College football teams tend to improve in a new coach’s second year. But not after that.

Last week, I took a look at how my S&P+ preseason projections performed. In all, they were pretty solid as far as projections go, but there was a theme among many of the bigger misses:

Seven of the 13 biggest overachievers are led by coaches in either their second or third seasons in charge. Three others are in their fourth. Only Memphis (under Mike Norvell) was led by a first-year guy, and only ODU was led by a guy who’s been around at least six years.

In all, the 29 teams led by first-year head coaches underachieved their projected S&P+ rankings by an average of 7.2 spots. Teams with coaches in their fourth year or later were nearly dead on their projected marks (minus-2.1 spots on average).

Second- and third-year coaches, however, thrived. Fifteen second-year coaches exceeded their projected rankings by an average of 12.2 spots; sixteen third-year coaches overachieved by an average of 10.8.

One of college football’s truisms is that a program hits the gas pedal once a coach begins to have his own pieces in place. The 2016 season appears to have been living proof of that.

Is that a long-term trend, though? Yes and no. And since recent success is part of those projections, your odds of overachieving also sort of depend on how much your program has already been overachieving.

From 2011-15, teams with first-year head coaches saw their S&P+ ratings change by an average of minus-0.2 adjusted points per game from the previous year.

Teams with third-year coaches changed by an average of minus-0.1.

Fourth-year or longer: minus-0.2.

No matter how good you’ve been, you’re likely to improve in your coach’s second year. But outside of that second-year window, your fortunes depend as much on recent fortune as tenure. To some degree, everybody regresses or progresses toward the mean.

Here’s a look at how much teams tend to change from year to year (again, using adjusted points per game) based on how long their coach has been in town and how well the program has performed of late. For quality, teams are broken into four groups: teams with a three-year S&P+ average of minus-15 points or worse (equivalent to a bottom-15 performance or so), teams between zero and minus-15 points, teams between zero and plus-15 points, and teams over 15 (equivalent to top-15 or so).

For the most part, the trends are easy to spot. If your performance has been awful, you’re probably going to improve by a decent amount. If you’ve been around average, you’ll move toward zero. And if you’re a first-year coach taking over an elite program, you’re probably going to sink.

But in your second year, no matter what, you’re probably going to improve.

Out of curiosity, I added a slight adjustment to this year’s preseason projections based on tenure length, and two contradictory things happened:

So maybe this isn’t statistically significant information.

But if you’re a fan of a team with a second-year coach in 2017 — Ball State, Bowling Green, BYU, ECU, Georgia, Georgia Southern, Hawaii, Illinois, Iowa State, Maryland, Memphis, Miami, Minnesota (maybe), Missouri, North Texas, Rutgers, South Carolina, Southern Miss, Syracuse, Texas State, Toledo, Tulane, UCF, ULM, USC (gulp), UTSA, Virginia, Virginia Tech — feel free to drop a “Yeah, but second-year bump!” comment at me later this offseason. You might have stats on your side.