furthermore, your "3rd/4th and shorts arent easy to make, ask the patriots" quip is not only irrelevant but kind of dumb, as the patriots did convert 3rd and 1, the refs just clearly blew the spot. even the announcers noted this. fumbles are a fluke, 9/10 times brady converts 4th and inches so yes, id say they are easy to make. in fact, someone should find pats on 4th and 1 as theyre actually one of the best at it but w/e
it was a joke, hehe. so was the next line, if anyone caught the reference.
your first point is incorrect. if they go for it and miss, the game is essentially over. not sure how much it's changed recently, but the conversion rate of a 4th-and-1 from a couple years ago inside the ten was
a shade under 70%. that means a 30% chance the game is over right then! add to that, they had only a
~70% chance of scoring a TD if they did make the 1st down (I forget the exact yard line they were on, it was something like the 5) comes to ~50% chance of scoring a TD on the possession, 30% chance of straight up failure, and 20% chance of another 4th down attempt that they'd either make or fail. yes, a 50% chance of a TD technically comes to more "net expected points" (3.5+ vs 3) than kicking, but it doesn't take into account the situation itself.
and then, you have to take into account the odds on the ensuing drive of the team scoring a TD vs the odds of the team scoring a field goal. I can't find any reliable data for it, but essentially you take the 50% chance of scoring that TD times the x% chance of scoring a field goal or a TD on the next drive, vs the % chance of kicking a field goal there (probably >95%) times the % chance of scoring a TD on the next drive.
this page suggests that the odds would then be about an 18% (.5*chance of score at 60 yards) chance of winning vs about a 20% (.95*chance for TD at 60 yards) chance of winning, but the graph doesn't look right to me so take from it what you will.
your 2nd point basically doesn't matter; the Patriots basically win with one first down (if they had gotten the 3rd down then gotten 0 yardage, Falcons would have had about a minute left after a Pats punt/missed FG/something) and certainly do with two. a field goal might have ended the game, but the game also would have ended on much less.
of course, a TD would have changed the dynamics of the game a lot; the Falcons would have kicked it deep probably, and the Patriots would likely have been more aggressive in their playcalling (how do you get more aggressive than 4th and 1? you know what I mean, haha)
it's a borderline call that's easy to look at in hindsight and say it was wrong, but you could say that about several things tonight. as you pointed out, Smith seems to make these kinds of errors fairly often, but I don't think kicking there was a mistake.
http://www.advancednflstats.com/2009/09/4th-down-study-part-4.html
in general in theory you should always go for it on 4th and 1 just about anywhere on the field...situationally you might have reasons not to, but in this case if it was indeed a 4th and 1 the falcons kicked the fg on, then they needed to go for it - you have to absolutely assume the next chance you get is just going to be worse
since you posted it while I was typing this up, a 4th and 1 from the 5-ish yardline is indeed about 3.5 expected points. while theoretically it makes it seem like the right move is to go for it, I've already explained why it might not be. if you know of any page that has expected chance at FG or TD percentage based on field position though, that'd be great.