Can statistics demonstrate a home advantage in the Olympic games?

Stephen R Clarke

Home advantage in the Olympic Games

This presentation is based on the paper:

Clarke, S. R. (2000). Home advantange in the Olympic games. Proceedings of the Fifth Australian conference on Mathematics and Computers in Sport. G. Cohen and T. Langtry. Sydney, University of Technology Sydney: 76-85.

Home Advantage

• Simple study done prior to Sydney Olympics

• Uses only Secondary School descriptive statistics

• The results of the study gained widespread publicity with several newspaper articles, 2 television segments and almost 20 radio interviews

History of the Ancient Olympics

• The ancient games began about 824 BC • initially consisted of a single foot race from one end of

the stadium to the other• they accumulated sports such as discus, javelin,

boxing and wrestling• continued for 12 centuries. • from 776BC they were held every four years. • abolished in 394 AD.

The Modern Olympics

• The Modern Olympics began in 1896• It now vies with the World Cup of soccer as the World’s

premier sporting event. . • The first modern games did not allow women. They

now make up 30% of the athletes. • The event list has steadily grown • An increasing number of medals awarded.

– In 1896, 122 medals including 44 gold – In 2000 928 medals including 301 gold.

Venues for the Modern Olympic Games.

Olympiad Year City Country

Number of countries to win medals

Number of Medals

I 1896 Athens Greece 10 122II 1900 Paris France 18 276III 1904 St. Louis U.S.A. 9 282

1906 Athens Greece 19 226IV 1908 London Great Britain 19 323V 1912 Stockholm Sweden 18 309VI 1916 Berlin Germany CancelledVII 1920 Antwerp Belgium 22 435VIII 1924 Paris France 26 366IX 1928 Amsterdam Netherlands 33 327X 1932 Los Angeles U.S.A. 27 348XI 1936 Berlin Germany 32 388XII 1940 Tokyo Japan Cancelled

Helsinki FinlandXIII 1944 London Great Britain CancelledXIV 1948 London Great Britain 33 409XV 1952 Helsinki Finland 43 459

Table 1: Venues for the Modern Olympic Games.

Olympiad Year City Country

Number of countries to win medals

Number of Medals

XVI 1956 Melbourne Australia 39 470XVII 1960 Rome Italy 45 464XVIII 1964 Tokyo Japan 42 498XIX 1968 Mexico City Mexico 43 525XX 1972 Munich Germany 46 596XXI 1976 Montreal Canada 41 613XXII 1980 Moscow U.S.S.R. 36 631XXIII 1984 Los Angeles U.S.A. 46 687XXIV 1988 Seoul South Korea 52 739XXV 1992 Barcelona Spain 64 815XXVI 1996 Atlanta U.S.A. 78 841XXVII 2000 Sydney Australia 80 928

Past studies

• Stefani - improvement in the various sports. • Condon et al - neural networks and regression to

model the number of medals won at the Atlanta, based on various economic variables such as area, population and length of rail road track.

• Sommers measures the success of nations at Atlanta per unit of population

• Leonard The "Home Advantage": The Case of the Modern Olympiads

Home Advantage

• The existence of HA in sport is well documented• Home teams win majority of the matches (~60%). • Causes of HA are

– positive effects for the home side due to ground familiarity and a partisan crowd.

– negative effects on the visitors mainly due to travel.

• Such effects are present during the Olympics - possibly to a greater extent for Australia

Home Advantage

• Visitors have change in season and time zones• Home crowd• Stefani shows that in soccer HA effects increase with

international travel • The home country has some choice in the sports that

will be offered• larger teams and competes in a larger range of events

than usual. • boycotts reduce the strength of competition.

Home Advantage

• Usual causes of HA clearly apply to all athletes from the host country

Research Question• Does the home team have an advantage in the

Olympic games• If so, can we quantify it

Home advantage

• In any analysis there are many statistical traps that await the careless– The increasing number of events– Increasing number of countries– Changes in the general level of sports performance of

particular countries– Boycotts

• Need to ensure results cannot be attributed to other causes

Method

• Compare the home performance of host countries with their away performances.

• Simple study, uses school mathematics, yet results achieved widespread publicity

• Analysis done on SAS/JMP, but Excel could have been used.

Data

• The final gold silver and bronze medal tallies of all countries that won a medal. – Wallechinsky has details for all events up to 1984 -

including 1906 – Later Olympics from the WWW– Collected by undergraduate students - 841 observations.

• There were no data on the countries that competed but won no medals.

(Latest edition includes Sydney)

Measure of Performance

• Number of Gold?• Number of Medals?

Number of gold medals won by the USA each year

The total number of gold medals awarded to all countries each year

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Gold medals versus total for USA

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Total number of medals won against number of gold medals won for Australia

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Measure of performance

• Less % variation in a total than individual items– Use total medals rather than gold

• Total number of medals awarded has steadily increased– Use % of total medals won as the measure of a countries

performance

Percentage of total medals won by the USA

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Outlier??

Percentage of total medals won by Australia

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Percentage of total medals won by Japan

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Of the 17 countries to host the games• 14 have won their greatest ever percentage of

available medals at home• Exceptions

– Finland– Canada– Italy

Percentage of available medals won by host countries at home and away

Country Percentage of available Ratio medals won Home:Away

Away HomeAustralia 2.3 7.4 3.2Belgium 1.3 8.1 6Canada 2.1 1.8 0.9Finland 3.3 4.8 1.4France 5 23.7 4.8Great Britain 5.3 25.3 4.8Germany 6.6 14.8 2.2Greece 0.4 26.8 62.3The Netherlands 1.7 5.8 3.4Italy 4.3 7.8 1.8Japan 3.1 5.8 1.9Korea 1.2 4.5 3.6Mexico 0.4 1.7 3.9Soviet Union 16.9 30.9 1.8Spain 0.5 2.7 5.1Sweden 4.5 21 4.7USA 17 37.9 2.2

Median

But?

Are there other effects• Boycotts?• Have times changes?• Averages (medians) over 100 years?• Countries interested in sport

– Get better at sport– Bid for host city

Percentage of available medals won at home and away by host countries at Olympic games 1960-1976, 1988-1996.

Country Percentage of available Ratio medals won Home:Away

Away HomeItaly 3.1 7.8 2.5Japan 3.7 5.8 1.6Mexico 0.2 1.7 8.6Germany 6.7 6.7 1Canada 1.3 1.8 1.4Korea 1.3 4.5 3.4Spain 0.7 2.7 4.2USA 15.8 12 0.8

Comparison of percentage of available medals won by host countries at home and in the Olympics before and after home games.

Year Country

Average of performance in games before and

after being host Home performance Ratio

1896 Greece 11.4 38.5 3.41900 France 13.4 37 2.81904 U.S.A. 14.7 84.4 5.71906 Greece 19.9 15 0.81908 Great Britain 12.2 44.9 3.71912 Sweden 11.1 21 1.91920 Belgium 1.4 8.1 5.61924 France 7.9 10.4 1.31928 Netherlands 2.4 5.8 2.41932 U.S.A. 15.8 29.9 1.91936 Germany 5.6 22.9 4.11948 Great Britain 3 5.6 1.91952 Finland 4 4.8 1.2

Percentage of total medals won by Australia

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Comparison of percentage of available medals won by host countries at home and in the Olympics before and after home games.

Year Country

Average of performance in games before and

after being host Home performance Ratio

1956 Australia 3.6 7.5 2.11960 Italy 5.4 7.8 1.41964 Japan 4.3 5.8 1.31968 Mexico 0.2 1.7 9.31972 Germany 5.7 6.7 1.21976 Canada 3.6 1.8 0.51980 U.S.S.R. 19.1 30.9 1.61984 U.S.A. 14 25.3 1.81988 Korea 3.6 4.5 1.31992 Spain 1.3 2.7 2.11996 U.S.A. 13.3 12 0.911.8 1.0

Percentage of gold medals won by host countries

Country YEARGold medals won as

Percentage of total won

Perc

Average away percentage of gold medals

Greece 1896 21.3 27.8France 1900 28.4 31.1U.S.A. 1904 33.6 43.1Greece 1906 23.5 27.8Great Britain 1908 38.6 23.5Sweden 1912 36.9 29.3Belgium 1920 40 23.2France 1924 34.2 31.1Netherlands 1928 31.6 20.8U.S.A. 1932 39.4 43.1Germany 1936 37.1 27.9Great Britain 1948 13 23.5Finland 1952 27.3 35.1

Percentage of gold medals won by host countries

Country YEARGold medals won as

Percentage of total won

Perc

Average away percentage of gold medals

Australia 1956 37.1 29.9Italy 1960 36.1 38.8Japan 1964 55.2 26.4Mexico 1968 33.3 12.4Germany 1972 32.5 27.9Canada 1976 0 24.7U.S.S.R. 1980 41 39U.S.A. 1984 47.7 43.1Korea 1988 36.4 11.6Spain 1992 59.1 14.7U.S.A. 1996 43.6 43.1

Original Conclusion

• Large random element in the performance of countries in the Olympic games.

• Percentage of available medals won is a better measure of a performance than the number of gold

• The home team wins more medals than expected on adjacent games performance (1.5 times?)

• The home team usually wins a richer mix of medals (more gold) than when away.

But??

• Is HA decreasing with time?• Does it depend on other factors

– the hemisphere of the host nation.– success rate of country– team or individual sport– the actual event

• Press only wanted prediction of Australian medal tally

How many medals for Australia in Sydney?

• Science becomes guesswork – At its last home Olympics, Australia gained 7.6% of

available medals, twice the percentage they achieved in the games immediately before and after Melbourne.

– However the isolation of Melbourne in 1956 resulted in a low number of athletes attending, and the games were also weakened by two boycotts

– In Sydney Australia was coming off a strong performance in Atlanta of nearly 5% so to expect a repeat performance of their last home games effort might be optimistic.

How many medals for Australia in Sydney?

• There is also strong evidence that the mix of medals is richer for the home teams, so Australia can expect to win a proportion of the gold medals greater than both their long term average of 30% and the actual percentage available at Sydney.

• In making predictions there is always the effect of randomness. Canada, a country similar to Australia , won no gold medals at the Montreal games.

Prediction

• 5% of 910 medals = 46• 7% of 910 medals = 64• 9% of 910 medals = 82 (record 41 in Atlanta)

• 33% of 46 = 15 gold• 33% of 64 = 21 gold (record 13 in Melbourne)

Prediction

Conclusion

• Simple statistical analyses can provide reasonable estimates.

• Many other variables could be taken into account in predicting medal tallies.

• Randomness means accuracy as much a result of good luck as good planning

Conclusion

• Athens?

• Beijing?

• Over to you, or your students

Statistics can demonstrate a Home advantage in the Olympic games

Stephen R Clarke