A nine-yard gain is better than a first down
What's better on first-and-10: gaining 10 yards for a first down, or gaining 9 yards for second-and-1?
Brian Burke shows us that the nine-yard gain is better. That's because, effectively, it gives the offensive team a free second-down pass. If they fail to connect, they just run on third-and-1, which has a very good chance of succeeding (and so does fourth-and-1, if they fail to make it on third down).
Brian studied all first-down plays between 2000 and 2007 outside of field-goal range in the first 28 minutes of the game. From that database, he was able to figure that the difference is quite large: almost a whole point on the scoreboard.
So should teams deliberately choose to gain nine yards instead of 10? Yes, in theory. In practice, of course, it doesn’t make sense to deliberately go down at 9, because you don't know for sure that you'll be stopped at 10 – you could wind up at 16 or 17. Also, as Brian points out, coaches are risk-adverse:
" ... the first time anyone actually did it intentionally, and his team failed to convert the 1st down, the criticism would be merciless and it would never be done again."
However: what's to stop teams from doing it "kind of" deliberately and hoping nobody notices? Nothing. And the evidence does suggest that it does happen. Although gains of more yards are generally less frequent than gains of fewer yards, the drop from 9 yards to 10 is particularly steep. Furthermore, 10-yard gains are actually less frequent than 11- and 12-yard gains.
Of course, that might not have anything to do with offensive strategy. As Brian says, it could have to do with the way the referee spots the ball. Or it could be that defenses are guarding the first-down marker so well that the offense is brought down at nine yards.
So we don't know whether the offense is being smart, or the defense is unwittingly playing into the offense's (perhaps also unwitting) hands.