Following methods used to estimate home advantage in team sports, Ray Stefani examines past Olympic home nation medal counts to estimate the home nation advantage and predict the number of medals to be won by Great Britain in the Summer Olympics in London, 2012.
HOME ADVANTAGE IN SPORTS
Even a casual sports fan realizes that the home team has an advantage, much of it created by that same fan. Fervent fans enthusiastically support every movement of the home team and criticize every adverse call by a referee. Naturally this affects the players and the results – though to different degrees in different sports.
A careful examination of home team win-loss record and margin of victory1 shows decreasing amounts of home team advantage in order for rugby, Association football, Australian Rules football, American professional and college football, hockey, and baseball. National identify in international sports and territorial identity in domestic competition accentuate home advantage in Association footall2. There are three main home team effects in team sports1,2: physiological, where the home team has traveled less far and is less fatigued; psychological, due to crowd support and territoriality pride; and tactical, in that the home team is more familiar with the playing conditions.
The home nation athletes in Olympic competition will clearly have all of those advantages. The host nation has yet another advantage: strength in numbers. The host nation is given automatic qualification in many sports that the nation might not otherwise have entered. Further, the national fervor following the awarding of the games may encourage many more athletes to enter competition than might otherwise have been interested, and elite athletes will try that much harder to make that country proud.
EVALUATING HOME NATION OLYMPIC MEDAL ADVANTAGE
How great is that effect? Table 1 below contains medal data for the last 12 fully attended Games (1956 through 2008, excluding the boycotted 1980 and 1984 Games). The first data column shows the total medal count (gold, silver and bronze) of the host nation (which we can refer to as y) while the second column of data shows that same nation’s medal count four years before being host (which we can refer to as x). The third column shows the host nation’s medal increase, y – x. Only one host nation won fewer medal at home than four years before. The USA won seven less medals in Atlanta in 1996 than it did in 1992 in Barcelona. The other host nations made four-year gains varying from three for Greece in 1996 to 37 for China in 2008.
The loss of seven medals for the USA at home cries out for an explanation, which is likely political in nature. In 1988, East Germany competed for the last time as an independent country. The top three medal winners were the Soviet Union (132), East Germany (102) and the USA (94), for a total of 328 medals in the 241 medal events. In 1992, the Soviet Union competed for the last time as a unified country. The top three medal winners were the Soviet Union (111), the USA (108) and Germany (94), for a total of 313 medals in the 270 medal events. In 1996, the constituent republics of the former Soviet Union competed as separate nations, each with their own Olympic team. That meant that the total number of elite athletes increased, chasing about the same number of medals as in 1992 (271 medal events in 1996 compared to 270 in 1992). Further, with the powerful Soviet Union no longer the juggernaut it had been, athletes from other countries could compete with more hope of winning medals. The top three medal winners in 1996 were the USA (101), Germany (65) and Russia (63) for a total of 229 medals, 84 fewer than the top three nations won in 1996. Arguably, it was increased competition that led to the USA winning seven fewer medals than in 1992. Notice that in 1996, the USA gained 22 medals on Germany relative to 1992, so there was a significant relative gain by the USA.
Two regression methods were applied to the y and x values in Table 1 to estimate the home nation medal advantage. First, what could be called a zero-order regression was applied to the model y = h + x + e. The goal is to find a single additive home medal advantage h, minimizing the sum of the squared errors e. Simply, h is the mean value of y minus the mean value of x, which, from the third data column in Table 1, gives h = 13 medals. The average absolute smoothing error was 7.7 medals.
Also, a first order regression was applied consisting of an additive h and slope term c for the model y = h + c x + e. Again minimizing the sum of squared errors, h was 14.5 and c was 0.95. The average absolute smoothing error was 7.6 medals. The two models had nearly the same form and errors. Had c been 1 with h = 13, the two models would have been identical. 88% of the variance was explained by the models. Now we can estimate the medals to be won by Great Britain in 2012.
LONDON 2012 AND BEYOND
By simply adding 13 medals to the 47 won in 2008, Great Britain is projected to win 60 ± 11 medals. Using the first order model instead, Great Britain is projected to win 59 ± 11 medals, nearly the same. Table 1 shows another benefit of being the host nation. The average host nation won seven fewer medal four years after being host, which was six medals more than four years before being host. That residual gain is likely due to the continuing benefit of infrastructure built for the Games. Also, many of those additional athletes enticed into competition by the Games remain in competition four years later.
Ray Stefani is a professor emeritus at California State University, Long Beach with over 40 years of experience at sports performance analysis.