May the best man lose?

Author: Tom Fanshawe

There are 302 events in 26 sports at the London Olympic Games. Many of the gold medals on offer will be won by the best competitor in the world in his or her specialist event. But many, perhaps more, will not. The skill, speed or strength of the athletes is just one of the many factors that will determine the winner.

Luck, of course, plays a major role, in a way that is impossible to anticipate and difficult to quantify. The fortune of a roll of a ball very often determines the winner in a contest between closely matched teams in sports such as football or hockey; less so in those with more opportunities for scoring points, like basketball and tennis. Much the same could be said of the impact of decisions by referees and umpires, whether they be for disqualifications in taekwondo or penalties in water polo.

On the day of the event, weather conditions may favour certain contestants, in sailing or the marathon, for instance. Athletes in all sports may be hampered by unexpected injury or illness, or even impeded by each other in the case of cycling or running.

Chinese gymnast Jiang Yuyuan on the balance beam at the

2008 Summer Olympics. Image by bryangeek/Wikimedia.

What can statistics make of all these imponderables? In many cases, very little, beyond recognising that events such as these, as far as one can usually educe, occur at random and hence unpredictably. These random factors are reflected in bookmakers’ odds for the various events, and in some cases are small enough to result in some very short-price favourites indeed: the USA are 1-100 to finish on the podium in the men’s basketball.

However, there are at least two other causes of variation in Olympic scoring. The first is the way in which the scoring system itself is devised, which can have a substantial effect on the approaches adopted by the athletes and their final placings. This is a particular issue in sports made up of more than one event, in which scores must be combined in order to determine a winner. Examples include the multiple-race system used in sailing, the equestrian scoring system and composite athletics events such as the decathlon and heptathlon, as described in this article.

The second is the impact of variability of judges in sports such as synchronised swimming, diving and boxing. In each of these sports there is a degree of subjectivity in the score assigned to each participant, which has often led to controversy and confusion. One of the most celebrated episodes occurred in the all-round women’s gymnastics competition at the 1980 Moscow Games, when home favourite Yelena Davydova took the title from Romania’s Nadia Comeneci by the narrowest of margins.

In recent years, the gymnastics scoring system has undergone a number of radical, complex and vociferously contested overhauls. Central to the system is the concept of a ‘trimmed mean’: the highest and lowest scores for each competitor are discarded, and the score is calculated from the remainder. The intention is to reduce variability and potential bias in judges’ ratings and provide a more robust estimate of the performance of the gymnast. Nevertheless, at the fine margins that separate many elite athletes, the composition of a judging panel alone has the potential to make the difference between gold and silver.