Much has been made thus far about BYU's success on 3rd and long so far this season. Specifically, on 3rd and 19 I believe they are 2/2, gaining a total of 154 yards and scoring one touchdown. I humbly suggest that they won't quite manage to keep this up over the rest of the season. (If nothing else, they might not be 80+ yards from the end zone the next time they face 3rd and 19.)
Since BYU is all but guaranteed to regress toward the mean in this area, let's look at where the mean is. In 2014, college football teams faced more than 26,000 3rd downs, virtually all of which were between 1 and 40 yards to go. (And then there is an odd clustering of data from 90 to 99 yards, which I think are errors where the spot was recorded at the wrong end of the field. It's a tiny number of downs, so I'm excluding it and not worrying about it.)
Here's how the data looks:
The blue line shows the odds of picking up the first down (or scoring a touchdown), which starts at 70% and drops pretty smoothly until it reaches 10% at about 3rd and 20. Beyond there it gets pretty noisy as the number of attempts drops. (Hint: 3rd and 39 isn't really just as easy to pick up as 3rd and 3.) The red line in the chart shows the number run where any play with a penalty is disregarded. On short distance attempts, penalties are hurting the offense on average - there are more holds and false starts than there are offside attempts. (These are primarily rushing plays.) On longer distances the penalties are helping the offense. Keep in mind, this isn't tracking 3rd down plays where there was a penalty and then the offense was successful at the subsequent attempt on 3rd down. This is where that play / penalty resulted in a first down. The key here is that there are certain penalties (pass interference, roughing the passer, face mask, personal fouls) which result in automatic first downs, and which are more likely to happen on passing plays. The chart below shows the percentage of first downs that come on plays with penalties.
As you can see, once you are beyond 3rd and 8, there are penalties on more than 10% of successful first down plays. To be sure, some of these plays would have been successful without the penalty - a 15 yard completion on 3rd and 12 with roughing the passer tacked on the end (or accepting a 15 yard penalty over a 12 yard completion). But it seems likely to me that the penalty itself is the likely mechanism much of the time. Beyond 15 yards, penalties are a part of 20% of successful conversions, and beyond about 25 yards they are almost the only way to screw things up.
One caveat to keep in mind on this is that sometimes a team isn't really trying to convert a long third down. You don't think those offensive coordinators really think the 3rd and 22 draw play is going to do work do you? Rather than take the 8% chance the a conversion is possible, they're content to try to pick up 10 yards of field position punt the ball away (or try a field goal). This is often a smart choice, depending on the game situation, but it's important to remember that these attempts are included in defining the success rate, and so the chart up there is understating the true likelihood of converting a 3rd down when you're really trying to. (If someone can help me filter the data for whether the offense is "really trying", I'd be very grateful.)
So, to get back to BYU's 3rd and long success, it isn't likely to hold up. 3rd and 19 was about a 10% deal last year in college football.
Finally, here's the number of attempts at each distance from last year, so you can understand why the data gets noisy past 25 yards or so. (Plus, how often do you get to make log plots about football?)
The chart shows spikes in attempts at distances of 10, 15, 20 and 25 yards, which makes sense with penalty distances and incomplete passes.
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