Every year since 1999, the Madden NFL video game cover has featured an NFL star player from the previous year, similar to an athlete being featured on the Wheaties box. Fans have noticed a trend where these star players end up playing worse or even getting injured the following year. Hence the idea of a “Madden Curse,” and a subset of fans who are adamantly opposed to their favorite players being featured on the cover.What does this have to do with statistics? Well, there is a concept in statistics called “reversion to the mean.” Reversion to the mean is the idea that if we observe an extreme event (e.g. a surprisingly strong NFL season), we can expect the following event to be closer to the average (e.g. the season following a particularly strong NFL season will be less impressive). This might explain why players featured on the Madden cover generally do worse the following year.
The player's reversion to the mean does not indicate that they are actually playing worse than they normally do, it’s just that we raised our expectations of them! We can look at a similar phenomenon at the team level. Historically, football teams that do very well (e.g. records of 14-2, 15-1, or 16-0) typically do worse the following season.
This concept relies on there being some randomness to the events. If an NFL season were purely the result of skill, then we would always expect the following season to be as good as the previous one (barring injury or other external factors). But as we all know, there is some luck (or randomness) involved in most human endeavors, and as a result we are all susceptible to reversion to the mean.
The good news is that reversion to the mean applies to extremely bad events as well. So, if you did particularly poorly on a recent exam (compared to similar exams you have taken), keep your spirits up because most likely you will do better on the next one!
Food for thought: Why do you think that when teams fire their coach, they usually improve? Does reversion to the mean play a role here? Can you think of any other situations where reversion to the mean plays a meaningful role? Let us know in the comments!
To learn more about the Madden Curse, check out this piece from Forbes.
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About the Author
Ben is a member of the HBX Course Delivery Team and works on the Economics for Managers course for the Credential of Readiness (CORe) program. He has a background in economics and physics and is interested in all things related to statistics and modelling human behavior.