The Two Point Conversion When Eight Down

[David Sklansky]

I've written about this before and I'm sure I am not the only one who has thought of it. But I felt it was important to bring it up with this group because so many people have a hard time fully grasping that serious decision making errors are made by mathematical illiterate "experts" regardless of the amount of experience they have. This most often occurs when the situation doesn't arise often enough for mere observation to be a reliable guide. Sometimes you just have to do the math. (I can hear some of you saying that if the situation rarely comes up, who cares. But what about if many different types of situations requiring math come up?)

The particular example I use here occurs when your football team scores a touchdown in the final minutes of the game when down by 14 points. Aside from extreme circumstances they should now go for two. (And then two again if they miss and score later.)

The math that proves this is amazingly easy and I will get back to that in a minute. But first I want to discuss the often stated objection that a coach might use. Namely "you haven't taken into account the psychological deflation a failed attempt will cause". My reply is twofold. First I do not for a minute believe this to be true. Players know the overall strategy which includes a miss now and a success later. To think that a miss psychologically deflates players to the point where it makes up for a fairly significant increase in the theoretical chances of winning doesn't seem right. I can't prove that though.

But the bigger problem with the coaches statement is that it was a RATIONALIZATION after the fact. If it was said by someone who understood the math and legitimately felt it should be rejected, fine. But this kind of thing is usually said by coaches AND ALL SORTS OF SUPPOSED EXEPERTS IN MYRIAD FIELDS to defend their stupidity. They didn't have any idea that theoretically the two point conversion or any of the myriad of mathematically based conclusions experts in other fields are unaware of, is the right decision. So they scramble to justify their ignorance. (Another weak excuse is that "my owner would fire me because he doesn't know the math". So spend three minutes explaining it to him.)

I changed my mind about doing the calculation. Anybody on this forum who can't do it should be ashamed of themselves.
Assume a two point attempt is 42%, a one point attempt is 98%, overtime is a 50-50 proposition, and there is time for one more score at best.

[El Diablo]

David,

"I changed my mind about doing the calculation. Anybody on this forum who can't do it should be ashamed of themselves.
Assume a two point attempt is 42%, a one point attempt is 98%, overtime is a 50-50 proposition, and there is time for one more score at best."

One point way, you win 48% of the time.

Two point way, you outright win 18% of the time pre-OT.
you go to OT 48% and win 24% of the time
you lose outright in reg 34%

Which says go for one point.

OK, it's late, so for your amusement I'll post this here and come back in the morning to laugh with you all at whatever trivial math error I made and be ashamed as you've instructed.

[Dementia]

David,

I don't think this applies for every team. What if they've been dominated up front all day and aren't controlling the line of scrimmage as they should be? If they can move the ball down the field and score at the 2:00 mark, they ought to just go ahead and take the FG - it's still a 1 possession game. Would your opinion change if the team had no timeouts and would be forced to attempt an onside kick? It would sure suck to drive the ball down the field again only to fail to complete another two pt conversion.

Even if the math justifies these slightly unorthodox playcallings, there is a danger in slipping too far into the "Mike Martz" syndrom where instead of pounding the ball up the middle on 4th & short you try some overly sophisticated double reverse and it ends up backfiring. There is more leeway for trickier play in defensive schemes imo, when the game is at a critical junction even if you have some minute mathematical edge you're better off not risking it and executing the simple & proven play.

Assuming you will make it into the endzone twice, going for it sends the wrong message to your team whom you are supposed to have faith in to either drive the ball in OT or make a big defensive stop, not to mention the heat that will undoubtedly be put on you from the GM, fans, and likely your players during the week should your brilliant idea spit in your face.

Btw on the subject of NFL, did you miss my question in the other ask me forum?

[El Diablo]

David,

Oh, nm, haha.

If they score 8 the first time, they don't go for 8 again, they go for 7.

[pete fabrizio]

I feel stupid for not having noticed this myself.

[kdotsky]

Are the numbers you gave somewhat accurate? If they are, I'm surprised that the differences in expectation of winning are that significant.

You could also argue that the fact that you're down 14 at this point is evidence that your chances of winning in overtime is more likely to be less than 50%.

[Alex/Mugaaz]

I think what you are trying to teach here could be accomplished more effectively by showing those who find this difficult the methods you can use to simplify problems with multiple parts. Even if they figure this out using one of those methods they won't draw those connections. People aren't going to magically become smarter, but maybe they can be less stupid.

[shemp]

My impression is that nearly every coach would go by a card that factors in losing on the road 60% in the case where they truly believed they had exactly one more posession possible via on-side kick-- so your question is a few years old.

[David Sklansky]

[ QUOTE ]
My impression is that nearly every coach would go by a card that factors in losing on the road 60% in the case where they truly believed they had exactly one more posession possible via on-side kick-- so your question is a few years old.

[/ QUOTE ]

Huh?

[PairTheBoard]

You might want to choose an example where the result doesn't depend so closely on your assumed percentages.

To simplify the calculation, assume the extra point conversion is made 100% of the time. Let x be the fraction of the time that a two point conversion is made. If another touchdown is not scored the question is moot. So assuming another touchdown, if the two point conversion is tried on the first (and second if you miss) you win if you convert the first or convert the second and then win in overtime. ie.

x + (x)(1-x)(.5)

If you kick two conversions you win in overtime .5. So the question is, for what values of x is

x + x(1-x)(.5) > .5 ?

x + .5x - .5x^2 > .5

3x - x^2 > 1

x^2 -3x + 1 < 0

Solving for the zeros of the quadratic,

x = [3 (+or-) Sqrt(9-4)] /2

x = .38 or 2.6

Which means that "going for two" on the first try improves your 50% chance of winning in overtime - by kicking each time - when the chance of making the two point conversion is greater than 38%. The 42% you assumed satisfies this. But if the coach thinks the chance is less than 38% he should kick-it.

PairTheBoard

(Edited to fix the first expression)