June 30, 2005

Performance Legacy Due to Olympic Hosting

Sometimes in this space, I pass along news; sometimes, I add my own opinion. What I enjoy most, though, are the essays where I present some numbers that support or knock down a theory. I've taken to calling these posts "left-brain specials" since Ratch poked some good-natured fun at my tendency to over-analyze. You can see a list of my left-brain specials over to the right.

Usually, I try not to knock down one of my own theories. It's a little embarassing. But you can't always make the facts fit your theory.

A couple of weeks ago, I stated my opinion that hosting an Olympic Games, summer or winter, can have a large positive impact on a country's future Olympic performance. After I wrote that post, I realized that if I was right, it should be pretty easy to back up that statement with some facts. What if we looked at medals won by the host country, leading up to and following the Games that they hosted? If hosting had some lasting benefit, then it should show up in the data. And if it didn't show up in the data, well then I would have to change my story, wouldn't I?

What followed next is pretty complicated, even by my standards, and it would take quite a while to describe the details of what I did, but I'll see if I can sum up the most important points.

The study includes all the Olympics between 1948 and 2004, excepting as usual the heavily boycotted games in 1980 and 1984. The summer study includes only the 45 winningest nations (counting medals) during this period. The winter study includes only the 20 winningest nations.

The performance score I used was the medal fraction; that is, the number of medals a country won, as a percentage of the total number of medals available. This method was used to account for the fact that the number of Olympic medals awarded has increased dramatically since 1948.

Within each group (summer or winter) I used the nations that did not host an Olympics to establish a baseline trend. In other words, I wanted to know if medal scores, on average, increased, decreased, or stayed the same during this period. I used the nations that did host an Olympics to establish an average trend for the long-term impact of hosting.

Where nations were created, or destroyed, or boycotted, unified, or divided, I tried to be careful about how they were counted.

Figure 1

Figure 1 — Effect of summer Olympic Hosting 1948-2004

Figure 1 — The effect of summer Olympic hosting on performance, 1948-2004 (click to enlarge).

OK, now for the results. Inset at right you will see two graphs, one for summer Olympic hosting and one for winter Olympic hosting. Let's just look in detail at Figure 1, and I'll try to explain what it shows. The formats of the two graphs are identical.

Here's how we should read the results. On the horizontal axis, 0 (zero) represents the present, -4 represents four years ago, +4 represents 4 years in the future, etc. Nations that have not hosted the summer Olympics in the post-war era are represented by the blue circles. The medal fraction at -4 years is defined to be 100. Figure 1 shows that the medal score for non-hosting nations at 0 years is 99, and at 16 years is 87. What this means is that, on average, a non-hosting nation's medal share will be 1% lower at this Olympics than it was at the previous Olympics, and it will decrease by another 12% over the next four Olympics.

Nations that are hosting the summer Olympics in the present year are represented by the red squares. Again, the medal fraction at -4 years is defined to be 100. Figure 1 shows that the medal fraction for the current host is 190 in the host year, 121 four years later, and 89 four years after that.

Figure 2

Figure 1 — Effect of winter Olympic Hosting 1948-2004

Figure 2 — The effect of winter Olympic hosting on performance, 1948-2004 (click to enlarge).

The error bars on each curve should not be taken too literally, but the relative sizes indicate how many independent measurements are included in each data point; where the error bars are large, there are only a few countries contributing to a data point.

I think that there are two interesting conclusions that we can draw from the data. First, the "home-field advantage" of hosting an Olympics is much larger than I would have guessed. On average, the summer host benefits from a 90% increase in medal fraction; the results for the winter Olympics are qualitatively similar, although the host benefit is a relatively modest 63%.

The point of the study, though, was to try to quantify the long-term benefits of Olympic hosting. I am forced to conclude that the results contradict my original hypothesis. Figure 1 shows a slight benefit four years after hosting a summer Olympics, but beyond that the host and non-host curves overlap. Figure 2 shows a "host hangover" effect where the host nation actually does worse than you would expect from a non-host nation in the Olympics following the home games.

There is some hint that countries may get a long-term benefit from the run-up to the Olympics. Note that the host nation scores at -16 years are very low for both winter and summer sports. This supports the idea that a host nation obtains its host benefit in the 16 years prior to hosting, as it prepares for the big event, and that this improvement is then carried over into the post-host period. However, I suspect that this improvement is not real. Note that the scores at -20 years are actually quite good, in line with non-host performance. If the improvement from -16 years to -4 years is real, then what explains the dropoff from -20 to -16?

Figure 3

Figure 1 — Effect of winter Olympic Hosting 1948-2004

Figure 3 — The effect of Olympic hosting on Canadian performance (click to enlarge).

This is not to discount the fact that Canada's Olympic performance improved dramatically following its two home Olympics. Figure 3 shows the data for Canada alone, presented in the same format as the host nation data in Figures 1 and 2. In this case, the two different data sets represent Canada's summer and winter Olympic performance in the post-war era. The winter data are presented with 1988 as the present (0 years), and the summer data are presented with 1976 as the present (0 years). In both cases Canada has seen a dramatic and sustained improvement that followed a home Olympics. However, the overall data suggest that this does not hold for host nations in general. Either Canada has managed that advantage particularly well, or the timing of the performance improvement was a coincidence.


Anonymous said...

I think that you need to break your analysis down into pre 1984 and post 1984 blocks -- as the character of the Olympics changed substantially after the Uberoth (sic) LA Olympics... but other than that I love the Left brain analysis

Amateur said...

A valid point; but the numbers are so small that it's difficult to draw a strong conclusion.

I'll make a follow-up on this sometime in the next couple of weeks.