Down by 8: PAT or 2 Pt Conversion?

Meaning down by 8 after having just scored 6 on a TD. And in a late Q4 situation where you have only one more realistic chance at the ball (either by defensive stop or onside kick recovery). We’re assuming that you get the ball back without the other team scoring and then score another TD. Otherwise the whole issue is moot anyway and you may as well go home. So the question is which option gives the best chance assuming you can pull off the hard part.

ISTM that the 2 pt option gives the best odds. Because it gives you a chance to win if you make it, and a chance to tie if you don’t.

My thinking is that you go for the 2pt conversion. If you make it, then you’re only 6 down. Then on your next TD you can go for the PAT and win the game outright. But even if you fail, then you go for the 2 pts again on your next TD, and can still tie it. By contrast if you go for the PAT both times you can at best tie.

I did the math assuming that 45% of 2 pt conversions are successful as are 99% of PATs. Based on these assumptions, the chances if going for the 2 pts are:

Win: 45%
Tie: 25%
Lose: 30%

Assuming ties are a 50% chance of ultimate victory, breaks it down to:

Win: 57%
Lose: 43%

By contrast, going for the PAT

Win: 0%
Tie: 98%
Lose: 2%

Again assuming ties are a 50% chance of victory, breaks it down to:

Win: 49%
Lose: 51%

Not a huge difference, although the discrepancy could be higher if the 2 point conversion percentage is higher (or the PAT percentage lower). But still, it seems clearly to be the better choice and I don’t recall an instance of a team going for the 2 in this situation - this came up most recently in the NY/Dallas game yesterday - or of the decision even being remarked on (although frankly it’s not the uppermost issue in the game at that point). Though I’m admittedly not a huge football fan and might have missed it.

It does happen. Here’s an article about a similar sort of case.

The problem is that the 2-pt conversion is a high-risk move, or at least is perceived as a high risk move. You’re putting all your chances for success on one play. Sports fans are as risk-averse as the rest of humans, and they’d much rather lose a game in overtime than lose it to a 2-pt conversion that fails.

Not all wins and losses have the same value.

You failed to calculate the odds if you kick the PAT on the first touchdown, and then go for 2 on the second. What’s the expected win/loss then?

Your premise is flawed, You can take the PAT on this score and still win if you make the two-point conversion attempt after the next score. Why would you go for two and take the chance of killing your momentum when you still need one more score? Take the PAT and reduce the lead to a score (7). If you score on your next possession, you can decide between the PAT to tie or the two-point conversion for a win, as it’s likely to be your and maybe the last play. I think most coaches in that situation would take the tie, as the come from behind team now has the momentum.

Looking at it statistically, going for two is correct, for a reasonable success rate on 2-point conversions. There is something to be said for considering the momentum swings on a missed or made 2-point conversion, although I wouldn’t assign too much weight to that myself.

The expectation for this strategy must be worse than the OP’s strategy. In your strategy, you win if you make the 2pt, and lose if you don’t. In the OP’s strategy, you win if you make the 2pt, but you don’t automatically lose if you don’t, because you have a chance to make the second 2pt and tie the game.

I can’t argue with momentum type arguments (nor do I put much stock in them), but from a math/odds standpoint it makes no sense at all to go for the PAT on the first attempt and the 2 pts on the second. Because that way if you fail on the conversion you’ve lost the game. If you went for it on the first opportunity you only lose the game if you fail on two consecutive attempts.

The odds for the reverse approach would be as follows:

Win: 45%
Tie: 0%
Lose: 55%

ETA: beaten to the punch by borschevsky

here’s the thing. The probability of making a TPC is pretty low vs a PAT. You take the easy points (the PAT) since you can still win w/a TPC IF you score again. Because the TPC/PAT on the first score is at the beginning of a long list of things you need to do to win, you don’t want to kill your momentum. Remember, this only matters if you score again, and practically, that might prove harder if the opponent is amped after stuffing your two point conversion attempt.

I am no statiostician, but in these scenarios you only need to get a TPC after one of two necessary scores. All I am saying is save it for last. I can’t see this chnaging the odds, but, again, I am no statistician.

No, in the OP’scenario, you still have to take the PAT after the second score. The question is really, if you’re going for the win, do you take the TPC after the first or second score. For reasons set forth above, I think you go on the second if at all. (In reality, you go for the tie and take momentum into overtime).

Initially my gut reaction was that it would make no sense to go for two in this situation, but you won me over (with maths, my favorite way).

What if assuming a 45% chance of conversion is too high? I don’t think it is, but I’ve seen estimates as low as 40% (and as high as 55%), so someone might disagree with you just because you overestimate the chance to make the conversion.

I figured I’d work out the “break even” point where going for 2 in this scenario gives you the same chance of winning as taking the PAT. The answer I got was 38%, meaning even if you accept the low value (40%) for 2-point conversion attempts it makes sense to go for 2 points on the first touchdown.

What you’re missing here is that if you miss the TPC on the second touchdown (after taking the PAT on the first) that’s it, you lost the game. So your chance of winning the game is equal to your chance of making the TPC. If, on the other hand, you go for the TPC on the first score and miss you get a chance to make up for it on the second touchdown. This makes your chance of winning the game higher than your chance of making a single TPC.

I see, now. I would still play for the tie, so I’d take two PATs.

The OP is certainly correct (though he’s hardly the first come up with the idea). It’s one of those little things that Head Coaches get wrong 100% of the time, even though it’s their job to think about these things and use them to help their teams win. Some of it no doubt is due to a selfish desire to avoid criticism for (seemingly) risky, unconventional moves which are only slightly better than the alternative. Most of it, I’m pretty sure, is due simply to ignorance.

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The kick is up - and it sails through IMHO, landing in The Game Room!

Moved.

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I’m curious…where did you get the 45% number for 2-point conversion success rate? I’m not arguing that it’s wrong; I’m just wondering, because I’ve seen that figure everywhere from 40% to 55%.

If it’s over 50% there’s an argument to be made to go for 2 ALL the time (except, I presume, in the obvious situations, such as a tie game with no time left pending the point after attempt).

Can someone run the numbers backwards? How low does your TPC rate have to be to make it a bad idea?

I can’t remember the last time someone tried a fake on a 1 point attempt-that’s what I probably would go for on the 1st opportunity.

The problem is that the success rate bounces around, partly due to small sample size and partly due to periodic swings in the balance between offense and defense.

It’s easier to locate statistics for college football; the NCAA annually publishes a table of conversion success in each division of college football dating back to the advent of the two-point conversion in 1958. In college football the PAT is attempted from the 3-yard-line. Major (FBS) colleges attempt 200-300 two-point tries per year, and the success rate bobbed from .456 in 2005 to .370 in 2006, for no discernible reason. Then it rose to .421 in 2008 and declined back to .370 in 2009. For a long time before 2005 it was over .400.

Single-point success, as you might expect, has been almost continuously increasing, save for a blip downward in 1992 when the goalposts were narrowed. It reached .965 in 2008 and is still trending upward.

I’m not aware of any such source for NFL statistics. The NFL conversion is attempted from the 2-yard-line, so I’d expect the success rate to be higher. But with 32 NFL teams versus 130 (?) FBS teams–albeit playing a longer season–I’d expect fewer attempts and even more variation from year to year.

What you’re missing is that the second 2PT is for the tie, not the win. If the tie is an acceptable goal, you should always go with PATs. If it is not acceptable, then going for the 2PT first is foolish because it maximizes your chance of losing. (Which is effectively zero if you go with PATs, so any deviation from PATs by definition maximizes your chance to lose.) Go for it second when the defense is more tired and the momentum is on your side.

However many 2PTs you need, always go for them last. Doing so minimizes the number of scores you need to win (or at least tie), which should always be the primary concern.

A game doesn’t end in a tie though. It goes to overtime where somebody (usually) wins.

Yeah, no kidding. I abbreviated “tie at the end of regulation” to “tie.” My whole post buys into the idea that not every team views overtime the same. An offensievly oriented team who couldn’t stop your grandmother from scoring obviously wants no part of overtime, while a real football team couldn’t care less.

While going for 2 PATs almost guarantees a tie, you have no chance to win (in regulation). If you make the 1st 2PC, then you only need the PAT on the 2nd touchdown to win. If you fail on the 1st 2PC, you still haven’t lost because you can try again (for the tie) after the 2nd touchdown.