Have you ever wondered why movie sequels or remakes and cover songs are never as good as the originals?  And why do so many athletes and singers suffer from the “sophomore jinx”?

I was watching some unknown singer do a cover version of Elton John’s Your Song on SNL, and the question “Why?” came to mind.  Why would anybody ever bother to do a cover version of a song or produce a movie remake or sequel?  They are almost never as good as the originals.  Then I realized that the reason has to do with a statistical phenomenon called regression to the mean.

Regression to the mean occurs whenever a given outcome consists of a fixed component (the mean) and a random component (the variance).  An example of such an outcome is the number of heads you get in 10 flips of a fair coin.  In this case, the mean is 5, but you don’t always get 5 heads and 5 tails in 10 flips of a fair coin.  Sometimes it is 5, but it could be 6 or 7, and it could be 3 or 4.  In other words, a sample of such outcomes has a variance around the mean of 5.

Regression to the mean refers to the statistical phenomenon that, whenever you obtain an extreme outcome far from the mean, the next trial will almost certainly result in a less extreme outcome closer to the mean.  So, for example, if you get 8 heads out of 10 flips of a fair coin, then, in the next 10 flips, you are likely to get 4, 5, or 6, rather than 10, 9, or even 8 again.  An outcome immediately following an extreme outcome far from the mean moves closer to (or regresses to) the mean.

This is why, among other things, children of extremely tall parents are likely to be shorter than them and children of extremely short parents are likely to be taller than them.  Height consists of both a fixed component (genes) and a random component (environment).  Extremely tall or extremely short parents are likely to be much taller or much shorter than what their genes inclined them to be, due to a particular combination of environmental factors.  So their children, who have all of their genes but few of the same environmental factors, are likely to regress to the mean of their genetic endowment.

Whether a given song or movie becomes a huge hit also contains a fixed component (its inherent and true quality) and a random component (all the unpredictable and unknowable factors that go into making it a success or failure in entertainment).  The problem with movie sequels and cover songs is that they only make them when the original was extremely successful.  Nobody produces a remake of a movie that bombed or a cover of a song that flopped.  They only remake “classics” that did extremely well critically or financially.

When a movie or a song does extremely well, it usually means that the outcome was extreme, far away from the mean of its true quality, rather than that its true quality was much higher than that of all of its competitors.  Somehow everything went right by chance to make it a huge success.  If you follow it with a sequel or a cover, then, by the law of regression to the mean, the next trial is virtually guaranteed to be worse than the original because not everything will go exactly right the next time.  Hence almost all remakes, sequels and covers fail to live up to their expectations.

This is also why athletes and singers suffer from the notorious “sophomore jinx.”  Their second season or their second album is almost never as good as their first.  Performance of athletes and singers also contains a fixed component (their inherent and true talent) and a random component (luck), and hence is subject to regression to the mean.  The trial after an extreme outcome (a very successful first season or album) is virtually guaranteed to be a disappointment.

Note that regression to the mean occurs in the other direction as well.  After an extremely poor outcome, the next trial is bound to be much better.  But we don’t produce sequels and covers of unsuccessful movies and songs, and we don’t follow the careers of unsuccessful freshman athletes or singers.  That’s why we don’t notice a “sophomore success” after a “freshman failure.”  Does anybody remember that Julia Roberts did a movie called Girls of Summer (later renamed Satisfaction), in which she got second billing to Justine Bateman, before she did Steel Magnolias and Pretty Woman?  Nobody calls Julia Roberts “a sophomore success.”  They only remember her “breakout roles” in Steel Magnolias and Pretty Woman.

The law of regression to the mean suggests that Ishtar II and Waterworld II will likely do much better than the originals.  But Hollywood doesn’t gamble on previous failures.  I wish Hollywood would learn about regression to the mean so that it would stop producing movie sequels and cover songs which are guaranteed to disappoint.

Follow me on Twitter:  @SatoshiKanazawa