Why KC should have gone for 2 and all that

[primetime]

That's not the way probability works, though. Observed probabilities are a sample, and a sample based on a basket of situations which is in no way representative of the entire host of situations. So we need to have a confidence interval, and we can only be certain that the true probability falls within a certain range. With as limited a sample as 2 point conversions are, it's a wide interval that's only mathematically usable in a certain context (since the sample itself contains very few instances, say, where it's a second 2 point attempt in a given game).

That 47% isn't a certain number, despite the seeming belief that it is since it is based on observation. It's a number that represents a center of an interval in which we can be reasonably certain that the real probability lies, with the real probability here representing only cases where all else such as quarterback and offense is held equal under a normal range of assumptions.

I'm not arguing that the conclusion is wrong, by the way, just pointing out that it not as straightforward as multiplying simple probabilities by other simple probabilities.

 

[Fencer]

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.

Actually, even at the low end of your broad range, the decision to go for 2 is correct.

That said, there are lots of reasons not to rely on the apparent probability from the sample, the simplest being that the trials were by other teams than your own. Using obvious proxies is also likely to lead to an overestimate, because the chance of a conversion SHOULD be less than the probability of getting equivalent yardage in almost any other scenario.

(Why should it? Because in the conversion scenario the defense can load up on exactly one thing, while in most other scenarios they also have other concerns. For example, on third and short at midfield you worry about a big TD play as well as the first down. Also, you worry about a play that comes 3 inches short of a first down, because that will lead to a conversion on the subsequent QB sneak.)

So my approach to the analysis would be to:

• Compare 2-pt conversion success rates to a larger sample of similar plays and their success.
• Look at my own similar plays and their rate of success.
• Estimate the chance of succeeding with the conversion based on the previous two parts.

And when all that is done, I expect the answer would be 40%+, in which case "Go for 2" is the correct decision.

 

[Fencer]

That's not the way probability works, though. Observed probabilities are a sample, and a sample based on a basket of situations which is in no way representative of the entire host of situations. So we need to have a confidence interval, and we can only be certain that the true probability falls within a certain range. With as limited a sample as 2 point conversions are, it's a wide interval that's only mathematically usable in a certain context (since the sample itself contains very few instances, say, where it's a second 2 point attempt in a given game).

That 47% isn't a certain number, despite the seeming belief that it is since it is based on observation. It's a number that represents a center of an interval in which we can be reasonably certain that the real probability lies, with the real probability here representing only cases where all else such as quarterback and offense is held equal under a normal range of assumptions.

I'm not arguing that the conclusion is wrong, by the way, just pointing out that it not as straightforward as multiplying simple probabilities by other simple probabilities.

And if you use the sample to derive a distribution for the possible "true probability", then calculate the appropriate integral to estimate the probability of success for a particular strategy -- how different from the naive calculation will the answer actually be?

 

[ThatllMoveTheChains!!!]

It comes down to one thing, do you think you're the better team? If you do you think you have a much better chance in OT. If you don't then the high risk high reward strategy makes sense.

 

[supafly]

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.

That's one hell of a decent explanation. Thank you for the post.

 

[pencilneckgeek]

Because being roasted gets you fired if your last name is not Belichick or Carrol.

Exactly. And I view this as a competitive advantage. Bill has luxury of being able to go for it on 4th and 2 and make other unorthodox decisions that could get him pilloried but give him a better chance of winning.

 

[1960Pats]

The math argues otherwise.

What math is that? I didn't look it up but it seems to me that going for two is more difficult now than it was in 2002. I could be wrong though. It wouldn't be the first or last time.

 

[pencilneckgeek]

That's not the way probability works, though. Observed probabilities are a sample, and a sample based on a basket of situations which is in no way representative of the entire host of situations. So we need to have a confidence interval, and we can only be certain that the true probability falls within a certain range. With as limited a sample as 2 point conversions are, it's a wide interval that's only mathematically usable in a certain context (since the sample itself contains very few instances, say, where it's a second 2 point attempt in a given game).

That 47% isn't a certain number, despite the seeming belief that it is since it is based on observation. It's a number that represents a center of an interval in which we can be reasonably certain that the real probability lies, with the real probability here representing only cases where all else such as quarterback and offense is held equal under a normal range of assumptions.

I'm not arguing that the conclusion is wrong, by the way, just pointing out that it not as straightforward as multiplying simple probabilities by other simple probabilities.

That's generally true, but meaningless in the sense that the data you seek do not exist. The fact is that the observed data is not just a sample, but is the full population in existance. Of course, that doesn't mean that the true probability of success is revealed by the data, but it does mean that the math is as simple as multiplying the probabilities by each other. The trick comes from determining what are the relevant data, and that is far from simple.

My belief is that if you gave Matty P some whiz kid (say a former Caltech QB) the job of breaking down the data, the Pats could earn a further competitive advantage by having a dataset that tells them things like the probability of winning in overtime for the team that tied it at the end of regulation, or the probability of a 2-point conversion when the game is on the line or when it's the second 2pt attempt if the game. There are a lot of situations where knowing how football outcomes trend to occur can be useful information. Nobody can know the true probability, but if a HC knows the tendencies accurately, he can make more informed decisions (assuming he has a brain that works that way).

 

[PATSYLICIOUS]

I do this in madden all the time, and probably would in real life. Anyone know the actual conversion rate of 2 point conversions?

 

[Fencer]

What math is that?

The math in this thread, for example in the article I linked to start it, or in my own posts.

 

[Fencer]

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.

Is your point that teams pull out super-duper great plays that they've been saving all season for just the right moment?

Even if it is, that doesn't speak hard against the argument in this thread, because we're still talking about a rare occurrence.

 

[Fencer]

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.

My post was about a 14-point deficit.

The correct strategy is to try for 15, doing the riskier part early. A big reason why it's correct is that if you fail, you still have a chance to get 14 anyway.

 

[Fencer]

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.

Yikes!

Fixed.

 

[convertedpatsfan]

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.

Is that you Herm?

 

[primetime]

And if you use the sample to derive a distribution for the possible "true probability", then calculate the appropriate integral to estimate the probability of success for a particular strategy -- how different from the naive calculation will the answer actually be?

You could run a bunch of simulations to determine something approximating a true probability in average conditions. Of course, there's still a bunch of calculations that go into this, such as how good your kicker is and such.

I tended to believe that the conclusion was correct but I'm also not willing to say that it's irrational to play for overtime, especially given the preference for risk aversion.

 

[PatsDeb]

Is your point that teams pull out super-duper great plays that they've been saving all season for just the right moment?

Even if it is, that doesn't speak hard against the argument in this thread, because we're still talking about a rare occurrence.

My point is more that the article basically says, statistically, it is better to go for two at the end of regulation and win by one (or lose by one if you miss) than to kick the extra point and play for overtime, because you are more likely to lose in overtime. However, so few teams go for two under any circumstances, let alone this one (go for 2 and either win or lose right there), the sample size is too small to reach this conclusion. I think if 50% of the teams went for 2 and 50% went for one and overtime all the time, the stats would end up even, or maybe slightly worse for the teams going for 2. But, you may be right that the super duper plays feed into the "going for 2" looking better with a small sample size. If you only call your super duper play once in a while (or even once in a season) you probably have a better chance of fooling the defense with it. Am I making any sense? Probably not. There is a reason I was an English major!

 

[convertedpatsfan]

My point is more that the article basically says, statistically, it is better to go for two at the end of regulation and win by one (or lose by one if you miss) than to kick the extra point and play for overtime, because you are more likely to lose in overtime. However, so few teams go for two under any circumstances, let alone this one (go for 2 and either win or lose right there), the sample size is too small to reach this conclusion. I think if 50% of the teams went for 2 and 50% went for one and overtime all the time, the stats would end up even, or maybe slightly worse for the teams going for 2. But, you may be right that the super duper plays feed into the "going for 2" looking better with a small sample size. If you only call your super duper play once in a while (or even once in a season) you probably have a better chance of fooling the defense with it. Am I making any sense? Probably not. There is a reason I was an English major!

What if we expanded the sample size? For example, the last 5 years have had 242 plays for 3rd or 4th down and 2 from the 2-yard line. In this instance, the conversion is worth 6 points instead of 2, so you'd imagine at least a similar value on the right play being called here.

Over the past 5 years, that conversion rate is 43.4%, a slight drop from the 47% on 2-point conversions. But that's a bit skewed too since team are more likely to throw the ball away or take a sack than risk an INT because they could then go for a FG after. On 4th down where they can't throw the ball away, it's 51.7%, but again, smaller sample size.

Even if we accept the 43.4%, that still translates to 52 wins vs. 46 on the 1-point conversion. Forget the strategy, forget the methodology, the unconventional approach, and just ask this. If the coach had a chance to increase his team's odds 5% of winning a game, shouldn't he do that?

 

[Fencer]

My point is more that the article basically says, statistically, it is better to go for two at the end of regulation and win by one (or lose by one if you miss) than to kick the extra point and play for overtime, because you are more likely to lose in overtime.

Actually, the article doesn't say that. Indeed, its main point is that it's better to be

Maybe down 6 or maybe down 8

than it is to be

Down 7


That's because in the first scenario you KNOW what the right choice is about the (second) 2-pt conversion, while in the second scenario you have to guess.

 

[supafly]

Only on patsfans.com.

Legal debates, medical expertise, scientific laws and theories, and lots and lots of boring formulas and equations!

As I've mentioned before, I highly doubt that we'd see anything like this on the Steelers or Jets fan sites.