Friday, August 17, 2012

Olympics 2012 - Another Perspective - I

Courtesy: Geograph
Number Games

Which country did best in London Olympics 2012? Does bigger countries play more sports than smaller ones? India performed its best ever in Olympics, but was it really best performance? We would try to answer all these questions with a pinch of statistics and I bet, answers will surprise you.

Olympics is an interesting event, not just from perspective of sports but also from statistical perspective as well, for example, to compare relation between sports, population, and GDP. If you take Cricket World Cup or FIFA World Cup, you get a skewed comparison because very few countries play cricket and in case of football, many countries might have competitive advantage in some other sports giving a wrong interpretation of data.

However, unlike Cricket World Cup or FIFA World Cup, we get a wider representation of countries and sports in Olympics allowing for a rather fair comparison.

Secondly, looking the medal tally, we cannot judge a nation's sports spirit because of varying factors such as population and economy. Here, I have tried to plug in those numbers and rank nations in a more justifiable way.

Finally, while the news papers are full of the wonderful performance of India and while the social media can't stop cheering the athletes even after the event is over, it is worth to introspect and find out where we actually stand and whether we are game for the games.

Let's get started with the basics stats of London Olympics 2012.

Maximum Number of Participants: Great Britain - 541 athletes
Maximum Number of Medals: United States - 104 medals
Most Populous Nation: China - 1.35 bn people
Wealthiest Nation (GDP Per Capita - PPP): Liechtenstein - 141,100 USD

Now, the more interesting (and more complex) stats.

Population Per Participant / Athlete Density: This number is the total number of participants divided by nation's population which gives an idea about how popular sports is in the given nation. In a populous country like China, there would definitely be many athletes and they would rank higher, but if you find higher density of athletes in nation, it implies people play more sports there. As the title suggests, it is simply the number of citizens out of which we would get one athlete.

Best Athlete Density: Cook Islands - 2224 people per athlete.
Worst Athlete Density: Bangladesh - 30,503,603 (3 mn) people per athlete.

What about India? It's third worst, 14,580,644 (1.4 mn) people per athlete, right above Bangladesh and DR Congo.

Correlation Coefficient - Population and No. of Participants: 0.3439

This number signifies the linear relationship between population and no. of participant of the nations, whether more populous nation field more athletes or not. The short answer is yes, they do. For the long answer, let's understand correlation coefficient first.

Basically, it tells us how two variable are related to each other. This coefficient may have value between -1 to +1. A value of -1 would mean that the variables are inversely correlated, i.e., if one goes up, the other goes down in the same proportion. Similarly, a value of +1 would mean that the variables are perfectly correlated, i.e., if one goes up, the other goes up in the same proportion. What about zero? Well, that means the variables are independent of each other and there is no correlation. Values in between -1 and +1 represents all the shades of correlation in between.

A value of 0.3439 would mean that there is a correlation, but not a perfect one (value of +1). In other words, even though populous nations have more athlete but not as much as less populous nations do when you take their populations into account. In other words, athlete density is more in less populous nations. In yet other words, people play more sports in small countries.

Population Per Medal / Performance Density: Population per participant gives us an idea about popularity of sports in each nation, but it fails to show how good the athletes are in sports. Pupulation per medal shows how good the nations are in the sports. The logic is that a tiny nation winning one medal should be ranked higher than a nation hundred times its population that has won ten medals. Here, we can only compare the 85 nations that has won medals out of the 204 participanting nations. The reason is simple, we cannot compare hair color of two bald people, can we?

Best Performance Density: Grenada - 105,000 people per medal.
Worst Performance Density: India - 201,698,903 (20.1 mn) people per medal.

What about the brouhaha surrounding India's wonderful performance? Well, looking at the athelete density and performance density, all one can make out is that it indeed is brouhaha. We are a nation of spectators and not players. We just want others to play the game and move our bums only when ordered to do so. India would definitely top the medal tally if the Olympic folks consider watching games 24/7 a serious game in itself. Until then, we gotta be content being first from the last.

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