Kenan Spruill, Adam Roberts, and Joseph Price, Department of Economics
“When the going gets tough, we fire the coach”, this quote from former coach and current ESPN analyst Jeff van Gundy represents part of the current trend in sports. Management fires the coach in the hope that the new one can lead the team to glory. Replacing coach’s midseason does not happen often, but when it does, it is the best choice for the team? We are attempting to see if there is a legitimate reason for firing a coach midseason. Considering the fact that changing coach’s mid-season requires the team to pay for both the old and new coaches’ salaries, the expected benefit from switching coaches would have to be larger than the new coach’s salary for the decision to be economically efficient.
There is already a pretty broad literature base that has focused on the effect firing managers has in many different sports, but many of these papers fail to account for a phenomenon known as mean reversion. Mean reversion is the simple fact that over time, statistics will move toward their average. For example, when the economy faces a period of recession we expect that eventually GDP growth with move back toward its long term average. Additionally, if a sports team that usually wins half their games has a 5 game losing streak, we don’t expect them to continue loosing forever but to move back towards their previous average.
In order to account for mean reversion, we needed to develop an estimate of what a team’s performance would have been if they had not fired their coach. To do this, we matched teams who fired their coach with similar teams who did not fire their coach. “Similar” being defined as teams that had a similar win/loss records and point differentials. After assigning each team who fired their coach a match, we were able to identify the difference between the number of games they would have won if they had kept their coach and the games actually won after the coach was fired.
These results both agree with and add to research that has been done previous on this topic. We agree with the results of others, that teams usually increase their win percentage after firing their coach, but reject this improvement as the causal effect of firing the coach. With all variations of our matching strategy indicating similar results, we conclude that true effect of changing coaches midseason is a significant decrease in the likelihood of winning each successive game. These result are consistent because teams who fire their coach do improve, but they improve four percentage points less than they we would have if they had kept the same coach. The combination of this effect and mean reversion result in an overall negative effect on their expected performance.
Figure 1 provides a visual representation of win percentage if coaches are fired or kept.
Under comparison, we see that the two groups were trending together until the coaches’ firing. At this point, they separated and remained separate thereafter. Under mean
reversion, an improvement from the coach-fired teams would be expected above the results of the control teams, to offset their earlier downward departure. Furthermore, figure 1 indicates that as time passes teams that have fired their coaches perform even worse. This provides a clear indication of the negative effect that firing a coach has on team win percentage.
The average NBA coach in 2007 earned $3.95 million. This, divided over the 82 games played per season by NBA teams comes out to a wage of over $48 thousand per game. Considering that on average coaches who were fired were fired around game number 35, that leaves 47 games left in the regular season. Multiply this by the pro-rated salary of an NBA coach and find that in 2007, teams who fired their coaches paid around $1.7 million in order to both hire a new coach and win fewer games than they would have otherwise. Over the course of an entire season, a four percentage point decrease in the chance of winning any given game would result in 3.3 additional losses, and over the average period of the replacement coach’s tenure (47 games) this equates to 1.9 additional losses. With the estimated value of each additional win to be $197,304, this puts the total cost for hiring a new coach at around 2.08 million dollars.
Our findings suggest that firing your coach mid-season is a poor financial decision for any team and these findings may also be applicable to other management decisions in government, business or elsewhere. Unless decision makers are careful to account for mean reversion, hasty decisions can easily leave those in charge feeling like they fixed the problem, even though their decision actually had a negative impact.