 19.4%
55% 40% 22.1% 13.0%
  50% 23.1% 16.3%
  60% 24.1% 19.5%
65% 40% 25.3% 13.1%
  50% 26.2% 16.4%
  60% 27.1% 19.6%

While some of these assumptions are unrealistic, the tables provide some perspective on the dominant strategy of attempting a two-point conversion after the first score. There are very few cases where this doesn’t hold, and we can see how the "stop and score" only affects magnitude but not direction in the decision. Also, a rule of thumb emerges that going for two is the right choice if your success rate is approximately 70% or greater than your chances of winning in overtime. With an NFL average two-point conversion rate near 50%, it is clear the Eagles' approach is correct in almost all practical circumstances.

Comments

77 comments, Last at 24 Oct 2021, 2:33am

1 I asked the other day, can…

I asked the other day, can anyone give some real world examples of this strategy working? the 2pc had been in the NFL 25 years before I believe it was the giants who tried this strategy on a MNF game in 2018.  College has had the two pointer much longer, although to be fair for many years college did not allow for overtime.  Surely something so smart and analytical can be backed up by evidence.

the biggest problem with this strategy is that it does not allow you to decide when you go up by 1 late in the game (assuming you do).  Just last week, down 1, Minnesota had to be uber-agressive with 37 seconds left instead of conservative.  How aggressive was Belichik yesterday up 1 vs down 5 just ten seconds later? 

3 Real life examples

The only times it's ever worked in the NFL (where "worked" means that a team went for two down 8 in the second half, then later scored a touchdown with a chance to tie or take the lead) all have asterisks:

1960 Patriots-Oilers: Midway through the 3rd quarter, the Patriots, trailing 20-12, go for 2 and succeed. They score another touchdown later in the quarter and kick the extra point to take a 21-20 lead. (The Oilers then scored the final 17 points of the game.)

1998 49ers-Colts: The 49ers scored a touchdown with 9:58 left to cut the lead to 31-23, but botch the extra point snap, forcing the holder to run. (Officially, this goes down as a 2-point attempt). The 49ers later tied the game on a late TD+2, and won on a last-minute field goal.

2013 Eagles-Lions: A blizzard means that neither team can attempt placekicks of any length. The Eagles went for 2 late in the 3rd quarter trailing 14-6, and eventually won 34-20.

There are no NFL examples of it "failing" (where failure means a team went for 2 down 8 in the second half, didn't convert, then scored a touchdown to go down 2 and then failed on the conversion again.)  Basically, it's a new strategy and teams that are down two touchdowns late don't usually come back.

4 We tried explaining

But going for 1 or 2 doesn't decide whether this "works."

The nature of play calling has nothing to with the strat. That's a completely separate thing that teams can determine outside of it. 

There aren't examples of it because the team is down for a reason and it's hard to complete such a comeback. 

The Eagles did the right thing. The actual outcome is separate.

5   the biggest problem with…

 

the biggest problem with this strategy is that it does not allow you to decide when you go up by 1 late in the game (assuming you do).

How does kicking the extra point allow this? Sure, you can choose to go for 2 the second TD only if there's a few seconds left. But the 2-point percentage and the overtime percentage are roughly equal, so that decision is almost purely preference. It's not allowing anything.

If you're the team that goes for 2 first, and everything works and now you're worried there's too much time on the clock and you'd like to just offer overtime to your opponent, there's nothing that says you can't go for 2 and kneel.

Of course, you're gonna look stupid if your opponent is like "no thanks," goes ahead and tries to drive down the field for a FG, only for you to stop them, go to overtime, and then the other team wins.

Also worth noting that you're using two of the most conservative coaches in the game as examples.

14 so you're saying I can't use…

so you're saying I can't use a Belichick example when describing good coaching? ok

When you kick the xp first, then if you get the second td you have added information about time left (as well as anything else that might've transpired in the meantime).  Is it then worth going for 2 if you don't trust your defense against a hyper aggressive offense for 30 seconds, maybe 90 seconds, maybe 3 minutes? Regardless, if this was the right strategy we would've seen it tried and succeed at some point in NFL history before 2018! 

16 so you're saying I can't use…

so you're saying I can't use a Belichick example when describing good coaching? ok

Coaches aren't universally awesome. Otherwise Andy Reid's clock management is awesome and everyone else in the league is dumb.

When you kick the xp first, then if you get the second td you have added information about time left

Which... is the same information you have if you go for the 2 point conversion first? If you think it's better to be tied than ahead, you don't have to score the extra point.

 Regardless, if this was the right strategy we would've seen it tried and succeed at some point in NFL history before 2018! 

Why...? There are a bunch of reasons why it wouldn't. First, strategy and the game itself obviously evolves over time (see fourth-down conversion rates, see pass/run percentages, see field goal percentages, see any trendy formation). Second, look at the table: the advantage is strongly dependent on the 2-point conversion percentage, and it's pretty clear that NFL coaches think that 2-point conversions are less frequent than they are. 

Two point conversions in the NFL aren't that old.

19 in two posts you've…

in two posts you've advocated that Bill Belichick isn't a good example of a great coach, and that coaches could kneel on a two point conversion.  

I understand coaches aren't universally awesome at everything.  But if the topic was quarterbacks, I'd probably trust Reid over everyone else.  Just like on the topic of game theory, I'd trust Belichick over just about everyone else.  To your last point, 27 seasons may not be that old, but that's still pretty old.  I guarantee you if this was some earth shattering game-theory strategy, either Belichick, Adams or someone in that building in Foxborough would've come up with it ages ago.  The reason is it adds unnecessary risk.  You have to convert on one of two coin flip plays just to tie the game, instead of converting on two extra points, which despite the rate going down from 98%-95% is still considered automatic by many coaches.  

21 in two posts you've…

in two posts you've advocated that Bill Belichick isn't a good example of a great coach,

No. I have absolutely not. Never, anywhere, did I even remotely insinuate that. I strongly disagree that a great coach can't be conservative.

I guarantee you if this was some earth shattering game-theory strategy

Who the heck is saying that? It's like, a few percent. Probably 3-5% for the likely true values in that table. It's probably on the order of the overall effect of icing the kicker, and that strategy took forever to show up.

9 You were wrong on Thu nite…

You were wrong on Thu nite when it was explained to you, you're just as wrong now even moreso that it has been comprehensively explained on this site, yet again. 

I'm sorry you don't understand it. Your ignorance doesn't make it wrong. You're just bad at math.

Most blackjack players don't understand optimal counting theories and shuffle-tracking. Most poker players don't understand Game-Optimal Theory, that doesn't make it incorrect or non-existent.

15 I was right on Thursday…

I was right on Thursday night and am correct now.  As a poker player I understand Game Optimal theory, and when winning a hand requires more information I wait.  When I play blackjack I do not use optimal counting theories because card counting is cheating and I would prefer to not be escorted from the premises over a game which has already taken away every single player advantage.  

I understand the math.  what you don't understand is that football is not played on a computer or by robots.  What you do directly impacts what the opponent does.  Below a commenter gave a perfect example.  a coach tied late in the 4th in own territory punts 100% of the time on 4th and 2 or more.  if he's down by 1, he punts 0% of time.  

17 Ah there it is

The, "the game isn't played on spreadsheets" response. 

You saw the comment below but you didn't see the replies? Specifically Josephs?

Yall are advocating for conservative ties. Acting like...leading late is...a bad thing????

Ok I think you gotta accept you lost your cover bet at this point. 

23 I think it would be more…

I think it would be more instructive if/when this strategy ever failed - namely, a team goes for 2 twice, fails both, and then loses by 2 points. If that happens, the coach is going to absolutely incinerated even if it was statistically the right call. Has that ever happened?

2 the tables provide some…

the tables provide some perspective on the dominant strategy of attempting a two-point conversion after the first score. There are very few cases where this doesn’t hold

The one assumption underlying it here is that the "stop and score" percentage (S) is uncorrelated to the decision. That is, it's the same "S" in both the 2PAT and 1PAT.

In an idealized situation where the opposing coach plays optimally, it's the same - teams should be trying to win as much in the regular game as in overtime.

But, currently, I doubt it is. There's plenty of evidence that coaches are too conservative in decision-making, which means it's entirely possible that the Eagles might've been better off tempting the Bucs into not pushing things too hard - which is similar to the question "is it better to try to go up by 4, or just go up by 3?". Then, of course, you get into the dangerous situation of trying to play your opponent, rather than playing optimally.

(But, I mean, that's like, half of football anyway, so...)

7 You make a good point, but…

You make a good point, but overstate it. Optimal decision would result in more aggression from a team up by only 6, because a touchdown probably means that they lose. If it’s third and 13 and you’re up by 7, maybe you call a WR screen, try to get the first down and make sure the clock is moving. If you’re only up by 6, now converting the first down has a much higher value, so you call a riskier downfield pass. 

So it might be more accurate to say that this strategy actually exploits the conservatism of the opposing team coach more than it is actually good in and of itself.

10 I think your logic's…

I think your logic's backwards?

If your opponent gets significantly more aggressive if they're only up 6 rather than 7 (edit: this is poorly worded: what I mean is if your opponent plays more optimally up 6 rather than 7), then you'd rather kick the XP and go down 7. It's playing possum. "Don't worry about us, you just go ahead and try to bleed out the clock, worst case you'll just go to overtime."

Assuming the opponent plays to win equally in all situations, going for 2 on the first TD improves your win % by ~10-15% (relative, not absolute). But because your chance of winning in those situations is already low, improving everything by ~10-15% might not win over improving the "stop" percentage by  manipulating your opponent's behavior, even if the end result is only overtime.

Look at the tables above: suppose going up 6 changes your "stop and score" chance from 35% to 15% because suddenly your opponent plays more aggressively. Now obviously you would've been violently better off kicking the extra point. Even if your chance at winning in overtime is only 40% the 1PAT column are all at ~13% in the 35% table, strictly better than anything in the 15% table.

33 I’m not sure, but you seem…

I’m not sure, but you seem to be making this assumption that the team that is up by 6 should make the same decisions as the team that is up by 7. That’s not necessarily true, assuming optimal play. First downs become more valuable, since turning the ball over to the other team gives a higher percentage chance of losing the game. It therefore makes sense to throw more, accepting the downside of stopping the clock or potentially an interception/fumble, because the upside is higher.

39 It therefore makes sense to…

It therefore makes sense to throw more, accepting the downside of stopping the clock or potentially an interception/fumble, because the upside is higher.

The downside to those risks is worse in that case, though, too! If you're up 7, stopping the clock or turning the ball over only results in a drop to 50%. If you're up 6, screwing up drops it to 0. It's the same multiplier either way.

I think the general gist of what you're saying is that if you're up 7, you can hand the ball back to them with more time because worst case they'll only have a 50% chance to win. But I don't think that actually works: you're trading direct chance to win (chance to gain a first down) for indirect chance to win (chance of failing * chance of them failing). And then you're saying that an even more indirect chance (chance of failing * chance of them succeeding * chance of you still winning anyway) is going to make the difference.

edit: Think of just, say, the value of a dangerous throw. Suppose it's got an 80% chance to give you a win, and a 20% chance to give the other team a TD immediately. If you're up 6, choosing that throw means you've got an 80% chance to win. If you're up 7, choosing that throw means you've got a 90% chance to win, because handing a TD to your opponent isn't an automatic loss.

6 I’m getting really annoyed…

I’m getting really annoyed with this analysis that just throws stuff out like “we don’t take into account more than 2 possessions, as that’s rare.” Yeah and so is converting 4th and 30, but I remember Ray “hit your wife like you hit the hole” Rice doing just that against the Chargers. That something is rare is not an excuse to not factor it in when you’re pretending to be some autist giving the gods truth about winning percentages.

But beyond that, I am also annoyed with this constant assertion, mostly in the comments, that being up by 1 point shouldn’t affect things because the opposing coach should be trying to win in regulation whether they’re tied or not. Uh, no. If Team A is down by 1 point with 25 seconds to go on their own 11 yard line on 4th and 10, they need to go. If they’re tied, they need to punt, and it would be crazy to go. If you force a team to score or lose, they will necessarily play more aggressively than optimal play for a tied game. 

Any analysis that doesn’t understand that getting the lead late in a football game is a dangerous thing, that gives the other team massive incentive to try their hardest to score, is pretty bad analysis. Again, this is assuming optimal decision making from both coaches, not playing on the cowardice of existing coaches.

8 This x 1,000

Other than that "the cowardice of existing coaches" isn't really a thing. (not in this particular topic, anyway)

A coach down 1 now has 4 downs to play with. A coach who's tied really doesn't.

This stuff wouldn't bother me without the 'It Has Been PRO-VEN!!!' garbage. Stuff like that is what makes you guys look like nerds to the actual practicioners. Basically because it does make you nerds.

27 "They look like the smart…

In reply to by BigRichie

"They look like the smart people who know things because they are the smart people that know things." Great dig. Really showed up everybody here. You are the exact problem with, well, everything.

29 The claim in this article…

In reply to by BigRichie

The claim in this article isn’t even defined. What exactly is “late in the game,” and then he just handwaives this subjective term and implies there will never be more than two possessions. 

Just like you, I’m not even saying that you shouldn’t go for two in many situations. But the absurdly overconfident “IT’S JUST FACTS AND LOGIC,” garbage is just annoying. There’s so much wrong and missing with this analysis, even beyond the point I raised earlier.

11 Decision Analysis

"Any analysis that doesn’t understand that getting the lead late in a football game is a dangerous thing..."

Anyone who makes a statement that getting the lead late in the football game is dangerous needs to rethink what he or she is saying--unless winning games is a dangerous thing. Is it true that team X will play more aggressively in the last seconds of a ballgame if they are behind versus if they are tied? Of course! But you have to play to WIN THE GAME! So, while I understand that people have different reasoning on whether to go for 1 and the tie versus 2 and the lead in the last minute or less of a game, this is not being discussed here. What is being discussed is whether you should go for 2 to narrow the deficit to 6 points. If your team is down 14 in the 4th Q, they were probably the weaker team coming into the game. This gives them another chance to win the game in regulation--the leading team will not play differently if they are ahead by 6, 7 or 8 points. They will still play to try and run out the clock first, with scoring more points an extra benefit. 

Even if we were discussing the differences between 1 & 2 at the end of the game when down 1, here are your scenarios: 1--You kick the PAT to tie the game, opponent kneels out the clock, you get the ball first in OT and score a TD. This is the only scenario where your defense doesn't have to stop the other team for your team to win. 2--You kick the PAT for the tie, the other team plays aggressively and scores the game winner. 3--You kick the PAT, game goes to OT (whether or not they play aggressively in regulation); your defense gets a stop, you win in OT. 4--You kick the PAT, they get the ball first in OT and score the TD--you lose. 5--You score the 2 pointer, your defense stops them and you win. 6--You score the 2 pointer, they score and you lose.

In the 6 scenarios, you win 3, you lose 3. In every loss, your defense doesn't stop them. in 2 of the 3 wins, they do stop the other team at least once. To win without the defense doing their job, you have to hope that the other team plays sub-optimally AND you win the coin toss. In other words, you have to gamble that the your opponent (who we are assuming is better at least today, since they were ahead late in the game) will not try to win, that the coin bounces your way, and that you can go (probably) 75 yards to score a game-winning TD in OT--versus a chance to get 2 yards on 1 play! Now there are lots of nuances in the 2 point play selection, but give me the chance to win the game IN REGULATION.

18 This gives them another…

This gives them another chance to win the game in regulation--the leading team will not play differently if they are ahead by 6, 7 or 8 points.

This is a really, really big assumption.

To be clear, they shouldn't play differently - they should play optimally in each case. And it's really dangerous to intentionally sacrifice your chance of winning on the hope that they'll make bad decisions.

But it's pretty clear that at least to some degree coaches are overly risk-averse, so this definitely seems like an assumption you'd want to test.

30 ”Anyone who makes a…

”Anyone who makes a statement that getting the lead late in the football game is dangerous needs to rethink what he or she is saying--unless winning games is a dangerous thing. Is it true that team X will play more aggressively in the last seconds of a ballgame if they are behind versus if they are tied? Of course! But you have to play to WIN THE GAME!“

I was writing a detailed response to this, before realizing that it is so utterly idiotic, that to even respond, at least on the object level, would be to somehow legitimize this statement as some sort of insight. 

Yeah, why bother factoring in how changing scores changes the other teams optimal play? You play to win the game right?

40 OK, let's take this to a…

OK, let's take this to a logical conclusion.  If "that getting the lead late in a football game is a dangerous thing" (your exact words, and I don't believe I've taken them out of context), then if you are down 6 and score a touchdown with 2 minutes left, should you not kick the extra point?  With 4 minutes left?  With 30 seconds left?

You're right that many coaches play too conservatively with the game tied, as opposed to being down, but how predictable is that?  Do you really want to base generic end-game strategy on it, to the point where you'd consider having a late lead to be a bad thing?

49 Well, I don't believe I did,…

Well, I don't believe I did, really.  I understand your point about opponents playing suboptimally, but if having a lead is really dangerous, there must a point where you'd elect to not take the lead, right?  So my question stands: how much time would have to be left for you to kneel on an extra point after you scored a touchdown when you had been down six?

If the answer is "never", then having a lead isn't really that dangerous, at least not in a way that impacts this specific strategy (when/if to go for two after scoring down 14).

51 Lead is better than tied, however...

It's obvious you'd prefer the lead over being tied with, say, 30 seconds left and your opponent having two timeouts.

However, you didn't get to that lead without taking risks.  The utility of those risks goes down as the opportunity for the opponent to score increases.  A higher two-point conversion success rate is required.

Let's reduce the game to just two conversions with no opportunities for the other team to respond.  If you get 3 or 4 points, you win.  If you get 0 or 1 point, you lose.  If you get 2 points, you flip a coin.  Assume kicked PATs are 100%.

In that case, you only need a 38.2% conversion rate in order for going for two to be correct.

If, instead, after the two conversions, your opponent has a 20% chance of coming back to win if they are behind or a 8% chance of winning in regulation if tied, then the math changes.  I think those are reasonable estimates for average 2021 teams receiving a kickoff with 30 seconds and 2 timeouts.

In that case, if you kick PATs twice, your chance of winning is half of 92% or 46%, since 8% of the time the tied team will win in regulation.

If you go for two, your odds of winning are 0.8 * P + 0.46 * (1 - P) * P.  The breakeven point is when that is 0.46.

80P + 46P - 46P² > 46
0 > 46P² - 126P + 46
P > 0.434

So, by just giving a small chance of the previously leading team to get the last score, the required success rate increased from 38.2% to 43.4%. 

While you might argue that the team receiving the kickoff with 30 seconds when tied should be more aggressive, they should definitely be less aggressive than the team receiving it with 30 seconds and down 1.  If they're down 1, there's no difference between a turnover and failing to score for other reasons.  If they're tied, that turnover could be a massive mistake if the other team can then score.

Kicked PATs aren't 100%, so that reduces the required 2-pt success rate.  Also, 2-pt success rates league-wide have been well-north of 43.4% for years.  So, yes, going for 2 is still correct.

The more time on the clock, the less utility this strategy has.  However, given the 94-95% kicked PAT rate and ~50% 2pt-conversion rate, I suspect it's correct to go for two in this situation even in the first quarter.

53 While simplified, this is…

While simplified, this is basically correct (rhinos are never wrong, after all). The important thing is the gap between the 20% chance for the last-second score when trailing by 1 versus the 8% chance for the last-second score when tied. If those numbers were the same, then this logic would not apply. But that difference doesn't have to be huge for the calculation to flip (and that's not including if you think you have a better than 50% chance to win in overtime for some reason).

54 My interest in football is primarily quadratic equation related

Yes, it was simplified so I could use actual percentages and math to see how the required 2-pt success rate changes based on the odds of a counter score from the other team.

I will note that while my 20% number was based on probabilities from an actual game, the 8% was a guess based on that 20% number and the behavior across all NFL coaches.  My 8% was supposed to incorporate the instances when, even being somewhat conservative, the team turns the ball over and the opponents score (e.g., 10% regulation win and a 2% regulation loss).  I know someone around here could find a decent number for the actual probability in a tied game, receiving a kickoff with 30 seconds and two timeouts.

From a game theory optimal (GTO) standpoint, if there is a 20% of scoring when down 1, the tied team should probably ramp up the aggression to where there's, say, a 12 or 14% chance of scoring, even if it comes with an additional 2 or 3% chance of a turnover with an opposing score in regulation.

With an 8% effective chance of scoring, that kickoff receiving team will win -> 0.08 + (1 - 0.08) * 0.5 = 0.54 or 54%

With an 12% chance of scoring, an additional 2% chance of a turnover & regulation loss, then -> 0.12 + (1 - 0.14) * 0.5 = 0.55 or 55%

A 14% with an additional 3% regulation loss -> 0.14 + (1 - 0.17) * 0.5 = 0.555 or 55.5%

A team's optimal aggression should be at the point where if you get more aggressive, your odds of losing in regulation increases faster than your odds of winning in regulation.  I suspect few teams will be that aggressive.  It's also not like teams can toggle a dial to set the optimal aggression.  The actual aggression is based on a sequence of discrete plays...what the play calls are and the behaviors/execution among 22 players.  That optimal aggression changes after each play.

For that matter, I don't know if aggression scales in that way and where that GTO peak would be.  I do know that it must be lower than the 20% number for when the team was down 1 or 2 points.

I'll conclude that if your opponent is going to play a Game Theory Optimal strategy if tied, that's even more incentive to go for two on that first touchdown to try to win in regulation.

63 > Well, I don't believe I…

> Well, I don't believe I did, really.

You clearly have no idea the quite basic point I was making, like, at all.

> I understand your point about opponents playing suboptimally

That's a point I made later. No, you and like 10 other midwits in this thread who are convinced that they are 300 IQ SuperGeniuses still don't seem to understand that optimal play changes depending on the score. In addition to this, you should also be trying to exploit legitimately suboptimal decision making by the opposing coaches.

> but if having a lead is really dangerous, there must a point where you'd elect to not take the lead, right?

Lol wut? Literally nobody ever said this.

> So my question stands: how much time would have to be left for you to kneel on an extra point after you scored a touchdown when you had been down six?

Lol wut?

> If the answer is "never", then having a lead isn't really that dangerous, at least not in a way that impacts this specific strategy (when/if to go for two after scoring down 14).

Again, why do I waste my time with these people?

65 "That's a point I made later…

"That's a point I made later. No, you and like 10 other midwits in this thread who are convinced that they are 300 IQ SuperGeniuses still don't seem to understand that optimal play changes depending on the score. In addition to this, you should also be trying to exploit legitimately suboptimal decision making by the opposing coaches."

How kind of you to break out the insults, but I'll reply anyway.

Of course the score affects optimal play.  In this specific case, I think that's an argument in favor of going for two on the first touchdown (when you had been down 14).  If you make it, then when you score again, you have multiple options for what to do, depending on the game situation.

If there's enough time left that you would rather be tied, in order to get the opponent to play conservatively and go for overtime - and you think your odds of winning in OT are greater than your odds of stopping them if they play aggressively - you can just kneel on your extra point, and leave the game tied.  But if there is little enough time left - or you don't like your odds in OT - you can just kick the extra point to win.  But worst case, you're at least tied.

If you kick the extra point on the first touchdown, your options are more limited.  The two near-guaranteed options after the second touchdown, kneeling and kicking, leave you down and tied.  So if there is little enough time left, to take the lead you'd have to take a roughly 50/50 shot at a true win/lose option (going for two).

Of course, the third alternative is that you miss the first two-pointer.  In that case, you're left with the same 50/50 shot, but to tie or lose.  That's obviously the worst outcome.  I personally think the tradeoff of having a near guarantee of taking the lead after your second touchdown is worth the risk of this situation, but that's definitely debatable.  (I'm not quite convinced this has been "mathematically proven" like some others have said, because it does assume too much about the subsequent probabilities.)

I think you (and a few others in this thread) are overstating how conservative coaches are these days, though.  Ten to fifteen years ago, I think all but one or two coaches would sit on the ball with a minute left in a tie game, but now I think you'd see more than half the league try to score in regulation, even if tied.  And one problem with limiting yourself to a scenario where you play for the tie, hoping they're conservative, is if you did get that wrong, you don't even have the lead if you do stop them.  You'll have to stop them twice or once and win the OT coin toss and score a touchdown right away.

(And you get super dismissive of my questions, but what did you mean by "getting the lead late in a football game is a dangerous thing"?  I'm not the only person to have misinterpreted it, so maybe everyone misunderstanding you isn't a "midwit", and it's more that you haven't explained your position well.  So I will ask again, what are the implications of having the lead late being dangerous?  Would you not want to actively avoid creating a dangerous situation, and thus at times elect to not kick the extra point that gives the lead?  If not, then what would be the point of including it in the analysis, if it doesn't change your decision?)

41 Lions v. Vikings game works as an example

If the team that was leading may have time on the clock after the second TD, then it does reduce the utility of the go for two strategy.  For a recent example, Detroit went for 2, down 1, during their Week 5 game with 37 seconds left.

Had there been no time left, the decision to go for two is fairly easy.  If P(2pt) > P(1pt) * P(OT) then going for 2 is correct.  If one assumes OT was a 50-50 deal in winning equity(?), then Detroit should have gone for 2 if their expected success rate was greater than or equal to half the expected success rate of kicking a PAT...or 47 - 47.5% for two average NFL teams with average kickers.

With time left, even as little as 37 seconds, then it's more complicated.  If the two-point conversion fails, then the Lions are almost certain to lose, given how rare successful onside kicks are.

Depending on how much time is left, the right half of the equation may stay the same since the Vikings would just accept OT rather than a desperation drive.  With 2 timeouts and starting from the Vikings 18 with 33 seconds post kickoff, I would try to score if tied, but I'd be a bit more conservative than if I were down 1.

Anyway, assuming that OT is assured if the Lions make the kicked PAT, the calculation becomes P(2pt) * (1 - P(Vikings Comeback)) > P(1pt) * P(OT).  Instead of a 47.5% success rate going for 2, they'd need even higher.  If the Vikings, down 1, have a 10% chance of scoring, then the needed two-point success rate jumps to 52.8%.

ESPN has the Vikings odds of winning at 17.7% after the kickoff return to the 18 with 33 seconds and two timeouts.  It must have been slightly higher before the kickoff, but even using 17.7%, the Lions needed success rate going for 2 jumps to 57.7%.  I would argue that it's actually a little lower than that, because the Vikings would be the favorite in OT, but I'm interested in the more general case.

My point of all this is to illustrate how the ability to counter with a last-second score at the end is very relevant in the going for two, down 8, scenario from this article.  You need a significantly better conversion rate if your opponents are left with as little as 30 seconds.

12 If you force a team to score…

If you force a team to score or lose, they will necessarily play more aggressively than optimal play for a tied game. 

No, you're misusing the term "optimal play." Optimal play is you play to maximize your win chance. If a team is forced to score or lose, aggressive play is optimal.

The point that's being made is that coaches should play optimally whether they're tied or not. What that means is that coaches should, for instance, go for it on 4th and 2 from the 50, say, instead of punting it with 25 seconds left even if they're tied. If coaches do not play optimally (for instance, they just kneel it out instead of trying to score a FG at all) depending on the score, then yeah, the best play for the opposing coaches is to goad them into making that mistake. The problem is that doing that will eventually go away.

31 Not sure where you were…

Not sure where you were going with this. The point is that a 4th and 25 from your own 5 yard line demands a punt with a tie game, and going for it when behind. All assuming the minimal time remaining. 

You have to factor in that optimal play changes if you have the lead. 

28 Any analysis that doesn’t…

Any analysis that doesn’t understand that getting the lead late in a football game is a dangerous thing, that gives the other team massive incentive to try their hardest to score, is pretty bad analysis.

I agree. Always play to not be winning late. We don't want to try to maximize our chance to win, we want to maximize the amount of time it is technically possible for us to win.

That's why, when me team is down 6 and stores a TD, I always argue for them to skip the PAT. I'd rather be tied than winning. Every coach already does this! That's how we know it's right!

32 Point that was made: You…

Point that was made: You have to factor in how the score changes optimal play from the other team. That influences your decision to go for it when down by 8 after scoring that first touchdown.

What midwit heard: Hurr Durr Winning Bad Never Have Lead.

I mean there’s really no dealing with these people.

42 I'm sure I could find…

I'm sure I could find hundreds if not a thousand examples in NFL history where coaches down 3 played for the field goal instead of the touchdown.  Or down 7 kicked the extra point instead of going for two.  Those coaches were playing in a way to "not be winning late." as you put it.  You, and Pat earlier, seem to base your argument on the premise that coaches could just forgo the xp and take the tie instead of the lead.  But in the scenario where the td ties the game, kicking the xp is of zero risk.  in the scenario where you're down 1, the 2pc carries massive risk.  you either lose the game, or get a lead where the opponent has time to comeback.  the missing information in any of these examples, is how much time defines your term "late." 

43 It’s like no matter how many…

It’s like no matter how many times one of us makes the “there is still time remaining on the clock,” argument they just don’t get it. They’ve convinced themselves they’re dealing with some 90 IQ coaches dealing with CTE from their playing career.

45 Yall are really being stubborn

It's after the first of two TDs needed, that the team should go for two. Thus keeping the game at 8 or cutting it to 6. This isn't putting them down by 1 and them deciding to tie or win by 1. It's easier forcing them to do another 2pt conversion (bound to get at least 1/2 chances) or kicking the 94% XP to win.

They can control the clock but yalls idea of being up 1 being dangerous is silly. Forcing them to be predictable isn't something you should avoid.

61 > It's after the first of…

> It's after the first of two TDs needed, that the team should go for two.
 

Oh really? Oh my god we had absolutely no idea Mr. Supergenius. We just had absolutely no idea that the point was to go for two after the first TD scored, despite explicitly mentioning this multiple times. Just literally no idea. Thank you Mr. Supergenius, you're so smaaaaaaart.

This was a common argument type encountered in this thread. The 200 IQ Critical Thinkers kept bizarrely assuming that people who questioned the laughably incomplete and frankly kind of stupid analysis presented Just Didn't Understand. Like, no, we understand, it's just stupid/incomplete.

64 Multiple ad homs

Your guys entire basis is that going up late will force the other team to go for it on 4th. Our point is who cares, you're winning and they become predictable.

Sorry so many of us here like leading late...like most winners. 

This is such a weird hill for you two to die on. Like, I'm not a math major whatsoever but it's pretty simple math you guys are try to deny because another team might be aggressive on 4th downs? As if you cant know that ahead of time and counter that?? As if 4th downs (against the clock mind you since it's late) are automatic???

Whatever. Ill leave you this explanation from ESPN if you wont listen to us for some reason.

"Only two teams ever have gone for 2 when down 8 and come back to win the game, according to Elias Sports Bureau data. One of them was the 1998 49ers, but that 2-point attempt was unintentional. According to the play-by-play, a bad snap on a PAT resulted in a failed rush attempt. The other was a snowstorm game in 2013, when the Eagles attempted a 2-point try on every touchdown they scored.

The reasons it hasn't worked:

  • By definition, the team that attempts the 2-pointer is losing by 8 points late in the game, which is already a long shot.

  • Most importantly, there just aren't that many teams that have tried it.

That doesn't mean the numbers behind the strategy are wrong, though, and soon the strategy could pay off."

 

69 i'm not dying on a 4th down…

In reply to by ImNewAroundThe…

i'm not dying on a 4th down hill.  i'm staking my flag on a hill of information.  regardless of whether or not you go for 2 first or second, the chances of you being up late in the game are about 45.1% using generic averages (the 48% 2pc success rate x 94% xp rate).  the main analytical thrust behind this strategy is that by going for 2 first, you have information on whether or not you get the 2 so you still have a mulligan to tie the game.  by going for it second, you are putting your eggs in one basket.

my contention is that for a strategy that gets you ahead only 45.1% of the time and has risk, i want to know if it is actually going to get me the win instead of just putting me ahead.  

70 You clearly are but

All that stuff is explained in the countless articles linked and online elsewhere. Here's another one. Trying not to be redundant. Click on the tweets of smart people discussing it if it still doesn't fancy for whatever reason. That chart shown easy to follow. 

Teams that (have to) employ this strategy are 

"By definition,...already a long shot."

45.1%? You mean the 45.5% in the ESPN article? Everything has risk! You have to be ahead to win! The strat doesn't guarantee a win because nothing does! If a team uses the strat and loses doesn't mean the strat process is bad! It's what helps them get closer to winning in the first place, hence all the numbers that back it up! 

 

46 I'm sure I could find…

I'm sure I could find hundreds if not a thousand examples in NFL history where coaches down 3 played for the field goal instead of the touchdown.

Sure. Why are you implying this is good? I can find an example of a coach calling a pass on short yardage in the Super Bowl with everything on the line, too. Strategy in the NFL evolves. Playing defense is hard now.

Or down 7 kicked the extra point instead of going for two.

Those two choices are identical in terms of winning percentage.

You, and Pat earlier, seem to base your argument on the premise that coaches could just forgo the xp and take the tie instead of the lead.  But in the scenario where the td ties the game, kicking the xp is of zero risk. in the scenario where you're down 1, the 2pc carries massive risk.

No one is talking about going for 2 down 1?

the missing information in any of these examples, is how much time defines your term "late." 

I don't understand why you keep bringing up the amount of time remaining. Teams can still score to win even if the game's tied. If they're more likely to score if they're losing than if the score is tied... something is very, very wrong with those teams.

Yes, you could say "but... they're desperate! they'll do anything!" But that shouldn't lead to scoring more often. All of the bad things that happen when you're desperate - interceptions, 4th down stops, etc. - those will still happen. If they don't happen often enough to counter out the rate that the scoring happens, you should be playing like that all the time.

50 The definition of "late" is…

The definition of "late" is an interesting point, and when you score definitely matters.  That said, I think this is another reason to go for two on your first touchdown down 14.  If and when you get that second touchdown, you now have the choice of whether to take the lead by kicking (if you score late enough) or just kneel on the extra point (if you feel that there is enough time for the opponent to come back, but they wouldn't try to if it's tied).

62 WTF? Holy shit, nobody ever…

WTF? Holy shit, nobody ever said that having the lead in and of itself provided negative winning chances, something you 400 IQ geniuses keep pretending we claimed. This was literally never said. What was said is that since optimal play changes to be more aggressive from the team down by 1, odds of them scoring in regulation increase, and this must be factored into the decision to go for 2 down by 8.

LMAO, why do I waste my time with these people?

66 To borrow a phrase from you,…

To borrow a phrase from you, "lol wut?"

Are you looking for one of us "400 IQ genuises" (or is it 200 or 300? you keep changing that) to just acknowledge that some opponents will be less likely to score when tied, instead of being down one?  In that case, most of us have (I know have, at least).  My stance is still that I like having the option to just kick to take the lead, so I think going for two on the first touchdown is a perfectly viable strategy.

20 Interesting, but...

... it's hairsplitting and overselling to call this 'optimal' and that any questioning of it is a cognitive defect, given how little this changes GWC. Which is a shame, because this is truly an interesting strategic idea. My biggest problem is that it's realized here how the magnitude of the effect needs to be sexed up:

 the value of this strategy has been settled for quite some time. Before we get into the proof, we should note that an extensive custom simulation by the EdjSports model shows the two-point conversion attempt to produce about 1.5% more wins on average for the Eagles in this situation. Since the Eagles were already huge underdogs at this point (~9.5% GWC), this was a very significant relative improvement of nearly 16%

"Significant" maybe, but not impactful. So essentially no leverage has been uncovered here. And this sort of analysis should be about uncovering otherwise hidden leverage, not "1.5% more wins on average", depending on all kinds of assumptions any one of which being off probably blows up the analysis. The main missing element is time: miss the 2PT and you need the ball back twice. 

So this is a huge fly in the ointment of an otherwise interesting tactical idea. Because there are perfectly valid use cases for it, most importantly an NFL coach not wanting to do OT, perhaps in a meaningless end of season game. 

25 The main missing element is…

In reply to by JacqueShellacque

The main missing element is time: miss the 2PT and you need the ball back twice.

Um, you need it back twice to what? To win? If you kick the PAT the first time, you are probably going to kick it again the next time, which means you need it back twice to win. If you're suggesting you could kick after the first TD and then go for two after the second score, your logic is faulty, because you're suggesting it's better to go for two after the second score and have no recourse if you miss; better to go for two after the first score and at least have the option of tying it later if you miss.

38 Neither faulty

Nor 'unquestionably correct'. This is a scenario where neither of those terms apply. It's an interesting decision, but nothing compelling from an analytical perspective has been uncovered here.

47 I'm not sure what you're…

In reply to by JacqueShellacque

I'm not sure what you're trying to say. On average it's definitely unquestionably correct, it's pretty straightforward. But you're absolutely correct that it's legitimate to point out that it's of minimal benefit. Frank, in the article, tried to stress that it's a "relative increase of 15%," as if that's a big deal.

But really, this is, in general, a criticism I have of these articles anyway. A 3% game-winning chance increase for a coach is almost pointless. I mean, it's almost not worth the coach thinking about this entire problem if it takes 1 second away from figuring out an optimal play call for the defense. It's almost like suggesting a clock hitting strategy in chess.

Look at the "2PAT and 1PAT" winning parlays above. There is literally 1 term you can factor out from both: "S." The stop percentage. It's the dominant term in your entire win chance, and a coach should focus literally all of their effort on maximizing that.

If you've got some boilerplate 2-point conversion plays you're happy with, cool, do it. But do it every time, because wasting one second of thought on anything other than "how do I stop them from making all this pointless" is a strategic mistake.

55 We definitely agree

Except on the 'average' part. Because I think with this sort of analysis you don't want the average, you want to find the edge, to find that little thing you can do now that is both disproportionate and impactful. If you haven't found it, as you suggest, you make a choice and move on. Some of the responses in this thread are simply too lengthy for the supposed benefit uncovered. If it takes too long to point out, it's probably not worth thinking about. 

73 Kindof? Icing the kicker,…

Kindof?

Icing the kicker, for instance, is/was/whatever a small effect, maybe a few percent. Took a while to catch on, then everyone did it, and at this point I'm not even sure it matters or happens anymore (the initial significance seems to have gone away).

If you think about it, icing the kicker is a lot like this. You can actually imagine it as a kicker attempting two kicks, and without knowing the result, the coach is forced to pick one of them, and the strategy is "always choose the second." A good fraction of the time you're going to be wrong, and screw yourself (miss the first, make the second) but on average you'll win out more than you lose.

The difference with icing the kicker (again, if it was clear) that makes it a no-brainer is that you can just not think about anything. You just force the second kick, always. So it's a no-cost choice.

In this case... there might be a cost (choosing the 2-point plays). If there's a cost, it's almost certainly not worth it to think about it. But if you've got 2-point plays you're comfortable with, just going for it period in these situations is perfectly fine.

22 I can not believe that this is still up for discussion

If I were a high school math teacher this would be a problem on the final exam.  It is just simple math, nothing more.  I read the article, but not the 21 comments preceding mine, this is a discussion that I refuse to have.

24 Agree with the overall…

Agree with the overall thrust, but as with all these debates, there are no generic football teams, and no generic football games, so there can be no generic correct answers.

26 There certainly can be …

There certainly can be "generic correct answers." In a vacuum, all else being even or league average, what's the correct play? That question has an answer. And we know what the answer is.

34 More bad math tonight

Mike Vrabel's clock mismanagement on Buffalo's final drive of the game. Let's recap the possible outcomes if he never leaves his team enough time to score in regulation:

  1. Buffalo scores a touchdown; Tennessee loses.
  2. Buffalo kicks a field goal at a time of its choosing and goes to overtime. Tennessee had Henry and six straight scoring drives, but Buffalo was a solid pregame favorite.
  3. Buffalo somehow turns the ball over without scoring.

Outcome #3 seems optimistic against a quarterback who had never thrown a red-zone interception in his career. Even if you thought the changes were high, though, consider the math if OT is a 50/50 affair:

If the odds of a turnover are higher than the odds Buffalo scores a touchdown, you're a favorite to win; if the odds are lower, you're a favorite to lose.

I know what the outcome was, but I don't deal in results-oriented thinking. There is no way the odds of a turnover were higher than the odds Buffalo was going to score a touchdown on that drive. Vrabel's time management on that last drive was terrible, especially once Buffalo had first-and-10 at the 12.

35 Getting ahead of it...

Buffalo was right!

Remember Titans playing with a lead is dangerous for TN!!!!

56 Neither right nor wrong

As a Bills fan, I agree with McDermott's choice but would not have gotten on him for kicking an FG. For reasons I've laid out in other Risky Business discussions, when you're faced with ending the game in the event of failure, it's perfectly legitimate for decisionmakers to see their role as extending the game (not just sports, could be investing, business, war) and doing anything necessary to avoid that absorbing barrier. The simplest logic is always the best though, and doesn't require probabilities: if you kick the FG and go to OT, you're really only trying for what you already have in your hands right now, with no guarantee you'll have it then.

It's odd that people have forgotten this is the exact Ice Bowl  (1967) scenario, as if in the interim a lot of common sense has been lost in risk-aversion and rationalization. I'm sure Vince Lombardi didn't consider kicking the FG, and it goes without saying for reasons that had nothing to do with GWC or 'odds'.

I'm not overly disappointed in the loss here though and my biggest fear isn't that McDermott will do the same again, it's that he won't.

57 Extending war is silly.

More people will get hurt. Well football is war and choosing to end the game there was the better decision given the situation.

Lombardi may not have used those exact words explicitly but he sure was applying them whether consciously or unconsciously. 

36 I can't resist...

Okay, so let's add in the calculation for a chance of a final score (before overtime) by the team that was initially up by 14 (team A). Under the assumption that the chance of that final score is completely unaffected by whether team A is now tied or down by one point, then the logic above holds. Sure the odds of team A getting a final score could vary from 0.1% (one second left after the second touchdown) to 90% (Brady with the 2007 Patriots against the 2021 Chiefs defense with 1:30 and three timeouts), but that just changes the odds of team A winning by the same amount regardless of whether the 2PT first tactic is used or not.

But, if the odds of team A scoring after the second touchdown are DIFFERENT, depending on whether they are now tied (playing conservatively for overtime) or down one (playing all-out to win now), then what happens? This is just a slight modification to the formulas above, adding in a variable for the "final stop chance when tied" (FSWT) and the "final stop chance when up by one" (FSU1). When using fairly reasonable numbers (such as used above) for all the other variables, if the FSWT chance is around 1.5 times larger than the FSU1 chance (say 85% and 55%), then the strategies become roughly even. If the FSWT chance is even larger, then kick the PAT on the first touchdown becomes the correct strategy.

Note that this 1.5 times value would be lower if team B (the team that was initially trailing by two touchdowns) has a low 2PT conversion rate and/or a high overtime win chance (I was using 50% for both). The reverse is also true (high 2PT conversion rate and/or low overtime win chance increases the value).

I personally think this means this strategy is correct in the modern NFL in the abstract, but in some extreme cases (an opposing coach you think is very likely to go unreasonably conservative in this situation, a very low likelihood of your team converting 2PT, a very high likelihood of your team winning in overtime), kicking the PAT is the correct answer.

The other thing, though, is that we will likely never have enough data to be confident about these numbers to a level of variance that would make this decision unquestionable. The situation is rare enough, that by the time enough instances had occurred, the game would probably have changed enough to make the older instances not very useful data points.

What a team could do, though, is have their own custom formula that plugs in what the coaching staff thinks any of these values are, then that will tell them what to do based on their own assumptions (whether those assumptions are right or wrong). This type of thinking would be the best way to mesh analytics with low-data specific situations that need an expert's intuition. Use the expert's intuition to modify the individual percentages (their HOF defensive tackle was injured on the touchdown play and we have Derrick Henry--analytics man, increase our 2PT chance by 50%!).

75 "I personally think this…

"I personally think this means this strategy is correct in the modern NFL in the abstract, but in some extreme cases (an opposing coach you think is very likely to go unreasonably conservative in this situation, a very low likelihood of your team converting 2PT, a very high likelihood of your team winning in overtime), kicking the PAT is the correct answer.

"The other thing, though, is that we will likely never have enough data to be confident about these numbers to a level of variance that would make this decision unquestionable. The situation is rare enough, that by the time enough instances had occurred, the game would probably have changed enough to make the older instances not very useful data points."

I agree with this, and I think this is very well-stated.

48 Algebra approach ~38.2% two-pt success rate

I've advocated going for two using a simpler, more idealized scenario, with the following assumptions:

0) The behind team scores two TDs, otherwise this is all moot.

1) OT is a 50-50 situation regarding winning equity (counting ties as 0.5)

2) Kicked PATs are 100% instead of 95%.

3) The other team does not have time to score after the second TD.

In this case, kicking the PATs for both TDs has 50% winning equity.

Going for Two

If the first attempt works (probability P), they win.

If that fails (prob: 1-P), the second attempt can send it to OT, which is 50-50. So, to find the breakeven point:

P + (1 - P) * P * 0.5 > 0.5
2P + P - P² > 1
0 > P² - 3P + 1

Solving for P using the quadratic formula, you get (3 - √5)/2 = 38.2%.

That makes going for two on the first TD correct if the expected success rater is 38.2% of higher.

Addressing my assumptions, the 95% kicked PAT percentage makes the required two-point success rate even lower. 

The possibility that there would be time left on the clock after the second touchdown means that the required two-point success rate would be higher.  How much higher can be complicated.

I went over the related, but less complicated scenario of going for 2 when there's still time left scenario in a different comment, using the Lions v. Vikings game as an example.

We have computer simulations that tell us the odds of a team scoring when receiving a kickoff with 37 seconds left and 2 two timeouts left if they are down 1.

What are the odds of a team scoring in regulation in that same situation if they are tied?  Odds that they turn it over and their opponents score?  That varies heavily on the coach's aggressiveness, their personnel, and their perceived odds of winning in overtime.

The later the first touchdown is, the more correct going for two would be, because it becomes closer to my idealized situation, except with a lower kicked PAT percentage.  As the game time increases, it becomes less clear, but I'd still generally be in favor of going for two after the first touchdown, barring significant mitigating factors.

52 The concept that there could…

The concept that there could be an unexpected relationship in team W-L results between leading by 6 points versus leading by 7 points versus leading by 8 points is interesting.

From a behavioral perspective, it likely shouldn't matter how the team with the ball got into the "late" game (last 5 minutes?) with the lead.  In terms of how they play, it presumably should only matter that they have the ball, the game is almost over, and they have a lead of either 6-, 7-, or 8-points.

Excluding behavior theory, the expected result should be that teams with the ball and a lead in the last 5 minutes of the game should have a rising W-L record depending on whether the lead is 6, 7 or 8, i.e. teams with a 6 point lead should win less than teams with a 7 point lead and those with a 7 point lead should win less than those with an 8 point lead.  However, if there's truth to the idea that shrinking a team's lead to 6 points from 7 points impacts how that team plays the final minutes of the game, then maybe this relationship doesn't hold?

It shouldn't be too difficult for someone with access to a proper database to identify all situations where a team held the ball and a 6-, 7- or 8-point lead in the last 5 minutes of the game, and then calculate how many of those teams won in regulation, lost in regulation, or went to overtime.

58 It really is amazing how…

It really is amazing how there were so many people in this thread making 100 IQ arguments, yet absolutely convinced they were 200 IQ supergeniuses. Thoroughly convinced that the only reason people like me, JetsPete, luvrhino, BigRichie, and others kept pointing out how shitty and worthless their "analysis," was, was simply because we were 80 IQ dumbdumbs suffering from CTE after our playing careers. Ignoring that the analysis in the article above:

1) Doesn't bother even defining what "late in the game" even means.

2) Simply assumes that there will never be more than 2 possessions for each team, for absolutely no reason.

3) Doesn't factor in how optimal play for the other team changes based on the score.

4) Doesn't factor in how current sub-optimal overly safe decision making from the other coach should be exploited in order to win.

5) Doesn't take into account that OT can result in ties, which in the regular season should be considered worth more than a win, most of the times for most teams.

6) That even with the nonsense analysis presented taken for granted, winning chances increase so little it's not worth any coaches time to focus on that as opposed to getting the next playcall right.

And many others.

59 As one simple example of…

As one simple example of point 3. Let's say we have a team that gets the ball back after a touchback kickoff at their own 25. There's 1:30 remaining, and they have 1 timeout. The other team has no timeouts. If they kick the ball to the other team, they have no way of getting the ball back, even with a defensive stop.

The "optimal decision making," is fundamentally different whether the game is tied, or if they are up by 1. While the drive should start out similarly, since all decent teams should be trying to score in regulation with that much time left, we can quickly conjure a scenario where a team down by 1 will behave completely differently than a team tied, with optimal play.

It's 4th and 40 with 30 seconds remaining, and the ball at their own 1 yard line. Tied, they punt. Behind, they go for it. And if the 200 IQ Intelligent Critical Thinkers want to handwave conversion chance as being so low probability that it doesn't matter, well it's a contrived example. It's not that hard to imagine a situation where the team needs to convert 4th and 15, 4th and 10, 4th and 7, multiple times on the same drive from deep in their own territory. 

And even beyond that, there are less cut and dry scenarios, such as running a draw on 3rd and 25 if the game is tied, making sure enough time has come off the clock to make it harder for the other team to score after you punt it back to them. Essentially choosing 10 yards and 40 less seconds over a higher, but still very low chance at converting, which is required for the team down by 1 point, and which knows it has two downs or it loses.

It is so odd that such a fundamental point was missed by the 200 IQ supergeniuses here who "have proven" that it you should always go two down by 8 "late in the game," whatever that means. The above, very obvious point, that you have to factor in optimal play changing for the other team, lowering the expected return of a lead late in the game, seems to have gone over their giant heads, stuffed to the brim with 40 lbs brains. That they displayed hilariously idiotic reading comprehension fails when I said that having the lead late in the game was "dangerous," for this exact reason, should not take away from their intellectual superiority. Smart people have incredibly idiotic takes all the time and basically don't understand anything ever. This is definitely a thing that smart people do. It's okay guys, you're still Intelligent Critical Thinkers.

60 And as for point 4, I…

And as for point 4, I thought it was pretty funny how the 200 IQ Supergenius Intelligent Critical Thinkers just sort of handwaved the practical aspect of exploiting bad decision making by opposing coaches. We see almost every week a coach take a kneeldown at the end of the first half in decent field position with multiple timeouts. Similar terrible decision happen at the end of the second half seemingly every week.

But Superintelligent Extraterrestrial Aliens Who Are Disguising Themselves Poorly As Mere Human SuperGeniuses The Likes Of Which The World Has Never Seen Before just sort of handwaved this away as not being important, for... reasons. Reasons that were never explained, but like it's okay, you're the one with the 6,000 IQ, not me. 

That you can do things that are optimal when facing a computer, but sub-optimal when facing fallable human opposition is like, I'm struggling to not come across as too snarky here, like kind of, you know, like, important? Like maybe an actual smart person would, like, maybe, you know, like, consider that in decision making. That like maybe possibly you know you're kind of retarded for not factoring in that you can force a dumb coach into making the smart decision when the game situation forces them to make the right decision, and that this can be bad?

No, that's just for intellectual mediocrities who live in the real world. Intelligent Critical Thinkers who get back and neck problems because their gigantic brains keep weighting them down know that you don't even need to consider trivialities like that. It HAs BeEN ProVEn.

67 I'm pretty sure luvrhino is…

I'm pretty sure luvrhino is not agreeing with you, at least not completely.  Their post #48 suggests that in an idealized scenario, and assuming extra points are converted at 100% rate, you should go for two on the first touchdown if you think your chances of success are 38.2% of higher.  They acknowledge there are a lot of assumptions, but luvrhino certainly doesn't sound like people in favor of going for two are "making 100 IQ arguments, yet absolutely convinced they were 200 IQ supergeniuses", like you are.

I suspect you're getting so many arguments because you're being super aggressive with the name-calling and insults.  Your actual stance doesn't seem too far off from many of the people you're arguing with.

68 You’ll notice that Eddo once…

You’ll notice that Eddo once again doesn’t bother actually debating the point. This marks perhaps the 7th time he’s responded to something I said, and he has yet to actually address anything I said. Okay that’s not quite true, he keeps pretending that I claimed having a lead was bad. No really, if you look above you’ll see numerous times he’s pretending that I’m advocating for deliberately not winning in order to have a better chance at winning the game. 

Again, I’m not making that up, he has attributed that position to me multiple times now. Then even more bizarrely, he claimed that going for 2 early was great because it gives you the option to kneel instead of kicking an extra point. 

Anyway, I’ll simply wait patiently while for Eddo, or really anyone else, who would like to respond to the actual points that I have made, here or elsewhere. 

71 Dude, I'm the guy who posted…

Dude, I'm the guy who posted what I believe backs up a lot of your points. But I'm not completely sure, because you keep getting in "screaming" matches with other people here because they either disagree with you or don't understand the point you are making. I'm not sure because I just skim over your posts, because your tone makes you seem extremely irrational. Are you right? Are you wrong? Why would I bother even trying to figure that out? I'm not even taking the side of the people you are so mad at--a number of them seem to just be yelling back at you. But for me (and a lot of other people on this board), you guys are just ignored because it isn't worth trying to wade through all the yelling. Just letting you know how this looks to people not really involved in or interested in this kind of discourse, because FO boards are some of the best and most civil on the internet (especially for sports) and I would like them to stay that way.

74 I have been trying to…

I have been trying to respond to your points, and I thought my tone was fine (at least until I started to snark back at you, and for that, I apologize).

I'll try to go through one by one, to make it clearer.

1) Doesn't bother even defining what "late in the game" even means.

You are correct I haven't explicitly declared what I think "late in the game" means; my assumption when advocating for going for two after the first touchdown is that it only makes sense when it's likely that you will only get one more possession in regulation.  This will vary game to game, depending on the teams playing.

2) Simply assumes that there will never be more than 2 possessions for each team, for absolutely no reason.

Again, I didn't state this explicitly.  But I am now - I believe the strategy is only advantageous when you think it's very likely you'll only get one more possession in regulation.

3) Doesn't factor in how optimal play for the other team changes based on the score.

4) Doesn't factor in how current sub-optimal overly safe decision making from the other coach should be exploited in order to win.

I'll respond to these together, since they're closely related.  And I absolutely did address them.

My post #40: "You're right that many coaches play too conservatively with the game tied, as opposed to being down, but how predictable is that?  Do you really want to base generic end-game strategy on it, to the point where you'd consider having a late lead to be a bad thing?"

My post #50: "The definition of "late" is an interesting point, and when you score definitely matters.  That said, I think this is another reason to go for two on your first touchdown down 14.  If and when you get that second touchdown, you now have the choice of whether to take the lead by kicking (if you score late enough) or just kneel on the extra point (if you feel that there is enough time for the opponent to come back, but they wouldn't try to if it's tied)."

My post #65: "Of course the score affects optimal play.  In this specific case, I think that's an argument in favor of going for two on the first touchdown (when you had been down 14).  If you make it, then when you score again, you have multiple options for what to do, depending on the game situation."

My post #65, again: "I think you (and a few others in this thread) are overstating how conservative coaches are these days, though.  Ten to fifteen years ago, I think all but one or two coaches would sit on the ball with a minute left in a tie game, but now I think you'd see more than half the league try to score in regulation, even if tied.  And one problem with limiting yourself to a scenario where you play for the tie, hoping they're conservative, is if you did get that wrong, you don't even have the lead if you do stop them.  You'll have to stop them twice or once and win the OT coin toss and score a touchdown right away."

You might disagree with my points here, but I've certainly addressed the substance.  At the end of the day - if it's unlikely you'll get more than one more possession after scoring the first touchdown - I'd rather gamble on my own team succeeding on one or two two-point conversions instead of the opposing coach making suboptimal decisions.

5) Doesn't take into account that OT can result in ties, which in the regular season should be considered worth more than a win, most of the times for most teams.

This is a really interesting point that I've seen Pat bring up from time to time, and I apologize if I've skimmed over you making the same point.  (It's been hard to separate the signal from the noise in some of your other posts, due to the name-calling.)

6) That even with the nonsense analysis presented taken for granted, winning chances increase so little it's not worth any coaches time to focus on that as opposed to getting the next playcall right.

I'll agree with you here, and I know have not claimed this increases your win probability that much.  The only reason I started commenting on this at all was because, in the open thread, there were a few posters (I'm honestly not sure if you were one or not) that acted like the Eagles loss proved going for two was always a bad strategy.

And I've also explicitly addressed this in my comments here.  My post #65, yet again: "I personally think the tradeoff of having a near guarantee of taking the lead after your second touchdown is worth the risk of this situation, but that's definitely debatable.  (I'm not quite convinced this has been "mathematically proven" like some others have said, because it does assume too much about the subsequent probabilities.)"

I'll throw something back to you, since I legitimately am curious: how does a having a lead being "dangerous" (your word) affect your own decision-making.  I understand how it relates in this specific case (scoring a touchdown when down 14), but what about in more general ones.  The term "dangerous" is pretty strong - to me, at least; I would definitely try to keep my team out of dangerous situations outside of very dire situations - and it suggests there would be game states where you would elect to not take the lead.  Is that true, in your opinion?  If you score a touchdown while down 6, is there a situation where you wouldn't bother kicking the extra point, to try to get the opposing coach to make suboptimal decisions?  In this case, it's you who replied to my post #40 with no substance, just an assertion I didn't understand you.

72 I was not and am not…

I was not and am not interested in discussing people's IQs and who is and isn't genius.

My posts were intended to provide the mathematical basis in going for 2 and a factual foundation upon which a reasonable debate could be held.  As you noted, I started with the simplest, easily calculated case.  I then tried to address each of my assumptions and working out what happens if you replaced those assumptions with reality.  See comment 51 and 54 for that analysis.

It is true that, if the team that was behind takes the lead and leaves too much time on the clock after their second TD, the advantage of going for 2 on the first TD goes down.  This means a higher 2-point conversion rate is required.  It's also the case that unless the first TD occurs with very little time on the clock, that team isn't going to know how much time will be left after their potential and required second TD. 

I don't think that extra time matters for most matchups and they should go for two on the first TD, anyway.  Assuming a 50% 2-point success rate, for kicking the PATs to be correct, extreme numbers would be required like:

- 100% kicked PAT
- 25% of the time the opposing team would score a counter if down by 1
- The opposing team would always kneel if tied after the last TD

That would be a breakeven point between kicking and going for 2.  Coaches are not going to be that outrageously conservative to kneel in a circumstance where, if down 1, they could score at least 25% of the time.

76 This more or less aligns…

This more or less aligns with my point of view.  I think this is an especially interesting paragraph (especially the part I've bolded):

"It is true that, if the team that was behind takes the lead and leaves too much time on the clock after their second TD, the advantage of going for 2 on the first TD goes down.  This means a higher 2-point conversion rate is required.  It's also the case that unless the first TD occurs with very little time on the clock, that team isn't going to know how much time will be left after their potential and required second TD."

One reason I like going for two on the first touchdown is that, when you score again, based on game state, you either (a) give yourself a two options that you're very likely to execute correctly or (b) give yourself one really clear option that you can plan for.

For both (a) and (b), you obviously need to stop the other team from scoring on their next possession, so let's assume that happens.  Let's also assume you score another touchdown, because otherwise, this all doesn't matter.

For (a), if you make the two-pointer, you now are in a situation where your next touchdown has tied the game before the extra point.  If you do think you're in a situation where the opposing team would have a greater chance of scoring quickly if they were down one than they would have of winning in overtime, and that they would choose to play conservatively if they were tied, you could choose to just kneel on your own extra point.  As you imply with your last paragraph, I think that is a pretty narrow space, so it's unlikely you'd ever elect to keep the game tied.  So instead, you wind up with a near-automatic extra point to take the lead.

(There's also an edge case here, where being down six would allow you to kick two field goals to tie, if you can manage to fit a third possession in.  I can picture a situation where the opposing team fumbles the kickoff, and you're then faced with fourth and long in field goal range after three quick incompletions, where this becomes a viable option.  But it would be really rare.)

For (b), if you miss the two-pointer, well... now you know you have to go for two again.  This could alter your play calling, too; you might try to score especially quick, in case you don't make the two-pointer to tie later, so you could maybe sneak in a third possession (sort of like the other edge case I just talked about).

77 Solving for the B/E Probability

Solving the quadratic equation for the break-even probability of 2-point success, you get 38.2% with an assumption of 100% success on the kick.

I'm an actuary professionally and I can honestly say that other from a few exam questions, solving a quadratic equation never had another use in more than 30 years in the profession.

2-point strategy sheets for coaches are usually arranged by the minimum percentage of 2-point success needed to go for 2 in a given game situation.  When I see such a chart, the easiest way to validate it (or disregard it) is to look for that 38 or 39% entry in the latest game situation where the scoring team trails by 8.

Brian Billick ordered just such a 2-point conversion on 10/14/2001 for the Ravens at GB which is one of the only times in the first 20 years of the 2-point conversion that a coach chose the strategy by the tables.  I had the good fortune to meet coach Billick at a company function and he had no real recollection of the event.  So he either trusted a chart or a headset elf to help him make the decision.  In either case, I was impressed.

EDIT: I see luvrhino solved the quadratic above.