Unless you're inside the 10 kicking on 3rd down isn't a good idea. Even a gain of 1 yd improves FG prob more than the chance of a bad snap.
— Brian Burke (@Adv_NFL_Stats) December 2, 2013
Admittedly, I wrote that just based on my familiarity with the relevant numbers, so I thought I'd do the legwork. FG% improves with every yard closer a team gets. Every yard matters. In fact, every yards matters to the tune of 1.6% per yard when the line of scrimmage is between the 35-yard line and the 10-yard line.
Yesterday, Keith looked at this kind of situation in the context of the CHI-MIN game, and his results suggest the same conclusion. This post will examine play outcomes on 3rd down when the game is on the line and teams are in deep FG (attempt) range, and compare them to the likelihood of a bad snap or hold.
Run plays average 4.3 yards, and pass plays average 6.3 when a team is down by 0 through 3 points in the final 3 minutes of a game and their field position is between the 35 and 25. (Those seem long to me, too--but the averages are 3.8 for runs and 4.6 for pass plays in situations under 1 minute to play.) But averages aren't everything--here are the distributions:
We also need to consider turnovers, which would typically be fatal or near-fatal. But there's not much to consider. In the last 13 seasons, there has never been a fumble lost on a 3rd down prior to a make-or-break long FG attempt, and there have only been 3 interceptions. Those 3 interceptions have come on 173 pass plays, for a 1.7% rate. Offenses are wisely protecting the ball.
A back-of-the-envelope analysis says that a run on 3rd down, which averages 4.3 yards improve the chance of making the FG by 4.3 yds * 1.6% = 6.8%. A pass on 3rd down improves the chance of making a FG by 6.3 yds * 1.6 = 9.9%. But when we consider the cost of a turnover, the benefit is cut by, say, about 2%. Ultimately, we'd be safe saying that the benefit of running a conventional scrimmage play on 3rd down improves the chances of winning by at least a net of 4%+.
What about bad snaps and holds? Unfortunately those aren't official league statistics. So how can we estimate their likelihoods? Well, extra points don't get any easier as a matter of a kicking exercise, so let's proffer that every single missed XP is the result of a bad snap or hold. Even if we do that, does the risk of a bad snap/hold outweigh the benefit of the potential yardage gain?
XPs were successful on 99.5% of all attempts in 2012 and 99.7% so far in 2013. The numbers for FGs inside the 29 are just as high. Someone with game-charted play-by-play might have a better number, but I'm confident bad snaps and bobbles occur in fewer than 1 in 200 FG attempts, or 0.5%.
Even with the most conservative of assumptions, a conventional play on 3rd down, on average, improves the chances of winning by at least 8 times greater than the risk of a bad snap or hold.
Inside the 10 yard line, things change
But what about the value of peace of mind to the snapper and holder, as @dmv726 pointed out on Twitter? I don't think there's much to that, based on what I've learned over the years. It's equally likely players focus even more is such situations. But the real evidence is that FG attempts are no less successful in clutch situations, so it's extremely unlikely snaps and holds are adversely affected by pressure. Run
Run a play on 3rd down and gain some yards. "Field goal range" is a myth. Closer is better, and the risks aren't big enough to make the difference.