If you have 95% of kicking the 1 and only 48% of getting the 2. Or roughly that. It would seem on face value that if you always go for 2 against a team always kicks the 1, that, like heads and tails, eventually, both teams would be tied on the same score after say 4 TDs or 10 TDs each.
But i am sure that the 48-50% isnt pure. Some teams have better weapons, some teams have days when their 3rd and short and 4th and 1 fail more than succeed.
It would make more sense to always kick the 1, and only go for 2 the times your kicker misses the pat, or times and situations in the game, when you need to get the score back to lots of 7, or behind 11, give yourself a chance to kick a FG to tie than to rely on a more difficult to score last second TD, and such
Actually 0.48+0.48 is 0.96, which is greater than 0.95. The math tells you to take the 2 and not the 1.
BUT I wouldn’t do it for a 1% increase. For a 8-10% increase, sure.
The thing about taking the 2 or not, is that it is situational and you shouldn’t always take the 2. Take the 1 BUT be ready to take the 2 when it will give you the greatest increase in winning percentage, which at 17-9, it’s one of those occasions.