Why KC should have gone for 2 and all that

NFL Coaches Are Getting Away With Crimes Against Middle-School Math argues that KC should have gone for 2 before the onside kick. It is very correct. Yet, with the single exception of Brian Billick one time in 2001, coaches apparently always make the wrong choice.

The question may be paraphrased as:

• If a team is down 14 points and
• If the team scores a TD and
  
• If it is safe to assume that the only additional scores before OT will be another TD by that team plus any conversions,
• Then should the team immediately go for 2?

And in obvious onside kick situations, the assumption is indeed safe, because there are only two possibilities with probabilities high enough to consider:

A. The team fails to score the second TD.
B. The team succeeds in scoring the second TD.

Since in case A the decision is irrelevant, the choice can assume case B will occur.

Exercise for the reader: Spell that out in the notation of conditional probabilities.

OK.
Let K be the probability of kicking an extra point. You may approximate it as 1.0.
Let T be the probability of succeeding on a 2-point try. You may approximate it as 0.5.
Let O be the probability of winning in overtime if things get that far. You may approximate it as 0.5

Strategy 1: Kick after both TDs.
Then the "probability" of winning is K * K * O, which is ~= to 0.5

Strategy 2: Kick after the first TD; go for 2 after the second.
The the "probability" of winning is K * T, which is ~= 0.5

Strategy 3: Go for 2 after the first TD; if you succeed kick after the second, but if you fail go for 2 again.
Then the "probability" of winning is T * K + (1 - T) * T * O, which is ~= 0.5 + 0.25 = 0.75 Edit: Actually, 0.625, with my error demonstrating that this stuff isn't totally easy.

That's a huge difference.

I put "probability" in quotes because it's actually the probability conditional on getting the second TD.

I posted something very similar to this last year, a scenario where a team is down 15 points in the second half and scores a TD. I also argued, in a less stat-based way than you, that it is better to know how many possessions/scores will be needed as the trailing team can adjust their strategy, whereas the leading team has fewer strategic options. So, going for 2 as soon as possible is the correct call.

I can't recall which game it was last weekend, but the team was down 15 and kicked the extra point, with the broadcaster applauding the decision and reasoning "You just CAN'T for for two because what it you miss it?" As if it's better to miss the tying 2-point conversion with no time left on the clock!

Fencer said:

Let K be the probability of kicking an extra point. You may approximate it as 1.0.
Let T be the probability of succeeding on a 2-point try. You may approximate it as 0.5.
Let O be the probability of winning in overtime if things get that far. You may approximate it as 0.5

Click to expand...

Why may I do this?

Yeah, I dunno. It's over my head a bit, but I think Ernie Adams and Bill Belichick would be all over these scenarios, and I've never once seen us go for 2 when down 14 points.

Had Andy Reid not kicked the extra point and NOT made the 2 point attempt, he'd not only be making the ensuing possession more difficult (if it came to that), he'd also be taking away any momentum his team had after making it a close game. We can debate the subject matter of "momentum" and the likelihood that it has bearing on the onsides kick, but it's got to be factored in nonetheless.

I still fail to understand why you take away the "sure thing" XPA which stands at 95%, to try a much lower percentage play from the two yard line, even if you get two separate cracks at it? Either way, you need 2 touchdowns, so I'd tend to stick to the easier, high percentage kicking attempts.

Ice_Ice_Brady said:

I posted something very similar to this last year, a scenario where a team is down 15 points in the second half and scores a TD. I also argued, in a less stat-based way than you, that it is better to know how many possessions/scores will be needed as the trailing team can adjust their strategy, whereas the leading team has fewer strategic options. So, going for 2 as soon as possible is the correct call.

I can't recall which game it was last weekend, but the team was down 15 and kicked the extra point, with the broadcaster applauding the decision and reasoning "You just CAN'T for for two because what it you miss it?" As if it's better to miss the tying 2-point conversion with no time left on the clock!

Click to expand...

I think it has more to do with the mental aspects. If you don't make it, your team's morale may drop as scoring twice is going to be impossible in most situations. It also takes the pressure off the other team.

Unless you're Andy Reid, you should be hurrying up to score anyways down multiple scores. Not sure how much more you could hurry it up knowing you needed that additional score.

If you knew you needed a TD and a FG to make up for that 2-point conversion miss earlier, you could kick the long-range FG first, then save time for the hail mary vs. eating up all the clock on the TD drive, then not having as much time to get into FG range. But I don't think that difference is that significant since you don't need as many yards for that FG. The more concerning thing would be the consumption of timeouts on the TD drive leaving you with none for that last extra drive.

supafly said:

Yeah, I dunno. It's over my head a bit, but I think Ernie Adams and Bill Belichick would be all over these scenarios, and I've never once seen us go for 2 when down 14 points.

Had Andy Reid not kicked the extra point and NOT made the 2 point attempt, he'd not only be making the ensuing possession more difficult (if it came to that), he'd also be taking away any momentum his team had after making it a close game. We can debate the subject matter of "momentum" and the likelihood that it has bearing on the onsides kick, but it's got to be factored in nonetheless.

I still fail to understand why you take away the "sure thing" XPA which stands at 95%, to try a much lower percentage play from the two yard line, even if you get two separate cracks at it? Either way, you need 2 touchdowns, so I'd tend to stick to the easier, high percentage kicking attempts.

Click to expand...

I think it depends on objective. Are you aiming to tie, or aiming to win?

If you hit that first 2-point conversion, your chances of winning go up. Score again and you kick the XP to go up 1. If you miss, you can potentially make it up. Over the course of 100 games like this, you would win more games with this strategy.

But that means there are also games where you will fail on both and lose. Over 100 games, it is the better strategy, but the minute you lost the game because of it, everyone would rip you apart for it.

Interestingly enough, the last time anyone can recall a coach being down 14 and going for 2 to close the gap to 6 was...the 1994 Cleveland Browns, who were down 14 to the Broncos and scored a TD and 2-point conversion to close the gap to 6. They lost when the Broncos scored another TD. That team was coached by...Bill Belichick.

Cleveland Browns at Denver Broncos - October 30th, 1994 | Pro-Football-Reference.com

supafly said:

I still fail to understand why you take away the "sure thing" XPA which stands at 95%, to try a much lower percentage play from the two yard line, even if you get two separate cracks at it? Either way, you need 2 touchdowns, so I'd tend to stick to the easier, high percentage kicking attempts.

Click to expand...

Because you get very valuable information from the first try, which lets you optimize what to do after the 2nd TD.

If you had to decide what you'd do on the second TD before knowing whether the first attempt worked, the right choice would be to kick both times. But you don't have to decide until after you know whether the first attempt succeeded.

I think Silver is wrong that this is middle school math. Conditional probabilities confuse people.

I actually got to grad school without knowing what they were, although that was decades ago. I wound up overcompensating, and wrote my thesis in a probability-related subject.

supafly said:

I still fail to understand why you take away the "sure thing" XPA which stands at 95%, to try a much lower percentage play from the two yard line, even if you get two separate cracks at it? Either way, you need 2 touchdowns, so I'd tend to stick to the easier, high percentage kicking attempts.

Click to expand...

Because you're making the all-too-common error of believing that postponing the moment of certain loss as long as possible is the same thing as maximizing the likelihood of victory. It isn't.

Fencer said:

NFL Coaches Are Getting Away With Crimes Against Middle-School Math argues that KC should have gone for 2 before the onside kick. It is very correct. Yet, with the single exception of Brian Billick one time in 2001, coaches apparently always make the wrong choice.

The question may be paraphrased as:

• If a team is down 14 points and
• If the team scores a TD and
  
• If it is safe to assume that the only additional scores before OT will be another TD by that team plus any conversions,
• Then should the team immediately go for 2?

And in obvious onside kick situations, the assumption is indeed safe, because there are only two possibilities with probabilities high enough to consider:

A. The team fails to score the second TD.
B. The team succeeds in scoring the second TD.

Since in case A the decision is irrelevant, the choice can assume case B will occur.

Exercise for the reader: Spell that out in the notation of conditional probabilities.

OK.
Let K be the probability of kicking an extra point. You may approximate it as 1.0.
Let T be the probability of succeeding on a 2-point try. You may approximate it as 0.5.
Let O be the probability of winning in overtime if things get that far. You may approximate it as 0.5

Strategy 1: Kick after both TDs.
Then the "probability" of winning is K * K * O, which is ~= to 0.5

Strategy 2: Kick after the first TD; go for 2 after the second.
The the "probability" of winning is K * T, which is ~= 0.5

Strategy 3: Go for 2 after the first TD; if you succeed kick after the second, but if you fail go for 2 again.
Then the "probability" of winning is T * K + (1 - T) * T * O, which is ~= 0.5 + 0.25 = 0.75

That's a huge difference.

I put "probability" in quotes because it's actually the probability conditional on getting the second TD.

Click to expand...

Uhhhh...none of this is gonna be on the final, right?

This is a crime against freshman stats. It assumes the observed probability is the population probability. Given the low sample size of observable 2 point attempts, you're looking at a 95% confidence interval with a wide range, let's say 10 percentage points. So we can be 95% certain the real probability of converting a 2 point attempt, all else held equal, is between 40% and 60%. There's no reason to believe it's 50% and not 42% for instance, and that uncertainty (even with all else held equal) is enough to render this a questionable decision.

Moreover, context of a decision is important. You wouldn't go for it on 4th and 2 from your own 40 to ice the game against Ryan Mallett like you would against Peyton Manning. This is a case where mathematical smoothing can only get you to a point.

538 sucks and I'm surprised it still exists.

supafly said:

Yeah, I dunno. It's over my head a bit, but I think Ernie Adams and Bill Belichick would be all over these scenarios, and I've never once seen us go for 2 when down 14 points.

Click to expand...

In instances like these I wouldn't expect Belichick to be the trend setter, after all, we don't have a lot of experience being down 14 points late in the fourth quarter.

primetime said:

This is a crime against freshman stats. It assumes the observed probability is the population probability. Given the low sample size of observable 2 point attempts, you're looking at a 95% confidence interval with a wide range, let's say 10 percentage points. So we can be 95% certain the real probability of converting a 2 point attempt, all else held equal, is between 40% and 60%. There's no reason to believe it's 50% and not 42% for instance, and that uncertainty (even with all else held equal) is enough to render this a questionable decision.

Moreover, context of a decision is important. You wouldn't go for it on 4th and 2 from your own 40 to ice the game against Ryan Mallett like you would against Peyton Manning. This is a case where mathematical smoothing can only get you to a point.

538 sucks and I'm surprised it still exists.

Click to expand...

You're a smart motha-****a.

QuantumMechanic said:

Because you're making the all-too-common error of believing that postponing the moment of certain loss as long as possible is the same thing as maximizing the likelihood of victory. It isn't.

Click to expand...

This is a huge and important point. The psychological pull to "still be in it" is so strong it can be hard to accept that it's not always rational. But...

primetime said:

Moreover, context of a decision is important. You wouldn't go for it on 4th and 2 from your own 40 to ice the game against Ryan Mallett like you would against Peyton Manning.

Click to expand...

And lots more. E.g....

- Is the probability of converting a 2nd 2-point attempt the same as the first? Maybe you've already shown your best deceptive formation, etc.

- Is the overtime probability really 50-50? If you're storming back from a huge deficit, couldn't that mean that you have established an advantage over your opponent -- perhaps your hurry-up has worn out their defense, or they've lost key players to injury, etc.

- In the regular season, what is the value of a tie? In some cases a tie can secure you a playoff spot, making OT somewhat more desirable.

I think the math is skewed on this issue because teams only go for 2 when going for 1 doesn't get them anywhere. If more teams went for 2 all the time, no matter what the situation, then the probability of success, IMO, would go down. Then it would not look like such a hot option.

brdmaverick said:

In instances like these I wouldn't expect Belichick to be the trend setter, after all, we don't have a lot of experience being down 14 points late in the fourth quarter.

Click to expand...

It's not exclusive to the 4th quarter, however. The situation applies no matter what, and as another poster pointed out, no one has done it in 22 years when down 14 points.

QuantumMechanic said:

Because you're making the all-too-common error of believing that postponing the moment of certain loss as long as possible is the same thing as maximizing the likelihood of victory. It isn't.

Click to expand...

Why are you "postponing the moment of certain loss" when you need to score 2 touchdowns nonetheless?

If you're argument is simply to go for 2 every time, we already knew that, even though no one ever does. Under the suggested scenario however, I fail to see how 2 low percentage plays are better than 2 high ones, especially if you're trying to come back from 14 down.

This thread reminds me of the time in 2002 when the Pats played KC and won it in OT. At that time I was an AOLe and argued that when KC had scored a TD at the end of regulation to make it 38-37, that they would have been better off going for two and the win right then and there. During that game KC had been running right through the Pats (221 yards and 6.5 ypc) and the odds were better than 50-50 that they would have won the game if they went for the two. Instead they went for the tie, lost the coin flip and the game 41-38. I was very relieved when they went for the tie. Was I wrong then?

Fencer said:

Because you get very valuable information from the first try, which lets you optimize what to do after the 2nd TD.

Click to expand...

I understand the idea, I just don't see how failing to score the 2 pointer and being down 8 instead of only 7 allows you to "optimize" what you do after the 2nd TD.

It forces you to need to score a touchdown AND a 2 point attempt, which means that as soon as you miss the first attempt your chances of tying/winning go down dramatically.

Going for two isn't as easy as it used to be, so it's wrong to do it in the down 14 situation.

Anyone notice the one of the few times someone did the right thing, mentioned in the article, was Belichick with the Browns?