Thanks for pointing this one out.

But an example of how complex math clouds a pretty simple question….

I think a prime example of how it can vary is the Broncos/Saints game from Sunday. The Broncos stopped the Saints 3 straight times inside the 3. At the time, the score of the game was 24-17 Broncos.

The Saints had 2 options on 4th and 1, kick the field goal or go for it. Kicking the field goal makes the score 24-20 heading into halftime. More on that later.

The Saints went for it and were stopped. The Broncos took over at the 1, and on the first play tried to run it out of the endzone but didn’t make it – safety for the Saints. Halftime score 24-19.

Now, for the rest of the game, the Saints were chasing that point they decided against. In the 4th quarter, the Saints were trailing 34-26 when they scred a TD. They felt obligated to go for 2 in order to tie. Had they kicked the field goal earlier, the difference would have been 1, or tied with an extra point.

The two point conversion failed, and the result was a 2-point win for the Broncos 34-32. I know this is just one example, and I’m not convinced that going for the TD in the 2nd quarter wasn’t the right thing to do. But when it comes to points, 3 is greater than 2….

the lack of time meant the value of the field position from sticking the opposing team at the one was at best severely discounted and pretty much worthless. Kicking the FG there was the better choice, but if there had been more time on the clock (so they could benefit from the field position following the turnout on downs) going for the TD would have been right.
http://www.advancednflstats.com/2008/09/paytons-gamble.html