This is ridiculous. All I hear is "Fez your wrong, I'm right".
Not a shred of mathematical assumptions to back anyone's position here! I guarantee all I've spent far more time thinking about this and analyzing it than anyone on the board.
I LOVE to start with the down 8, what do you do scenario? EVERY "expert" says, you gotta kick it. The numbers show what a horrific assumption this actually is!! The truth is you gotta go for two.
Assuming you always make the extra point, and two even teams, and you will get 1 final score at the end of the game, you obvously go OT and have a 50-50 chance to win.
If you have just a 40% chance to make a two point conversion, then obviously you now have can win by 2 scenarios (remember all analysis assumes you will get in the endzone again, otherwise nothing matters).
1. Go for two, make it (and then win with your next TD) prob= 40%.
2. Go for two, miss it (and then go for two again and make it, and then win in OT. Prob = .6 * .4 * .5= 12%
So even with very conservative 40% conversion assumption, we can see that going for two after the 1st TD gives you a 52% chance to win.........and this assumes kicking is 100% foolproof.....which we all know isn't the case.
The bottom line: THe math is crystal clear. No logical person could disagree with this. Given the go for two down 8 is so clear, surely any logical person would start sweating bullets about his preconceived notion that one should kick for 1 when down 4.
Now I agree the analysis becomes more complex when down by 4. To sum it up mathematically, your expectation when kicking is almost 1.0 points, going for two is more like .80-.90 points. So obviously, early in the game, going for two is a mistake (but not much of one, it has a trivial cost in expectation).
However, by going for two when down 8 or 4 late in the game, you will win lots of games by 1 point only, and you will never lose by just 1, therefore over the long run, your opponents will ever so slightly outscore you, but you will win more games (since you will win evey game decided by 1 point).
Getting off topic a bit, I might add that this is a VERY complicated situation when down 4. I'm fine with someone saying "Let me think about this" or "Let me run some simulations". Those saying "I'm right, that is it" I simply don't relate to. I will say the "old school" thinking is that one should never gamble. There is a feeling that one "deserves" 7 points for a TD, and one should never fool with this. The math of course says something different.
I don't know why we debate letting the opponent score when you are down 1 out of timeouts. A sharp 8 year old knows this.
A better question is what to do when tied with a 4th and 1 on the opponents 10 with 1:15 left, and the opponent with 1 timout left. The answer is to go for it, and it is not even close. Assuming the kicker is a stud, and a team makes the 1st down 60%, they will win the game around 80% of the time going for it. When kicking the 3, they win WAY less than this.
Yet 90% of the old schoolers would kick in this situation. The Virginia team faced this situation vs. Cuse and actually made the right call, and bet bashed by the media. Why? Because people HATE any play call resembling a gamble, even if it is totally justified.