In both cases, missing the 2PT virtually guarantees you lose. In one case, you actually have a chance to win (go to OT) until the end. In the other case, there’s a 47% chance that you lose immediately.
The other team’s possession, where your defense has to hold, could result in a fumble and your chances to get that game-tying TD go way up. Not a huge probability, for sure, but weigh that against the chance to 1) hold the other team, 2) score a TD, 3) recover an onside kick, and 4) score a FG. That’s roughly equivalent in terms of “wishing for a miracle” as hoping the other team fumbles.
Yeah, I’m pretty sure we’ve had this discussion before :D. To me it makes no difference that you maintain a chance to win longer; it only matters whether your winning chances are greater or less at the point where you make the decision.
But you have to do all these things under your strategy too! You just don’t know it yet when you’re driving for the TD, because you haven’t missed the 2-point yet, so you can’t optimize your strategy for it.
The difference is the % chance to get the touchdown. You’re saying increase your chances from “zero” to “miracle” on the field goal at the expense of lowering the chance on the touchdown. I’m saying maximize your chance at the touchdown, because converting the 2PT conversion is your only realistic shot at winning.
In both scenarios, your maximum chance to win is less than 47%. My strategy gets you closer to 47%. In other words, a higher chance of winning.
Yes, you do :D. In the scenario under your strategy that’s comparable to the reduced-touchdown-chances scenario under my strategy, you do.
What are the chances of getting the second touchdown under your strategy? Whatever they are, call that X%. So under your strategy, you have a 0.47 * X chance of getting the second TD and the 2-point, and making OT. Under my strategy, I have a 0.47 chance of getting the 2-point, and in that case my chances of getting the second TD are the same X%, because I’m playing for a single TD just like you are. The chances of making OT are the same under both strategies. The only difference is that in my strategy I have the extra “miracle” chance when I miss the 2-point, while in your strategy when you miss the 2-point you lose.
Here is how I’m comparing the chances:
2-point strategy:
Make the 2-point (47%), score a second TD with a single, final drive (X%), go to OT.
Miss the 2-point (53%), get the miracle TD + FG to win (miracle %)
1-point strategy:
Score a second TD with a single, final drive (X%), make the 2-point (47%), go to OT.
Score a second TD with a single, final drive (X%), miss the 2-point (53%), lose.
The 2-point-first strategy gets you (.47 * X) chance of making OT, plus (.53 * miracle) chance of winning in regulation.
The 1-point-first strategy gets you (.47 * X) chance of making OT, plus zero chance of winning in regulation.
(Of course there are details: the chances of your loss aren’t exactly zero, you might miss an XP, etc., but this is the essence of the argument)