Olympics and participation

If I don't post my Olympic medal plots soon, I'll have wait four more years to make it as relevant. Also my coach John Lofranco was hoping to see this stuff months ago. Life things happened, but at last here they are. Nothing do I hate more than sitting on perfectly good data.

First off, what am I talking about? I posted a while back my thoughts about Olympic standards being too high for Canadian track and field athletes. I believe that if Athletics Canada renounced their A+ standards, and allowed more athletes to participate, it would increase our overall chances to medal. I would say this is intuitive in the sense that lower standards automatically means more athletes, which in turn allows for surprise wins to occur. No more surprising than buying more lottery tickets earns better odds of hitting the big jackpot.

My approach, or how I want to tackle the relationship between 'lowered standards' and 'medal count' is as follows: disregarding the fact that the Olympics are officially hosted by cities and not countries, countries of that host city do get automatic entry into most events. Great Britain, along with every previous 'host' country, has taken full advantage of this rule and sent more athletes than years before or since. See the graph below:

Number of participants for host countries the four years before and after they hosted the summer Olympics, as well as the Olympics thereof. Note the missing entries in 1976, 1980 and 1984 for Canada, USSR and USA, respectively, due to the two boycotts.

Without exception, i.e. in every single summer Olympics games, the host country has had more competitors than either the four years before or since. This year, 2012, Great Britain has athletes in all 26 olympic events. But the one exception to this automatic entry is athletics, where "the British team did not receive any automatic places for representing the host nation, as they had done in other sports".

Many national track and field committees (including Canada's) impose the A and B standards, or worse, upon their athletes. The IOC rules permit a country to enter one male and one female athlete for each track and field event, hence no country can be completely shut out. Somehow many countries, often rich ones, continue to not send the maximum number of participants.

Thanks to the free entries in most events, there is an opportunity to compare both overall and specific medal counts based on these entries. Below is a normalized plot of medals taken in by the host country (by normalized I mean the % of total medals available to be won):

 Here is the same plot again in logarithm form:

I choose to make the y-axis a percentage and not absolute to compare earlier olympics with more recent ones, where many events have been added. What can be seen, clearly I hope, is that more athletes means more medals. In 15 olympics there are only two narrow exceptions: the USA won comparatively more medals in Barcelona than Atlanta and Finland won comparatively more in London '48 than at home in 1952. Otherwise the trend holds true.

I compiled a list of host countries showing the percentage increase in medals (with respect to previous year) versus the increase in athletes. The black line has unity slope; points above the line are host countries that got more medals than expected and those below got fewer. The point at 450% is Spain, who went from 4 medals in Seoul '88 to 22 in Barcelona '92. Any point occupying the first quadrant {x > 0, y > 0} is a positive correlation, which herein is all but one point (USA, Atlanta games '96).

Another way to look at the data is a cross section of one year. Below is the Beijing 2008 medal count (for all medal-winning countries) plotted against the number of athletes sent per country. There is a 'hockey stick' shape to the relationship: below about 32 athletes the chances of winning a medal collides to near zero. This probably has to do with quantized nature of medals. I labeled a few prominent countries:

But here is the same plot of athletics, which is a little less consistent but some of the same basic principles still hold. (I used absolute here as total athletic events changes very little from one olympic year to the next)

Yet still there is a link between participation and medals won. Though weaker than the earlier plot of total medals, I would say athletics is still important to have as many competitors from your country as possible. 

Athletics only medal comparison: medals won vs athletes sent

Sometimes the host country does not win any medals in athletics, such as Japan, Mexico, and South Korea. For those countries that win some medals, there is still some positive trending between having more athletes and more medals. It helped make a difference for Australia (1956), Italy, West Germany, USSR & US (which count for less due to boycott), Spain, and Greece. The Chinese, US in Atlanta and Aussies certainly did OK while hosting.  

Although I cannot argue that more athletes definitely wins more medals, there is a the positive trend nonetheless. There is a chicken-and-egg problem lurking here: perhaps only potential "winning" athletes are sent to the olympics and any positive correlation is a self-fulfilling prophecy. I don't disagree with this notion, but consider another way of looking at this data: wealth.

Here is a plot of every single country entered in the Beijing games based on number of entrants and their wealth. I divided them into three groups of countries: green = population less than 1 Million, black = between 1 and 50 million, and orange = grater than 50 million people). Canada is coloured red. The closer you are (as a country) to the upper right, the better. Note that smaller countries tend to send comparatively more athletes relative to their population, however there is plenty of overlap.

The number of athletes sent is shown as a function of their countries' wealth. This plot is set to a log-log display. Depending on where you live, you may have many-orders-of-magnitude better chances to enter the olympics ranging from less than 0.01 per 100,000 (India) to 30 in 100,000 (Tuvalu). This graph includes almost every country in attendance and the trend is definitely positive: More wealth usually means more athletes. And more athletes means more medals, as seen above.

Now look at athletics only, where I have lumped together all countries above 1 million persons:

The trend between wealth and athletes sent, though still positive, is much weaker.  Canada is buried deep inside the cluster despite being one of the richest countries in the world. If counting metals and not participation, as plotted below, money is now an especially weak predictor of overall success. The two richest countries on the list, US and Norway, do not collectively surpass poorer competitors by any severe margin. 

I am not doing the potential of many of these graphs justice and there is a much more data that could be discussed here. What I surmise, however, is that money does not buy medals in athletics but it helps in overall, and athletic, olympic participation and attendance. Many sports have expensive equipment, but athletics is based mainly in human capital, i.e. participation and quality coaching (which isn't necessarily cheap, oddly). I consider countries like Kenya, Jamaica, and Ethiopia to be a good examples of this disparity: money is not in large supply (GDPs of 1700, 9000, and 1100 USD), but enthusiasm is high, coaching is well-executed, and the results speak for themselves.  

The take-home message is that participation, even at the highest levels, cannot be a neglected factor. By contrast, arguing that restricted participation (by enforcing higher standards) does not do anything but limit chances in overall medal hopes. I would be interested to hear any counter-arguments on this final point by Athletics Canada.