so much for that
Down 14 And Going for 2
The situation: You are down 14 and probably only have 2 possessions left. Obviously, it will take two touchdowns to get back into the game. My question for you is, what combination of 2 point and 1 point conversions should you take to maximize your chance of winning the game?
Let's start off with a few assumptions. According to this rivals article, the average 2pt conversion rate in the NFL is 44%. I'll assume that it's about the same for CFB and that our team's conversion rate will be about the same in whatever specific situation we're in. We'll assume that we can estimate a PA kick as a sure thing. We'll also assume that we have a 50-50 chance of winning in OT.
So working with these assumptions, what is the optimal combination of 1pt/2pt tries?
Kicking 1pt tries only
This one is easy. Assuming we get 2 TDs to come back, taking 1pt each time will give us a 50-50 chance to win
In this situation, we get the first TD and take the 1pt. On the second TD, we 'man up' and go FTW BABY! Our chances of winning are equal to the chance of converting obviously, so 44%.
In this situation, we'll go for 2 after the first TD. If we convert, then we'll kick a 1pt try. If we do not convert, then we'll go for 2 again.
This is a slightly more complicated calculation, but here we go:
1.) 44% of the time we make the first 2pt conversion and go on to win the game.
2.) (.56)*(.56) = 31% of the time we miss both 2pt tries and lose despite making two TDs
3.) (.56)*(.44) = 25% of the time we miss the first but make the second 2pt. This ties the game and we go to overtime.
So what is our final equity? It is:
.44*1 + .31*0 + .25*(.5) = .57 or 57%
A quick explanation of this equation. We basically multiply the probability of an event by the outcome of the event. So 44% of the time we win (1), 31% of the time we lose (0) and 25% of the time we go to OT with a 50-50 shot (.5).
Now why isn't this done in the real world? Well part of it is that some of our assumptions aren't known. However, mostly it is coaches covering their ass. No one gets criticized for taking the safe route to force OT, only to lose. If you go for 2 twice and don't make it, you'll be torn apart in the press. Not to mention that football coaches don't focus much of their time on equity calculations.
The common belief of kicking 1pt to tie or going FTW! at the end with a 2pt conversion is clearly wrong, even if it is most commonly done.