Down by 8: PAT or 2 Pt Conversion?

The Game Room
21

And also no chance to lose.

If your team actually has a defense, go for PATs and stop them in overtime. If the only thing on your team is offense, by all means go for two and the win. But don’t do it until the last touchdown.

EDIT: Someone argued that you shouldn’t go for the 2PC on the second one because you lose if you miss it, but that makes no sense. The fundamental idea of going for the 2PC on the first one is because you can “make up for it” on the second one. But that’s the exact same situation: Miss the 2PC on the second one and you lose. Only this time if you make it you tie instead of win, which hardly seems better.

I’ll put it this way: If you want to go for two and the win, always go for it on the last one to “keep hope alive.” If you kick a PAT first, you know you can go for two and the win on the final touchdown. If you go for two on the first one and you miss it, you cannot win on the last touchdown. Always maximize the chance you can win on the last touchdown.

22

Unless they win the coin toss.

23

I’m surprised the situational history of the game hasn’t really come up at all to this point. What I mean is, I’d first consider how my team has fared in short yardage situations up to that point against that defense. I’m not going for any 2pt conversions at all if my team hasn’t yet converted a single 3rd and <2. Secondly, the old adage is to go for the win on the road and the tie at home. I would only consider that as an NFL coach in a handful of stadiums, but it’s there (there don’t seem to be many daunting road stadiums left in the NFL) .

Part of the original arguments for going for 2 seem flawed to me. If you go for 2 on the first score and fail, why are you going to count on succeeding the second time? And by the time you have failed, your only option left is to try something again that failed the first time. There are too many variables that affect your chances of succeeding on a 2pt conversion for it to be a pure test of probability, and many of those variables are, by nature, unquantifiable. Unless I’ve really dominated a team in short yardage I’m probably going to go for a tie and ride the shifting momentum into overtime.

24

I’m having a hard time understanding what contribution you’re trying to make. Are you just throwing out nonsequitors, or do you have a point?

25

His point is no doubt that a team with a great offense who wins the coin toss going into overtime in the pros (they still do sudden death, correct?) has a good chance of winning the game by scoring first since they get the ball first.

26

You’re right that if you make the second 2pt it’s for a tie instead of a win, but that opportunity for a tie is not available in the case where you only try for a 2pt on the second TD. Here are the two scenarios:

Try for 2pt on the first TD:

  • If you make the 2pt, you win
  • If you miss the 2pt, you either tie or lose with the second 2pt

Only try for 2pt on the second TD:

  • If you make the 2pt, you win
  • If you miss the 2pt, you lose

The first strategy must be better than the second, because “you either tie or lose” is better than “you lose”.

This idea of keeping hope alive is the conventional wisdom, but I’ve never really understood why. I think you should play to maximize your chances of winning the game, not to stay in the game as long as possible.

For example, say you’re down 15 near the end of the game, and you score a TD. Pretty much every coach in the NFL would kick the PAT, and then go for 2 if they score the second TD. It seems more useful to me to go for 2 on the first TD, because it’s useful to have the information of whether the 2pt was successful, although of course it’s useful for the defense to know this as well.

27

OK, first of all, this whole discussion hinges on the assumption that in the remainder of the game, we manage to outscore the other team by exactly one TD. If we don’t do that, it doesn’t matter what we chose, because we’ll lose regardless. If we get more than one TD (a TD and a field goal, say), then we win regardless. There is some probability, P[sub]T[/sub], that we’ll get exactly one more TD, and another probability, P[sub]F[/sub], that we’ll get more than 1. We don’t know what these probabilities are, but they won’t change which choice is better. There’s also a probability of success on a point after, P[sub]1[/sub], which I’ll call .95, and a probability of success on a 2-point conversion, P[sub]2[/sub]. In addition, there’s the probability that we’ll win if we go to overtime, P[sub]O[/sub], which should be .5 (since, in every scenario where we go into overtime, there’s no way to distinguish between the two teams).

All right, then. The two strategies to consider are strategy A, where we try to make a point-after after each TD, and strategy B, where we first try to get a two-pointer. Under strategy A, we try to make the point-after right now, and then another point-after if we succeed, or a two-pointer if we fail, tying the game either way, and then hope to win in OT. This makes our probability of winning

P[sub]A[/sub] = P[sub]F[/sub] + P[sub]T[/sub]*( P[sub]1[/sub]^2 + (1-P[sub]1[/sub])*P[sub]2[/sub] )*P[sub]O[/sub]

In strategy 2, we first try for the 2, and if that succeeds, we try for the 1, and if it fails, we try for 2 again and hope to win in overtime. That makes our probability of winning

P[sub]B[/sub] = P[sub]F[/sub] + P[sub]T[/sub]*( P[sub]2[/sub]*P[sub]1[/sub] + (1-P[sub]2[/sub])*P[sub]2[/sub]*P[sub]O[/sub] )

Comparing these two, we see that P[sub]F[/sub] and P[sub]T[/sub] don’t matter. We have to compare

( P[sub]1[/sub]^2 + (1-P[sub]1[/sub])*P[sub]2[/sub] )*P[sub]O[/sub] >?< ( P[sub]2[/sub]*P[sub]1[/sub] + (1-P[sub]2[/sub])*P[sub]2[/sub]*P[sub]O[/sub] )

Plugging in our values for P[sub]1[/sub] and P[sub]O[/sub], we have

( 0.45125 + 0.025P[sub]2[/sub] ) >?< ( 0.95P[sub]2[/sub] + 0.5*(1-P[sub]2[/sub])*P[sub]2[/sub] )

I don’t feel like solving the quadratic to find the break-even point for P[sub]2[/sub], but assuming it’s 0.45, then we have

0.4625 >?< 0.59875

which strongly favors strategy B, going for the two-pointers. Assuming it’s 0.4, then we have

0.46125 >?< 0.5

which still favors B.

Quoth whole bean:

Because you don’t have any momentum to kill. The statistics are clear that “scoring momentum” exists only in the minds of coaches and fans: It does not show up on the field. And coaches who make decisions based on things that don’t matter on the field really ought to be fired, though of course they aren’t. The real problem is that the skill set that would make for a good coach is completely different from the skill set that’s actually used to select a coach. Most coaches are former players, but if players were able to make the hard decisions, then we wouldn’t need coaches in the first place.

28

Do you have some stats on this? I don’t doubt you. just looking for data.

What?

Even if every player is willing to make the hard decisions and be as unbiased as possible, you can’t get around having a leader and 1 coherent strategy instead of 80 different opinions based on 80 different levels of intelligence, experience, etc. This applies to most activities not just football.

29

He’s not saying get rid of coaches. He’s saying get rid of coaches that make bad decisions. But that’s not going to happen, because the prevailing “wisdom” is to only select coaches out of a pool of people that don’t make good coaches.

30

Many NFL and college coaches (even real good OC’s like Weiss - let’s not talk about his HC gig at Dame) have had no appreciable college or pro player experience. Your comment regarding the momentum shifts ignores a very real component of the game.

To begin with, we have the following scenarios:

The PAT
1.a Kick the PAT and likely make it
1.b Kick the PAT and miss

Go for the two
2.a Go for two and make it
2.b Go for the two and miss

which lead to (assuming a subsequent score - the conditions of the OP were suh that only one more offensive possession is realistic)

1.a.1 take for the PAT to tie
1.a.2 go go for the two to win
1.b.1 go for the two to tie

2.a.1 take the PAT to win
2.b.1 go for the two to tie

So if your take the point under scenario one and make it, you’ll have a choice of whether to go for the win or the tie. If you miss, you’ll have to convert. If you go for two and make it, you’ll have a tie after the second TD and a chance to win. If you miss, you’ll have to convert the two (that you just missed).

Going for the two onyl offers the possibilty of sealing a tie with a subsequent score, but is this really that great of a benefit where PATs are converted at a rate of 95%?

31

Yes, it is. Chronos already went through the math above, but I’ll use a simplified version. Say you make 100% of your PATs, and 40% of your 2PCs. I think 40% is the lowest 2PC rate that’s been given in the thread, and obviously 100% is high for PATs. Therefore this is understating the value of going for 2.

A. Kick both extra points:
OT is guaranteed. 50% chance of winning the game.

B. Kick PAT on first TD, go for 2 on second TD:
40% chance of making the 2PC, so 40% chance of winning the game.

C. Go for 2 on the first TD:
40% chance of making the 2PC.
60 * 40 = 24% chance of missing the first 2PC and making the second, forcing OT.
60 * 60 = 36% chance of missing both.
So 40% + 24%/2 = 52% chance of winning the game.

32

Let me try to frame it differently. I give you a coin to flip. You can either call it in the air, and if you’re right I’ll give you $1.95. If you don’t call it at all I’ll give you $1. You can flip it as many times as you like. What would you do?

33

This is a no-brainer. Always kick the PAT first to get within one score. If you go for two and miss it you’re still down by two scores. It’s always smarter to reduce the number of scores you need.

Going for two right away only makes sense if you’re itching to try out a new onside kick play.

34

But people are arguing that the actual situation is that you get $2.05 if you call it right, and $1 if you don’t call it at all.

35

I don’t believe this. Cite?

I don’t believe this either. Of the 32 current head coaches – and it’s only head coaches who decide whether or not to go for two – who are the former players?

36

Not if they’re claiming less than 50% chance to convert.

Here’s a different way to look at it. For those who claim you should go for two as early as possible, doesn’t that mean you should always go for two? Earlier is better, right? So why not go for two right out of the gate?

37

As with the infamous Pats (i.e., the team, not the scores) discussion of a few weeks ago, I think the fallacy is that you can come up with any reliable, scientifically sound batch of “probability” factors. Football is not a game of chance.

38

I suppose it wouldn’t much matter if I can just keep flipping and take your money :). But there’s an important reason why your coin flips aren’t analagous to the game situation we’re discussing. In the game, we don’t want to maximize our points; we want to maximize our chances of winning the game.

To use your idea, say in our football game we can just have a 1-point conversion (ie PATs are 100%), or flip a coin for the success of a two-point conversion (ie 2PCs are 50%). I say go for two on the first TD:

50% of the time I make the 2PC, and I win the game by 1
25% of the time I miss the first 2PC and make the second, and tie the game
25% of the time I miss both, and lose the game by 2

This losing by 2 is where the advantage comes from for this strategy. There’s no difference in the number of points I get by going for two compared to going for 1. However, by going for 2 I’ve changed the distribution of the points - I win 2 games by 1 for every 1 game I lose by 2.

Edit: This is in reply to Ellis post #32.

39

Why? Not all scores are the same.

40

So you guys are saying the smartest play of all is to go for two on your first TD of the game, and if you make it go for 1 every TD thereafter. If you miss it, chase the points by continuing to go for two until you at least break even with what you would have had if you went for one each time.

Is this the idea in a nutshell?

In what way?