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BMJ Confidential: For Review Only Dissecti ng the curse of the rainbow jersey: historical cohort study Journal: BMJ Manuscript ID: BMJ.2015.027973 Article Type: Christmas BMJ Journal: BMJ Date Submitted by the Author: 07-Jul-2015 Complete List of Authors: Perneger, Thomas; University of Geneva, Division of Clinical Epidemiology Keywords: regression to the mean, causal inference, myths https://mc.manuscriptcentral.com/bmj Page 1 of 13 BMJ 1 2 3 Dissecting the curse of the rainbow jersey: historical cohort study 4 5 6 7 Thomas Perneger 8 Confidential: For Review Only 9 Division of clinical epidemiology, Geneva University Hospitals, CH-1211 Geneva, Switzerland 10 11 Thomas Perneger, clinical epidemiologist 12 13 14 Correspondence to Thomas Perneger [email protected] 15 16 Copyright: The Corresponding Author has the right to grant on behalf of all authors and does grant 17 18 on behalf of all authors, a worldwide licence to the Publishers and its licensees in perpetuity, in all 19 20 forms, formats and media (whether known now or created in the future), to i) publish, reproduce, 21 22 distribute, display and store the Contribution, ii) translate the Contribution into other languages, 23 24 create adaptations, reprints, include within collections and create summaries, extracts and/or, 25 26 27 abstracts of the Contribution, iii) create any other derivative work(s) based on the Contribution, iv) to 28 29 exploit all subsidiary rights in the Contribution, v) the inclusion of electronic links from the 30 31 Contribution to third party material where-ever it may be located; and, vi) licence any third party to 32 33 do any or all of the above. 34 35 Competing interests: I have read and understood BMJ policy on declaration of interests and declare 36 37 that I have none 38 39 40 Authorship: TP has conducted the study, written the paper, and approved the version submitted for 41 42 publication 43 44 Transparency: The paper contains an honest, accurate and transparent account of the study 45 46 Ethics approval: none was obtained (not required, publicly available data) 47 48 Funding: none 49 50 Data sharing: the dataset will be available on datadryad.org 51 52 53 54 55 56 57 58 59 60 1 https://mc.manuscriptcentral.com/bmj BMJ Page 2 of 13 1 2 3 Abstract 4 5 Objectives: To dissect the underlying mechanism of the “curse of the rainbow jersey”, i.e., the lack of 6 7 wins that purportedly affects the current cycling World champion 8 Confidential: For Review Only 9 Design: historical cohort study 10 11 Setting: on the road 12 13 14 Participants: professional cyclists who won the World championship road race or the Tour of 15 16 Lombardy, 1965-2013 17 18 Interventions: test of 3 hypotheses – the “spotlight effect” (i.e., people notice when a champion 19 20 loses), the “marked man hypothesis” (i.e., the champion, who must wear a visible jersey, is marked 21 22 closely by competitors), and “regression to the mean” (i.e., a successful season will be generally 23 24 followed by a less sucessful one). 25 26 27 Main outcome measures: Number of professional wins per season in the year when the target race 28 29 was won (year 0), and in the two following years (year 1 and 2); the World champion wears the 30 31 rainbow jersey in year 1. 32 33 Results: On average, World champions registered 5.04 wins in year 0, 3.96 in year 1, and 3.50 in year 34 35 2; meanwhile winners of the Tour of Lombardy registered 5.08, 4.22 and 3.77 wins. Globally, the 36 37 baseline year accrued 31% more wins than the other years (95% CI: 9% to 59%), but the year in the 38 39 40 rainbow jersey did not differ significantly from other cycling seasons. 41 42 Conclusions: The cycling World champion is significantly less successful during the year when he 43 44 wears the rainbow jersey than in the previous year, but this is due to regression to the mean, not to a 45 46 curse. 47 48 49 50 51 52 53 54 55 56 57 58 59 60 2 https://mc.manuscriptcentral.com/bmj Page 3 of 13 BMJ 1 2 3 What this paper adds 4 5 What is already known on the subject 6 7 • People love a good curse 8 Confidential: For Review Only 9 • Cycling World champions have a horrible year wearing the the champion’s stripes (a.k.a. the 10 11 12 curse of the rainbow jersey) 13 14 15 16 What this study adds 17 18 • World champions indeed win significantly less when they wear the rainbow jersey than 19 20 during the previous year 21 22 • … but this is no different from the following year, and similar to the experience of winners of 23 24 25 the Tour of Lombardy 26 27 • Regression toward the mean explains this pattern best 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 3 https://mc.manuscriptcentral.com/bmj BMJ Page 4 of 13 1 2 3 We humans struggle with randomness (1). When we see a pattern, we look for a causal 4 5 agent. When we cannot find one, we make up a curse (2). 6 7 Consider the “curse of the rainbow jersey” (3). In 1965 British cyclist Tom Simpson won the 8 Confidential: For Review Only 9 World championship road race, then broke his leg while skiing during the following winter, and lost 10 11 his 1966 season to this and other injuries; famously, Simpson died in 1967 during the Tour de France. 12 13 14 In the ensuing years several world cycling champions encountered all manner of misery while 15 16 wearing the distinctive white jersey bearing five horizontal color bands: lack of racing success, injury, 17 18 disease, family tragedy, doping investigations, even death (3). It soon became obvious that the 19 20 rainbow jersey was cursed. 21 22 Several explanations can be entertained for the curse. One is that the world champion is as 23 24 likely to encouter sporting and personal difficulties as anyone, but being the champion, people notice 25 26 27 more. This is the “spotlight effect”. Another explanation is that the world champion, very noticeable 28 29 in the hard-to-miss rainbow jersey, is marked more closely by his rivals, which lowers his chances of 30 31 winning. This is the “marked man hypothesis”. Finally, random variations in success rates ensure that 32 33 a very successful season, such as one during which the rider has won a major race, will likely be 34 35 followed by a less successful season. This is the “regression to the mean” phenomenon (4). In this 36 37 study I explored to what extent these hypotheses are supported by racing results of cycling 38 39 40 champions during the past 50 years. 41 42 43 44 Methods 45 46 The study population includes winners of the Union Cycliste Internatinale mens’ World 47 48 championship road race from 1965 to 2013, and for comparison the winners of the Tour of Lombardy 49 50 of the same years. The latter race is of comparable importance – it is one of five “monuments” 51 52 53 among classic one-day races – and takes place at the end of the racing season, just like the World 54 55 championship. 56 57 58 59 60 4 https://mc.manuscriptcentral.com/bmj Page 5 of 13 BMJ 1 2 3 The outcome variable was the number of individual wins in professional races during a given 4 5 year, obtained from a publicly accessible database ( www.procyclingstats.com ). All wins were given 6 7 the same weight. Wins in team time trials were not counted. 8 Confidential: For Review Only 9 Win counts were obtained for 3 calendar years: 10 11 a) Year 0, at the end of which the rider won the championship or the Tour of Lombardy. 12 13 14 b) Year 1, during which the world champion wore the possibly ill-fated jersey. 15 16 c) Year 2, which follows the possibly cursed year, when all riders returned to curse-free status. 17 18 19 20 Study hypotheses 21 22 The hypothesized patterns for the average numbers of wins are as follows (Figure 1): 23 24 a) “Spotlight effect” hypothesis: the problems of the world champion are only apparent, due to 25 26 27 increased meadia attention, so the numbers of wins should remain at the same level for the 28 29 three years. 30 31 b) “Marked man” hypothesis (or, equivalently, the rainbow curse, which is indistinguishable): a 32 33 decrease in wins should affect the current world champion, but this effect should disappear 34 35 in the following year when someone else is the champion, and should not affect the winner 36 37 of the Lombardy race. 38 39 40 c) “Regression to the mean” hypothesis: the baseline year 0 (when the championship was won) 41 42 should be a high outlier, and the number of wins should return to a lower level in years 1 and 43 44 2. The pattern should be identical for the Lombardy winner. 45 46 47 48 Statistical analysis 49 50 The mean numbers of professional victories per rider for years 0, 1 and 2 were tabulated 51 52 53 separately for the winners of the World championship and of the Tour of Lombardy.