26 to 21: Going for Two a Mistake?

Mathematical Modeling

We'll assume that the probability of successfully converting an extra point is p1, the probability of successfully converting a two-point attempt is p2 and the probability of winning in overtime is one-half1. Furthermore, we'll assume that the probability of your opponent scoring a subsequent touchdown is q. Our last assumption is that your opponent will attempt a two-point conversion when trailing by 8, an extra point when trailing by 7 and will lose if trailing by 9. (The assumed conversion strategy is not only the optimal one for your opponent, but in agreement with conventional coaching behavior.) Now, let's examine your chance of winning for each strategy:

Go for two: There are four ways to win the game if you go for two:

1. Convert the two-point attempt.
2. Miss the two-point conversion and prevent the opponent from scoring a touchdown.
3. Miss the two-point conversion, allow a touchdown and prevent the opponent from converting the extra point.
4. Miss the two-point conversion, allow a touchdown and subsequent extra point but win in overtime.

These outcomes are illustrated in the decision tree below:

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Assuming independence2 we can calculate the probability of each of these outcomes.

1. p2.
2. (1-p2) × (1-q).
3. (1-p2) × q × (1-p1).
4. (1-p2) × q × p1 × ½.

Similarly, there is only one possible way to lose under this scenario, and to do so, everything must go wrong. First you must fail on your own two-point conversion, then allow a game tying touchdown and extra point and then lose in overtime. The probability of all these events happening together is (1-p2) × q × p1 × ½.
Go for one: There are six ways to win the game if you kick the extra point and two ways to potentially lose.

1. Convert the extra point and prevent the opponent from scoring a touchdown.
2. Convert the extra point, allow a touchdown and prevent the opponent's two-point conversion.
3. Convert the extra point, allow a touchdown and subsequent two-point conversion but win in overtime.
4. Miss the extra point and prevent the opponent from scoring a touchdown.
5. Miss the extra point, allow a touchdown and prevent the opponent from converting the extra point.
6. Miss the extra point, allow a touchdown and subsequent extra point but win in overtime.

Assuming independence the probabilities of these outcomes are:

1. p1 × (1-q).
2. p1 × q × (1-p2).
3. p1 × q × p2 × ½.
4. (1-p1) × (1-q).
5. (1-p1) × q × (1-p1).
6. (1-p1) × q × p1 × ½.

Similarly, there are only two possible ways to lose:

1. Convert the extra point, allow a touchdown and subsequent two-point conversion and lose in overtime.
2. Miss the extra point, allow a touchdown and subsequent extra point and lose in overtime.

The associated probabilities are:

1. p1 × q × p2 × ½.
2. (1-p1) × q × p1 × ½.

Again, the potential outcomes can be organized using a decision tree:

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1. Since the teams must have been of comparable abilities to get to overtime, this assumption is not unreasonable. Another way of looking at this is that half the teams the end up in overtime win and half lose. (You'll notice that this implicitly neglects the slim possibility of a scoreless overtime resulting in a tie.)
2. Essentially, independence states that the results of one event have no influence on the results of another.

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Discussion

For either strategy, the potential ways to win (or lose) the game are mutually exclusive and collectively exhaustive3. Therefore, the probability of winning under each strategy can be determined by summing the probabilities of the various outcomes corresponding to a win. Therefore, the probability of winning is [1 - p1q(1-p2)/2] for the two-point strategy and [1 - p1q(1-p1+p2)/2] for the one-point strategy.

Based on the preceding arguments, the two-point strategy results in a higher probability of winning the game if and only if [1 - p1q(1-p2)/2] ≥ [1 - p1q(1-p1+p2)/2], or equivalently, when 2p2 ≥ p1. Assuming the probability of successfully converting an extra point is p1 = 0.96 and the probability of successfully converting a two-point attempt is p2 = 0.44, the optimal strategy is to attempt the extra point. It's clear, though, that even if the extra point was guaranteed (p1 = 1), the two-point strategy is preferable if p2 ≥ ½, since the two-point strategy results in a higher probability of winning when 2p2 ≥ p1.

So there you go... it was most definitely the right call... :wave:

 

The exact same thing happens if they block the X-point and return it for a safety. In that regard, I think the odds are greater that a kick is blocked and returned rather than picked and returned.

Either way, the right call was made and I can't believe anyone would even question it.

 

Wow

 

Yeah, I didn't even TRY to read that...

 

Well I figured it to be a good response to a dumb thread... LOL

 

I thought you had morphed into JohnLSU for a second, scary stuff.:wave:

 

:rofl: :rofl: :rofl:

 

<--- Is not smart enough to know if Kliee is pulling our leg. :shock:

 

LOL... you may have to do some research... hehe

 

I liked the call myself in going for two. It was the play call I wasn't so fond of. I would have preferred to be in the pistol with at least the thought of running scott or playaction. But that's why Miles and Crowton get paid the big bucks, and I just get to sit watching the game and have a heart attack.