Bottomfeeder Sports
Footballguy
Of course. There real probability of making a two point conversion is more like 47%, and if you can run the ball it is 57%. Sure if you give up a long return such that leading team is in field goal range or better the probabilities become 3,4,5 and the available precision is such that the team up 8's 4% is better than the 3.9%. But what percentage of a time is there a 60+ yard return when the probabilities shift in your favor versus the number of kick offs that are for less than 60 yards? So yes there are places on the field where going for one was the right call, but those are unlikely places to be and the differences are smaller (because the chances of winning are decreasing across the board pretty much linearly).Okay, and if I change the assumptions, you could come to the opposite conclusion. This really isn't that difficult- there is no mathematically correct answer to the question.Oh, for actual math.
Assumptions:
45% chance of making 2 point conversion at 7:00 minute mark
Down
9 at seven minute mark, opponent has ball at 20 6% chance of winning
8 at seven minute mark, opponent has ball at 20 - 8% chance of winning
7 at seven minute mark, opponent has ball at 20 - 12% chance of winning
(Since field position is mostly linear I don't believe that changing it will change these calculations.)
.45 * .12 + .55 * .06 = 0.087
0.087 > .08
Now if the team down by 9 tries an onside kick at this point they will likely kill their chances.
Down 9 at seven minute mark, opponent has ball at your 45 - 3% chance of winning
Down 9 at seven minute mark, you have the ball at your 45 - 8% chance of winning
That the success rate will be about 20%
.80 * .03 + .20 * .08 = 0.04
So if you can find probabilities for various kickoff field positions the match could be made more complete, but the end result will not change. The team going for two sooner will have a slightly better chance of an improbable win. NFL coaches seldom go for "slightly better chances" though.