Rainbow worrier – Mean regression lies behind so much of life, including sporting superstition


Andrew Williams

Andrew Williams

Investment Director

‘The curse of the rainbow jersey’ may sound like an episode of Scooby Doo but, if you have not come across it before, it is in fact a cycling term. It has its origins in the extraordinary array of misfortunes that have befallen various cyclists in the year after they have won the World Championship Road Race – the period in which they get to wear the distinctive rainbow-coloured top. 

The concept of bedevilled sportswear appears to have captured the imagination of Thomas Perneger, a clinical epidemiologist from Switzerland, whose paper Debunking the curse of the rainbow jersey came across the radar of The Value Perspective via some off-piste reading – specifically, the BMJ – over the Christmas period.. 

The paper notes how, in the years since a skiing injury prevented British cyclist Tom Simpson from defending the world title he won in 1965, “champion after champion encountered all manner of misery while wearing the jersey – injury, disease, family tragedy, doping investigations, even death, but especially a lack of wins”. Thus a colourful sporting curse was born. 

In a bid to understand the curse’s “underlying mechanism”, Perneger tested a number of hypotheses – described as “the ‘spotlight effect’ (that is, people notice when a champion loses); the ‘marked man hypothesis’ (the champion, who must wear a visible jersey, is marked closely by competitors); and ‘regression to the mean’ (a successful season will be generally followed by a less successful one)”. 

These plus a fourth hypothesis – a mix of ‘marked man’ and ‘regression to the mean’ – underwent some fairly rigorous analysis that you can read more about at the above link. Here though, we will skip straight to the conclusion, which is that “the cycling world champion is significantly less successful during the year when he wears the rainbow jersey than in the previous year”. 

Without wishing to disappoint those readers who also happen to be Scooby Doo fans, however, Perneger feels his findings have less to do with any curse than one of The Value Perspective’s favourite ideas. “The current road racing world champion wins less on average than he did in the previous season,” he notes, “but this phenomenon is best explained by regression to the mean. 

“The relative lack of success was not restricted to the season in the rainbow jersey but persisted in the following season and affected equally the winners of the Tour of Lombardy. There was nothing remarkable about the year spent wearing the rainbow jersey.” The author does add a few caveats here – as well as the presumably tongue-in-cheek observation the study does not rule out the curse entirely. 

Nevertheless, he argues, regression towards the mean is unavoidable wherever three factors are involved. These are where the variable under study – in this instance, sporting success – fluctuate over time; the correlation between consecutive observations is less than 1; and the baseline observation is defined by an arbitrarily high or low value (here, a season marked by an important win). 

This being the BMJ, the study also offers some interesting examples from the world of medicine – suggesting regression to the mean may explain “why patients who lose bone density in the first year are likely to reverse this trend at follow-up or why HIV-related risk behaviours improve after enrolment into a prevention trial”. 

Perneger even mentions Samuel Johnson’s view that doctors were more likely than any other people to mistake “subsequence for consequence” – in other words, that any improvement in their patients must be attributable to the treatment they prescribed rather than the alternative explanation, that patients consult when they feel poorly and most will get better regardless of treatment. 

Johnson may have been a bit hard on doctors, however, as ideas such as randomness and regression do not come any easier to people in other walks of life – including investment. After all, if we return to the three variables mentioned a little earlier and replace both “sporting success” and “a season marked by an important win” with “company valuation”, we can see value investing fits very nicely. 

Look at valuations in the UK market today, though, and you will also see a dramatic polarisation –between stocks that are now greatly overvalued because, for the last few years, they have been perceived as ‘stable’ or ‘bond proxies’ and other businesses, such as mining, that are just as greatly undervalued because they are out-of-favour and essentially now priced for Armageddon. 

Both history and the law of mean reversion suggest this situation cannot last forever and that both these overvalued and undervalued businesses will eventually snap back towards their longer-term averages. Furthermore, basic human nature suggests many investors will not benefit from such a development as an inclination to run with the crowd will have left them more exposed to the former than the latter. 

Thanks to their willingness to swim against the tide – and through their use of bottom-up stock analysis to identify cheaply valued stocks with strong balance sheets – value investors may, on the other hand, reasonably hope that regression to the mean will lead to any rainbow-related consequences being not curses but pots of gold.


Andrew Williams

Andrew Williams

Investment Director

I joined Schroders in 2010 as part of the Investment Communications team focusing on UK equities. In 2014 I moved across to the Value Investment team. Prior to joining Schroders I was an analyst at an independent capital markets research firm. 

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