Does firing the head coach actually lead to more wins?

49ers fire Chip Kelly, seek fourth head coach in four years (1:05)

Following the recent firing of Chip Kelly as head coach, Adam Schefter explains the franchise is looking for someone who can turn around the program. (1:05)

Five NFL teams had already fired their head coaches by the morning after the regular season ended. The good news for these franchises is that teams that replace their head coaches tend to improve the next year. Since the dawn of the 16-game regular season in 1978, teams coming off losing records with new coaches tend to improve by an average of 1.6 games. But there's a big problem with that number taken by itself.

At first glance, that jump in wins could seem like evidence that firing a coach at the helm of an underperforming team is generally a good decision. But this by itself it can be very misleading. Here's the thing: Teams with losing records that don't fire their coaches also tend to improve the following season, by an identical 1.6 games.

With some unusual exceptions, teams with very good records tend to do worse the following year, and teams with very poor records tend to improve. It's a natural phenomenon common to almost all systems like pro sports leagues, which tend to be stable, drawing outcomes toward the average. When a team has a very bad season, it's because a lot of things didn't go right -- injuries, opponents, free-agent busts and plain old bad breaks such as missed field goal attempts or bad calls at critical moments in games. It's very unlikely for all these same factors to break against a team in the same way in consecutive years. Plus, the NFL is structured by design to help struggling teams improve, with elements like the draft system, salary cap and scheduling rules.

So the question then becomes: Do teams who fire their coaches go on to do better than those that don't with equivalent records?

It might surprise you that, since 1978, teams with below .500 records who fire their coaches tend to rebound less compared to teams below .500 that don't fire their coaches. Although both group of teams improve by an average of 1.6 games, that average doesn't account for the fact that teams who fire their coaches tend to have slightly worse records and should be expected to rebound by that much more. Team records can be estimated as a function of prior-season records from year to year, which measures how much teams tend to rebound from poor seasons. There are many different ways to model how teams rebound, but one straightforward method is a regression. This method has the benefit of "holding equal" prior-season records rather than simply comparing the average improvements of each group of teams, and allows us to compare apples to apples. Win-loss records of teams that don't fire coaches rebound about 6 percent better than those that do, given their prior records.

Applying that same analysis in the salary-cap era exclusively (since 1994) produces the same pattern of results. When we look at team performance two years following each losing season, again, teams that did not fire their coaches tend to outperform those that did by 6 percent.

That isn't to say teams should never fire their coaches, as there are certainly good reasons to replace a head coach and his staff. Even a highly skilled coach can lose the confidence of his team after a bitterly unsuccessful season, even if it's undeserved -- there are only so many locker room speeches and motivational tricks a head coach can use.

But these results do suggest that teams are probably too quick to fire coaches. At the very least, it's not the panacea that some owners, front offices and fan bases sometimes believe it should be. If you think about it, a new coach never just means positive change and new energy. It can also mean greater personnel turnover, and perhaps even more patience for losses. "He needs some time to right the ship," we hear. That is just another way of excusing more of the same -- losing.

There could also be more complex effects involved. These results would be consistent with another explanation: Perhaps teams are fairly shrewd about when to fire, and only do so when things look bleak over the long term, leaving the new head coach with a roster less likely to rebound. Even if this explanation holds any weight, teams on the coaching carousel today shouldn't expect a new coach to spark a reversal of fortunes.