Ignoratio Elenchi said:
SSOG said:
While it's true that a TD wins it outright whether you're down by 3 or by 4, the odds of you actually scoring a TD are significantly higher if you're down by 4.
I do't think that's the right way of looking at it. The probability of scoring a TD isn't significantly higher down by 4 than it is down by 3 - at best it's probably the same, and it might even be lower because of the way your opponent will play defense in those situations. Historically, teams down by 4 have probably scored far more TDs than teams down by 3 - because NFL coaches don't attempt winning TDs when they can kick a FG to tie. But if we're trying to figure out what gives us the best chance to win, we don't care what coaches have historically done, we only care about what we should do. So it's circular to point out the fact that coaches have
more frequently gone for a TD down by 4 than by 3, and use that to support the idea that you're
more likely to score a TD down by 4.
You *ARE* more likely to score a TD when down 4, though, simply because (like all coaches who have come before you), you're more likely to go for the TD. When down 3, coaches are content to kick the 80% field goal that, if good, gives them a 50% chance to win. When down 4, coaches are more likely to go for the 20% 4th down conversion that, if good, will give them a 50% chance to score a TD which will give them a 100% chance to win. Obviously, using those (arbitrarily assigned) percentages shows that you're more likely to win by kicking a FG when down 3 (40% chance to win) than going for it on 4th down when down 4 (10% chance to win), but that's not the point- the odds of scoring the TD when down 4 don't have to be better than the odds of winning in overtime when down 3, they just have to be enough better that, when combined with your odds of winning outright with a FG if you convert the 2pc, the EV of going for 2 outweighs the EV of going for 1.Since 2002, teams that were down by 4 with 2 minutes remaining have scored 38 TDs compared to 25 TDs by teams that were down 3 with 2 minutes remaining, despite the fact that historically 3-point deficits have been 2.27 times more common than 4-point deficits (a figure partially influenced by the fact that overtime games have such a high probability of ending in a 3-point margin, but still, it's safe to say that there have been more teams down 3 late in the 4th than down 4 late in the 4th over the last decade). Beyond that, it makes intuitive sense that it's easier to score TDs when you treat the entire field like 4-down territory than when you don't. So I do think your odds of scoring a TD to win outright in regulation are higher when you're down 4 than they are when you're down 3. Also, to inject some completely anecdotal evidence, in the past I've always felt more comfortable when my team held a 3-point lead with the opponent driving than I have when my team held a 4-6 point lead with the opponent driving, simply because I knew that the opposing team was going to be playing for overtime so my team would have two chances to beat them (by stopping them in regulation or by winning in overtime) instead of just one (albeit noticeably better) chance of beating them. But again, that's strictly anecdotal based on my experience as a fan and I'm not holding it up as proof or anything.
I do think it's possible for the numbers to work out in favor of going for 2 when down 4 with 2 minutes remaining, although I don't think that one's anywhere near as clear-cut as the situation in the OP.