Gophers up 7 on Oregon State Beavers with under 2 minutes left at home; Gophers went for 2. Missed. Twitter Gopherites went crazy saying the Gophs were insane to try it. I said it had to be the far better play mathematically. Then I sat down at the kitchen table at 12:30 a.m. and realized we were both wrong.
If you assume that there is a 50-50% chance that a 2-point conversion will be made, we can do the math.
GOING FOR 2 -- You Will Win 75 times out of 100
If you go for two 100 times and make it 50% of the time, you will win the game 50 times on offense. (Up 9 under 2 minutes is virtually a certain win). You will miss 50 times. Since we are assuming that the opponent always scores exactly one TD, in those 50 times you miss we will 100% of the time be headed to OT. (There is a chance the Gophers kick and miss their PAT and there is a chance the Beavers score and kick and miss their PAT. But we will assume those wash out from a math standpoint).
You win 75% of the time (50 times you make the 2 and 25 of the 50 times you go to OT).
KICKING AND GOING UP 8 -- You will Win 75% of the time
If you kick, we will assume that is a 100% proposition (it isn't, but see above re the other team might miss a kick too), You are up 8.
When the Beavers score a TD, they now have a 50% chance of missing the 2. You will win 50 times out of 100 in regulation. On the 50 times that the Beavers make the 2, you will go to OT and win half the time. So, 25 more times.
You win 0 times on offense, 50 times by stopping the two and 25 times in OT -- you win 75 times out of 100.
VARIABLES -- OFFENSE AND DEFENSE
Now, suppose your offense just blows and will make a 2 20% of the time. And assume your defense is awesome and will allow a 2 only 20% of the time.
Going for 2 -- win 20 times out of 100 on offense, of the other 80 that you miss you are going to OT and win 40 times. 20+40 = 60 wins.
Kicking to go up 8 -- you win 0 times on offense, 80 times by stopping the 2 and 10 in OT. You should kick because you will win 90% of the time.
OFFENSE IS GREAT, DEFENSE BLOWS
Flip the scenario -- offense scores 80% on 2s and defense allows 80% on 2s.
Going for 2 -- win 80 times on offense and of the other 20 you go to OT and win 10. 90 wins.
Kicking to go up 8 -- win 0 times on offense, win 20 on stopping the two, 80 games go to OT and you win 40 of those. 20+40 = 60 wins.
If your chances of making and stopping the two are roughly the same, it will make no difference whether you go for two or kick. You will win roughly the same amount of times. If your offense is way better than your defense in that particular game, you should always go for 2. If your defense is way better than your offense in that particular game, you should kick and go up 8.
WILD CARD -- OPPOSING COACH DOWN 7 SCORES AND GOES FOR 2
Will a team down 7 after a failed 2 pointer by its opponent ever drive the length of the field and go for 2 and the win? I agree with Tracy Claeys that 99% of coaches are not doing this. But while you could lose to the Beavers in this scenario, this also permits you a backdoor way to win in regulation. You are up 7, they score and go for 2. You now have a chance to win in regulation and to lose in regulation. If your defense stops the 2 50% of the time, the chance of a bad beat or a lucky win is the same. Again - if you have a great D, you want them to go for 2 and if you have a wretched D, you want them not to go for 2.
AND KEEP IN MIND
The Win Probability calculators say there is a 97% chance you win up 8 and a 93% chance you win up 7 in under 2 minute scenarios. The biggest blame will be not in kicking or going for 2, but rather in allowing a late TD up a TD with under 2 minutes left at home. The odds say that should not happen.