Rio Olympics: the hidden statistics

With 1,417 days until the Tokyo 2020 Olympic Games, actuaries Amanda Aitken and David Kwak look at who topped the Rio Medal Tally and why. Did you know that if results are adjusted for population size, the Isle of Man, Grenada and the Bahamas top the table? And Australia beat out the UK and US! Read on for some fascinating insight into what drives country performance, based on actuarial analysis.

Most people focus on the overall Medal Tally, with an equal weighting for gold, silver and bronze. As typical actuaries, we weren’t happy with this overly simple approach and have instead examined the following two results:

• Medal Score (with a weighting of 3 for gold, 2 for silver and 1 for bronze)
• Medal Score per million population

Our Medal Score tally results in the following Top 10 countries:


Medal Score 

Medal Tally





Beijing (2008)




250 (1)

225 (1)

220 (2)

121 (1)

Great Britain

144 (2)

140 (4)

98 (4)

67 (3)


140 (3)

190 (2)

223 (1)

70 (2)


112 (4)

155 (3)

139 (3)

56 (4)


86 (5)

85 (5)

83 (6)

42 (5)


80 (6)

67 (6)

70 (7)

42 (6)


73 (7)

66 (7)

46 (10)

41 (7)


56 (8)

65 (8)

89 (5)

29 (8)


56 (9)

53 (10)

54 (9)

28 (9)


42 (10)

38 (11)

34 (14)

19 (13)

* Numbers in brackets represent relative rank

Two things are clear from this tally:
• Our weighting of gold, silver and bronze medals doesn’t have a big impact on who places in the Top 10 (although in 2016 it did lift Great Britain to 2nd and Netherlands into the Top 10).
• USA, Great Britain, China and Russia have consistently ranked in the Top 4 over the last 3 Olympics, and consistently scored well above the next 6 countries in the Top 10 (clearly not breaking news!).

Much research has been conducted to understand what drives the performance of such countries. Gonzales (2016) suggests that four factors are key:
• population size;
• wealth;
• previous Olympic performance; and
• whether the country is hosting that year’s Olympic Games.

Research conducted by Bredtmann and colleagues (2016) found that other influential factors included:
• planned economies (these countries tend to invest more in sport as they value the prestige associated with sporting success); and
• religion (some religions ban or discourage female participation in sport, reducing the medal opportunities from women’s events).

Research conducted at Ruhr-Universität Bochum suggests that factors such as funding support and political systems also influence Olympic performance.

We conducted our own research by collecting a range of economic, cultural, political and demographic variables and running these through a Generalised Linear Model (GLM), which suggested the following as being the most significant predictors of Olympic success (listed in order of significance):
• population
• number of colleges/universities in the country
• previous Olympic Medal Score
• total government spend (not just sports related)
• host country impact
• female mortality rates

Most of these are fairly intuitive and consistent with the research outlined above. The number of colleges in a country is likely to be highly correlated with overall population size. The larger the population, the larger the pool of athletes from which to choose an Olympic team. Previous Olympic performance is likely to reflect the current Olympic training regime and team members and the importance the country places on sport.

The host country impact is also well documented as having a large impact on a country’s performance, perhaps by increasing sports-related spending, reducing travel-related fatigue/jetlag/acclimatization issues and increasing the number of supporters cheering the athletes on. When Great Britain hosted the London Olympics in 2012, their Medal Score jumped to 140 from 98 in Beijing in 2008. Brazil’s Medal Score jumped from 24 in 2008 and 28 in 2012 to 39 when they hosted the Rio 2016 Games.

Total government spend is one measure of wealth, which allows for more money to train athletes and invest in sporting equipment and infrastructure.

Female mortality was a more surprising finding. Perhaps it simply reflects the overall health of the female population and therefore a bigger pool of high-performing female athletes. However, other variables tested such as average female body mass index (“BMI”) and female economic participation did not prove to be significant.

Clearly, overall population size has a significant impact on performance. So how do countries rate if we adjust for population size? The table below shows the Top 10 countries by Medal Score per million population.

table2olympicsarticle* Numbers in brackets represent relative rank

This list is very different to that using the unadjusted Medal Score! On this measure:
• Australia ranked 16th with a score of 2.4
• Great Britain ranked 18th with a score of 2.2
• USA ranked 39th with a score of 0.8
• Russia ranked 40th with a score of 0.8
• China ranked 74th with a score of 0.1

Small countries such as Isle of Man, Grenada and Bahamas are able to make it to the top of this list because of 1 or 2 superstar athletes. What becomes obvious though is that countries such as Jamaica, New Zealand, Croatia and Denmark perform very well considering their small population.isleofman

To try to understand what might be driving the success for these countries, we reran our GLM and found the following variables to be the most significant in predicting Medal Score per million population:
• prior Medal Score per million population
• GDP per capita
• average monthly income
• male mortality rates
• religion

These are largely consistent with other research which found that prior Olympic performance, wealth and religion may all be influential factors. However again mortality rates make an appearance, although this time male rates were found to be significant when female rates were not.

Of course, other variables, some of which are difficult to source and/or quantify, are also likely to play a part in determining Olympic success. These include:
• government spend specifically on sport
• sports culture
• individual country circumstances such as the banning of the Russian athletes
• Olympic training regimes such as hours of training and beginning ages for athletes

So with Olympic fever still in the air following Rio 2016, why not do your own investigating and pass any significant findings on to the Australian Olympic Committee!

Aussie Aussie Aussie, Oi Oi Oi!

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Image of Chao Qiao
Chao Qiao says

October 5 2016

Have always been fascinated by the analytical nuances of the Olympic medal count and how to do an adjusted medal count controlling for the following:-
- the max number of athletes allowed to compete per country per event and the fact there's only three medals per event ... populous countries dominating certain sports are clearly disadvantaged here since there's a cap on the max possible medals (per capita or not) they can get (e.g. Russia with rhythmic gymnastics, S Korea with archery, China with table tennis)
- team events vs individual events (e.g. a rugby sevens medal vs an individual archery medal by virtue of the amount of work multiplied by the number of players involved; so had Fiji specialised in athletics like Jamaica, their medal count would have been much higher)
- sports that have lots of events vs sports that have one or two events (e.g. tennis has four events, whereas diving as eight, and swimming has lots; had there been 100 medals awarded for archery then S Korea's medal count would probably top the US)

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