Even as great a quarterback as Peyton Manning has his ups and downs. Figure 1 shows Payton’s Total QBR for each of the 16 regular-season games in 2013. The week-to-week fluctuations are a reflection of how much randomness there is in athletic performances. Sometimes, a quarterback is sick or banged up. Sometimes, the play calling works, sometimes it doesn’t. Sometimes a pass is deflected, sometimes it isn’t. Sometimes the ball slips or is dropped. Sometimes, a fumbler’s team recovers the ball; sometimes, it doesn’t. Sometimes, the official throws a flag, sometimes he doesn’t. The commonplace observation, “On any given Sunday, any team can beat any other team,” reflects the reality that there is a lot of randomness in football games.
Manning had an incredible year in 2013, arguably one of the best years in his 15-year career (to that point). He threw 55 touchdown passes with only 10 interceptions. The next closest in touchdowns was Drew Brees with 39. Manning’s Total QBR was 82.9; the next closest ratings were Philip Rivers (71.1) and Drew Brees (70.5).
Looking forward to the 2014 season, the commentators talked about Manning’s age (38), his pass receivers (Demaryius Thomas, Wes Welker, Julius Thomas, and Emmanuel Sanders), the running backs, and the offensive line. They predicted he would throw 48 touchdown passes and 12 interceptions and, once again, be the top NFL quarterback by a wide margin. For those fans who play Fantasy Football, they predicted that Manning would have 368 fantasy points, well above the predictions for Aaron Rodgers (347 points) and Drew Brees (329).
They didn’t talk about luck—about how unusually good or bad performances typically involve some fortune or misfortune. No one said a word about how Manning might have had good more good luck than bad in 2013. The more extreme is the good luck, the less likely it is to be repeated. The more Manning benefited from good luck in 2013, the less likely he was to have so much good luck, or even more, in 2014. Since Manning, at age 37, had one of his best years ever in 2013, I reasoned that good luck must have had a lot to do with it. So, I posted a blog before the 2014 season started titled, “Peyton Manning is Likely to Regress to the Mean.” I ended the blog with this prediction:
Manning is a Hall-of-Fame quarterback, but 2013 was not a below-average season for him. Manning is surely not as good as he seemed last year, and almost certainly will not do as well this year. You can take that to the bank.
Manning regressed to the mean in 2014. Instead of the predicted 48 touchdowns with only 12 interceptions, he had 39 touchdowns and 15 interceptions. Instead of leading the league with 368 fantasy points, Peyton finished fourth with 307 points, behind Aaron Rodgers (342), Andrew Luck (336), and Russell Wilson (312). Peyton’s Total QBR was 77.4 and he finished third, well behind Tony Romo’s 82.7 and Aaron Rodgers’ 82.6.
Peyton didn’t have a bad year. He was still one of the top quarterbacks in the league. But he didn’t have as much good luck as the year before and he didn’t finish in first place.
It’s not just Manning who regresses to the mean. Figure 2 is a scatterplot for the 2013 and 2014 seasons for those players who played both seasons. The average Total QBR increased from 58.6 to 63.5 between 2013 to 2014, so Z-scores are used in Figure 2 to make the data comparable. If there was no regression to the mean, players who did very well one season would be equally likely to do better or worse the next season. the QBRs would be evenly scattered about the 45-degree line drawn through the origin with a slope of one.
It is not that the best performing players had their skills deteriorate in 2014 while the worst performing quarterbacks had their skills improve. It is that the best performing players had good luck in 2013 while the worst performing quarterbacks had bad luck.
The role of luck is confirmed by the fact that there is a similar regression going the other direction, from 2014 to 2013, since regression to the mean has nothing to do with players’ abilities evolving over time. It has everything to do with performances fluctuating about abilities because of good and bad luck. Three of the top for quarterbacks in 2014 were closer to the mean in 2013, as were all four of the lowest rated quarterbacks.
The correlation between 2013 and 2014 QBRs is 0.46, which means that a quarterback who is one standard deviation from the mean in either season is predicted to be 0.46 standard deviations from the mean in the other season.
Peyton Manning is human and, like other humans, is susceptible to regression to the mean.