What does AttM mean?

Aggression to the Mean (AttM) is a play-on-words regarding a statistical concept named regression to the mean. Regression to the mean describes the natural phenomon whereby extreme observations (e.g. fight performances) tend to be followed by more moderate ones.

This statistical phenomenon appears in many spors contexts, including MMA. We’ll examine how regression to the mean may manifest itself in the UFC.


Extremely Good Performances

Max Holloway recently had a record-setting performance against Calvin Kattar. Many would argue that it was his very best performance in the octogon. As such, Holloway’s performance can be considered an extreme observation. Although it is possible that Holloway performs even more ably in his next fight, it is more likely that his subsequent performance regresses toward the mean. In other words, statistically, we would expect that Holloway’s next performance will not be as impressive as his last.

Importantly, we can make that statement without knowing much about who Holloway’s next opponent will be. As long as his next opponent is a top-ranked UFC fighter in his weightclass, it is likely that Holloway’s subsequent performance will more so resemble what we would consider an average UFC performance, or an average Holloway performance.


Extremely Poor Performances

Holloway’s performance was extreme in a positive sense. However, the idea of regression to the mean can apply to cases of extremly poor performance. For instance, back in July 2020, Joseph Benavidez got dominated in his title fight against Deiveson Figueiredo. It was probably one of the veteran’s all time worst performances. Therefore, we would expect the veteran’s subsequent performance to regress toward the mean in a positive sense: Benavidez will likely perform much more ably in his next UFC contest.


Don’t Misunderstats Me!

I expect that many of you reading this might be thinking “yeah, but Holloway is probably going to fight Volko next - of course he won’t look as good as he did versus Kattar!”. Or, “Figueiredo is one of the best, of course Benavidez will look better against some lower level fighter”. Importantly, I actually agree with those statements! That level of detail (i.e. the prospective opponent) is beyond what can be explained by the general statistical concept of regression to the mean.

The point is that even if Holloway fought a ranked opponent other than Volko (e.g. Korean Zombie), or if Benavidez fought someone nearly at the same level as Figueiredo (e.g. Brandon Moreno), we would expect them to perform more moderately (i.e. we would expect them to regress toward the mean).

Regression to the mean is a statistical tendency. It applies on average. It is not a deterministic natural law. Of course, Benavidez could perform even worst than he did against Figueiredo in his next fight. However, that just might not be as likely as the alternative.


Why you Should Care

It important to be aware of the idea of regression to the mean to avoid the common mistake of over-interpreting certain shifts in performance and reading causation into potentially irrelevant factors. For example, if Holloway starts sparring again before his possible Volko trilogy and loses in a fashion similar to their first two fights, it does not necessarily mean that the sparring had a negative impact on his performance. Although that could be a plausible hypothesis, it could simply be that his Kattar performance was exceptional and that various unexplained random factors made that so (i.e. he ended up regressing to the mean). Of course, it could also be that Volko is just that good and adaptable. At the end of the day, these things are difficult to know for certain.

MMA is a volatile sport. There are so many factors that can influence the outcome of a fight. Understandably, commentators are paid to try to understand these factors and often infer causality in the process. Sometimes, however, it is beneficial to approach these topics with a bit of humility by appreciating that some things in the fight game are difficult to understand.


Additional Info

If you want to learn more, check out this great Article by Farnam Street blog describing the phenomenon of regression to the mean in other contexts.