Why KC should have gone for 2 and all that

I did really well on my math SATs, but the logic of this is beyond me.

supafly said:

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.

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Here's the key: The kicking scenario is NOT just 2 high percentage plays. It's 2 high percentage plays times the odds of winning in overtime.

If you convert the low percentage plays it's over, you've won.

EDIT: or to put it another way, you're not "trying to come back from 14 down." The comeback itself has no value, the goal is to win the game.

patchick said:

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.

- 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.

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PatsDeb said:

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.

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For a male Pats fan, hearing two gals talk football stats like this is a little like some unexpected...



...dirty talking.

patchick said:

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...



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.

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Yup, the sample probability we see is, in fact, itself skewed by the fact that observable 2-point conversions are situational. Pulled out of that situational context, we can't even be certain that this probability holds.

Math is helpful but it's not everything. There's also a tendency towards risk-aversion, which is sensible. A coach that goes for 2 in the playoffs and loses is much more likely to get fired than a coach that plays for overtime and still loses. The first is considered a maverick move (like 4th-and-2), even if we assume mathematical probability is even or better, and only a coach with adamantine job security like Belichick could fail and not suffer any ill consequences.

I totally agree that this is a much more context-dependent thing than the 538 article makes it seem (and that's not even counting the off-the-field context of the coach being crucified by an ignorant media).

So I agree with @primetime that the specifics of the situation absolutely can easily mean not going for it.

However, outside of this, the mistaken belief that maximum deferral of point of certain loss is equal to maximizing chance of victory is still widespread and causes plenty of other scenarios to be misplayed.

Ive never seen NFL HCs do that.

If the Pats were down by 14, Brady would try to drive for the TD/6 and BB would kick the PAT/1. Going for 2 doesn't change the fact that you still need another TD/6. This type of thinking would play right into the teams hands like the Patriots who emphasize excelling in redzone defense where there less room to operate for the offense.

Think of how a HC would get roasted for missing the 2 point conversion TWICE and losing the game where kicking the PATs would have at least tied.

The 538 math is a useful tool to consider. Coaches shouldn't underestimate it's utility by saying that the actual probability is dependent on other factors. That's a truism and not particularly useful. The math obviously should not be the deciding factor, but it raises some important questions and allows a coach to think strategically, rather than relying on habit. If a coach knows the base probabilities, he can make a more informed judgment based on specifics.

For example, while the probability of winning in overtime is close to 50% (disregarding for now the home/away distinction that 538 uses), there is a higher probability that the team that gets the ball first wins (~54% under the current OT rules). In a high-scoring game where defenses aren't making stops (like 1960Pats' case of the 2002 KC game), the probability of the team winning the toss winning the game would go up significantly. In that case, the value of going for two is far higher than that shown by the math, and it should be a no-brainer, provided you have some good 2-pt conversion plays. Otherwise, you give-up your advantage of having the ball in your hands to win it now and hope the coin toss to puts the ball in your hands to win it later.)

Honestly I'd like to see more teams go for two. There are so many situations where going for two makes sense and the coach doesn't do it

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Triumph said:

Ive never seen NFL HCs do that.

If the Pats were down by 14, Brady would try to drive for the TD/6 and BB would kick the PAT/1. Going for 2 doesn't change the fact that you still need another TD/6. This type of thinking would play right into the teams hands like the Patriots who emphasize excelling in redzone defense where there less room to operate for the offense.

Think of how a HC would get roasted for missing the 2 point conversion TWICE and losing the game where kicking the PATs would have at least tied.

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Who cares if you get roasted? The object is to win, not to prevent talk radio from having a big day. Most head coaches play scared when the game is on the line and they are in the spotlight. That's the point of the analysis: to show that there is a better way. I'm not sure I buy the GB case, as he's getting a little fancy to show more than a nominal difference, but the KC case is pretty strong - at least as a base case. As you say, if you are playing a strong red zone/goal line defense, your decision could change dramatically.

One thing that Brian Burke used to do before getting bought-out by ESPN is calculate break-even probabilities for certain situations. This is done by back-calculating the probability of success for the 2-pt conversion, holding all other variables constant (in this case, e.g., overtime win probability, XP success probability) to figure out what probability of success you would need on your 2pt conversion to break even. If you feel your probability better than that, you go for it. If not, you don't. This is probably a much more useful tool for a coach than simply calculating expected win probability for a decision. I'd think Ernie Adams would be all over this..

patchick said:

Here's the key: The kicking scenario is NOT just 2 high percentage plays. It's 2 high percentage plays times the odds of winning in overtime.

If you convert the low percentage plays it's over, you've won.

EDIT: or to put it another way, you're not "trying to come back from 14 down." The comeback itself has no value, the goal is to win the game.

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Then like I said before, coaches should just go for 2 on every attempt.

Here's my 2 cents:

I see that OP was aware of the fact that kicking is not automatic ,two-point conversion is not really 50/50 and overtime is not really 50/50. But I agree as a simple mathematical model in middle school, you may assume 1 and 0.5 as probabilities for kick and 2-pt conversion respectively. However ,strategy 3: 0.5*1 + 0.5*0.5*0.5 =0.625.

supafly said:

Then like I said before, coaches should just go for 2 on every attempt.

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I'm not sure that follows. Early in the game, exact point differentials aren't terribly meaningful because there's vast uncertainty about the scoring to come. The logical strategy in that situation is simply to maximize the expected value of each play -- e.g. kicking a field goal on 4th & goal at the 20-yard line, even if you're down by 7. Late in the game the scenarios narrow and the point differential becomes more germane.

supafly said:

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.

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You're confusing posts that are talking about 15 point deficits for ones that are discussing 14 point deficits. Both QM and Fencer's comments (the ones you quoted) are referring to 15 point deficits and that it is more useful to know after the first TD whether the 2pt attempt will fail.

pencilneckgeek said:

Who cares if you get roasted? The object is to win, not to prevent talk radio from having a big day. Most head coaches play scared when the game is on the line and they are in the spotlight. That's the point of the analysis: to show that there is a better way. I'm not sure I buy the GB case, as he's getting a little fancy to show more than a nominal difference, but the KC case is pretty strong - at least as a base case. As you say, if you are playing a strong red zone/goal line defense, your decision could change dramatically.

One thing that Brian Burke used to do before getting bought-out by ESPN is calculate break-even probabilities for certain situations. This is done by back-calculating the probability of success for the 2-pt conversion, holding all other variables constant (in this case, e.g., overtime win probability, XP success probability) to figure out what probability of success you would need on your 2pt conversion to break even. If you feel your probability better than that, you go for it. If not, you don't. This is probably a much more useful tool for a coach than simply calculating expected win probability for a decision. I'd think Ernie Adams would be all over this..

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Because being roasted gets you fired if your last name is not Belichick or Carrol. Of course the object is to win. No sh#t.

Oswlek said:

You're confusing posts that are talking about 15 point deficits for ones that are discussing 14 point deficits. Both QM and Fencer's comments (the ones you quoted) are referring to 15 point deficits and that it is more useful to know after the first TD whether the 2pt attempt will fail.

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If true, that would explain a lot, but there's still the comments by @patchick stating that "you're not trying to come from 14 down," since the comeback itself has no value. "You're trying to win the game."

To me, that suggests that some are speaking of 14 point deficits, as does the title of the thread itself. I appreciate the clarification, though.

patchick said:

I'm not sure that follows. Early in the game, exact point differentials aren't terribly meaningful because there's vast uncertainty about the scoring to come. The logical strategy in that situation is simply to maximize the expected value of each play -- e.g. kicking a field goal on 4th & goal at the 20-yard line, even if you're down by 7. Late in the game the scenarios narrow and the point differential becomes more germane.

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I certainly trust your analysis and I admittedly did have some difficulty picking up analytical methods in grad school, but I just still have a hard time getting past what seems like common sense to me.

If I'm coaching a team down 14 points, I'm trying to score a TD and XP every time. Perhaps that is ultimately wrong.

1960Pats said:

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

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The math argues otherwise.

supafly said:

I certainly trust your analysis and I admittedly did have some difficulty picking up analytical methods in grad school, but I just still have a hard time getting past what seems like common sense to me.

If I'm coaching a team down 14 points, I'm trying to score a TD and XP every time. Perhaps that is ultimately wrong.

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You and every other coach except Brian Billick.

And you're all doing it wrong.

supafly said:

Then like I said before, coaches should just go for 2 on every attempt.

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No.

In cases where it benefits you much more than it benefits the other team to know whether you succeeded or failed, you should go for it. "Down 14 with little time left and having just scored a TD" is one of those cases, as explained in this thread.

This is a case of "creating" information that then has great value.

supafly said:

I certainly trust your analysis and I admittedly did have some difficulty picking up analytical methods in grad school, but I just still have a hard time getting past what seems like common sense to me.

If I'm coaching a team down 14 points, I'm trying to score a TD and XP every time. Perhaps that is ultimately wrong.

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I think the simplest way to sum this up is that when you go for 2 first, you give yourself a chance to win the game in regulation. When you don't go for 2 first, you only give yourself a chance to tie the game.

Think about it in terms of 100 games where you're down 14 and you're sure you will score two TDs.

Obviously the success rates are based on various factors and we can argue whether it's 40% or 55% or whatever. And real-game scenarios present other factors as well.

But understanding probability is helpful in decision making. It doesn't have to be the single greatest determinant, but a part of that equation. And that part of the equation strongly suggests that you'll win more than you lose by going for 2.

Real world assumptions below.

- 47% success rate on 2-point conversions (this is the success rate of the past 5 years of 2-point conversion attempts)
- 94% extra point success rate (this year's success rate from the new FG range)
- 50% overtime win. Different models project win percentage based on receiving vs. kicking off and whatnot, but first you have to win the coin flip.

In 100 games going for 2 first, that means:

- 47 times you get it. That means on your next score, you can kick the XP to win the game. Of course 6% of extra points miss, so on 47 conversions, you can expect 44 wins, 3 ties.

- 53 times you won't get it. So you go for it again, and 47% of those times, you get it forcing OT. That's 25 times you will convert and tie the game.

Combine that with the 3 ties above and you get 28 overtime games. 50% based on the coin flip = 14 wins and 14 losses in OT.

- 28 times, you lose because you missed both 2-point attempts.

That gives you:

- 44 wins in regulation
- 14 wins in overtime
- 14 losses in overtime
- 28 losses in regulation

Add it all up and it is:

58 wins vs. 42 losses

Now go the XP first route.

- 94% of the time, you will get that XP, or 94 games. Out of those 94 successes, you will succeed on the follow-up kick 94% of the time, or 88 games where you hit both. That doesn't win you anything though, just forces OT. Using our 50% assumption, 44 wins in OT, 44 losses in OT.

- Of the 6% of the time you fail the first time, you could pick up the 2-point conversion to force OT. Let's say that is 3 of the 6, but you will lose half those games in OT, or 1.5 games.

That gives you:

- 45.5 wins in OT
- 45.5 losses in OT
- 3 losses from missing the XP and 2-point conversion
- 6 losses from missing the second XP

Add it up and that's:

45.5 wins vs. 54.5 losses

Again, the difference is in the first scenario, you give yourself more chances to win the game outright even before OT. In the second scenario, you give yourself 0 chances to win the game outright before OT. The difference can be 12 to 13 wins over 100 games.

I think most opponents take issue with the 47% conversion rate. It's hard to be really certain because of the small sample sizes, but 5 years of data is pretty decent. We could use 3rd/4th and short data (1-3) which isn't perfect either because there's often more space than the goal line to work with, although if anyone's interested, the Patriots converted 57% of those this year.

But whatever that number may or may not be, this strategy still makes sense so long as you think it's above 36%. 36% means:

- 34 wins in regulation
- 11.5 wins in overtime

45.5 wins, just like the XP scenario. So if you think the 2-point conversion rate is above 36%, then it makes sense to go for 2 first.