Yeah, IMO this is an area where smart coaches are outsmarting themselves. In a pure hypothetical state, the math works out the way people are explaining here to favor an earlier 2-pt attempt. BUT FOOTBALL IS NOT PLAYED IN A PURE HYPOTHETICAL STATE. There are many other factors this math doesn’t account for. For instance: Not all 2-pt playcalls are created equal!
I saw this from a former player on Twitter (can’t claim I thought of it), but most teams have ONE 2-pt play that they’ve practiced and feel good about, and one or two more in their back pocket that they can pull out if needed, but that they’ve practiced less and are less confident in. That 52% success rate is across all 2-pt attempts by all teams. If you measured success rates for a single team attempting multiple 2-point tries in a game, I suspect the success rate goes down with each attempt.
Its like how the lions went forn2 in the cowboy game- they are going for the win imstead of playing for a tie in overtime. If you wish to go for win- it is smarter to go for 2 the fiest time rather than waiting for 2nd touchdown- because the chances of you missing both 2 point conversions is much lower than missing one. So if you makenthe 2 point conversion- you can then go for extra point and win next touchdown- butnif you miss 1 point convwrsion- then you still have chance to tie game on next touch down by going for 2 again.
Now lets say instead of going for 2 after first touchdown you make kick to makenitn6 point game- the mext drive you decidento go for win put miss 2 point conversion- you now are done.
Its better to go for 2 the first time because odds are greater rhat you wont miss it twice.
The odds of missing the second time are the same as the first. The two events are independent.
The other issue with conversion rate for 2 point conversion is there is a smaller n. As you get more n you would get a truer conversion percentage chance. Also many teams go for 2 now if there is a penalty moving it from 2 to 1 yard line and those have to be taken out of calculations.
Your data is off though. It is under 50%. I have cited NYT article and I will assume they are correct.
And independent events. Nothing additive about it.
Playing 1 draw of lotto tickets every drawing your chance of win stays the same.
Chance of a heads on all flips is 50%. The coin does not care if it has been flipped 2 times or 200.
Also a lot has to go into these statistics. Road vs home. Crowd noise. Etc. It is not as straightforward as an xp which rarely affected by noise. And xp attempt indoors probably has higher conversion percentage.
You have 100000000 and 95% chance of winning or
100000000 and 47.5% (lets use accurate percentage). But you have 2 chances with 47.5% which do you take?
I can ask questions also.
On independent events I take 95% unless score dictates otherwise.
One pie. Because next time I score I can also get 1 pie again. I am not done scoring. If that is my last score the also does not matter getting 2 pies when the other team has 6 more.