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MTZehvor on 12 January 2020
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RolStoppable said:
MTZehvor said:

Assuming you're committed to a scenario where you're down 22, have to score three times and never let the other team score to win, going for 2 on the first try is exactly what you should do, because you're going to have to try a two point conversion regardless.

On the one hand, if you try the 2 point conversion on the first attempt and fail, then you at least still have a chance (albeit a small one) by getting successful conversions on the next two tries. Failing the first two point isn't an immediate death knell.

On the other, if you wait until the last touchdown to go for two and fail, then you're almost assuredly screwed. There's no way to make up those lost points, barring an onside kick or something. Failing the first (and only) two point try is a near guaranteed game over.

Whether you try sooner or later, your chances of converting a two point are the same. But if you try it early on and fail, you still have opportunities to make up for it.

When the game is already in the fourth quarter, you have to calculate with most likely only three remaining possessions anyway. You need time to get into the endzone thrice while the opponent takes time off the clock. It gets down to the wire in any case.

The maths is also simple: If you do it like I suggested, it's virtually guaranteed that the team will have an opportunity to tie the game with the third TD, because PATs have a success rate of ~98%. That helps to keep hope alive which is a crucial factor when attempting a comeback from a huge deficit. When you do it like the Ravens, you put more pressure on the team because it's required to get 8 points twice and the success rate for 2PCs sits at ~45%. Of course it works out well if you converted the initial 2PC, because then you only need 7+7 to tie the game. But this is a gamble because of the low success rate of 2PCs.

By the way, what would you do when you are 15 points down? Attempt the 2PC on the first TD or the second one? I'd hope you say the second TD because if the 2PC fails on the first TD, you are staring at a two score game.

2 score game is a different ball game, assuming you only have time for two possessions. If you fail the two point conversion, you're screwed regardless. You still need to score again.

But that aspect is why it's so crucial to go for two the first time in a three score game. If a team goes for two on the first try and misses, they can still tie the game with two more TDs. It's unlikely, but the opportunity is there. You can miss the first two point conversion and still tie the game with three scores. However, if you wait until the final TD and miss, then you need another score, and you will have needed four scores to tie the game.

Both outcomes produce the same reward from the initial two point conversion if it succeeds, so there's no reason to prefer one there. However, if the initial two point conversion fails, it's much better to have it fail at the beginning rather than the end, because you now have additional opportunities to get those points that you wouldn't have if you wait until the end and bet it all on a single two point conversion. You can think of it like a probability equation. The odds of tying the game if you go for it on the first touchdown are your chances of getting a successful two point conversion plus the odds of you getting two 2 point conversions if the first one fails. Assuming your 45% statistic is right, your odds of tying the game (assuming you can score those three TDs necessary) is .45+(.45*.45), or roughly 65%. Compare that with your odds of tying the game assuming three TDs scored with only one two point conversion, which is just the odds of converting a single two point try, i.e. 45%.

I suppose you can make an argument for hope as an important aspect, but that's a kind of percentage point drop off that seems worth the risk in hope to me.