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At the moment New Zealand is doing well at the London Olympics. As of this morning, we're ranked number 14 in the medal table (yeah, that means ahead of Australia). There are all sorts of other ways to rank this too. Crude ways to look at medal tallies include relating it to population (in which case we look fantastic) or to GDP (drop a few places lower).

The problem is that a lot of these ways are crude. This relates to a host of factors. First up, how we rank countries isn't based on the total number of medals. Australia has got (as of today), 1 gold and 12 silver. NZ has 3 gold and 0 silver. The ranking-system means that 1 gold medal always beats 1 silver…or 10 silver…or 100 silver. Gold medals are really nice to have. Gold medals should count for more than silver. It's just hard accepting that no amount of silver medals would ever equal a gold.

The second problem is that medals aren't statistically independent of each other. In some sports the ability to win a gold medal in one event, is strongly linked to others. A good example is sprinting. If you are an Olympic-class sprinter, then the odds you can win gold medals in the 100m, 200m, 400m, 4×100 relay and long-jump are actually linked. Jessie Owens proved it at Berlin. Carl Lewis proved at Los Angeles. These are events that use similar physical aptitudes. Conversely, there's less options with boxing or long-distance running. You'll notice that Marathon runners don't come back with a bag of medals. The events you compete in, give different medal tally distributions.

There are some general things that do affect medal-tallies. Population-size is one of them. It's not a precise line up, but if we imagine the distribution of athletic talent follows some kind of bell-curve, then countries with big populations will have a larger upper tail to recruit athletes from. This isn't a simple translation of population to medals. To be a top athlete also requires motivation (it's not obvious that this is linked to GDP, athletic prowess can be a path out of poverty to some). It also requires both training and exposure to top-level competition. So this might be linked to GDP. Nonetheless, it doesn't have to be. In fact, the enormous variation in medal performance linked to GDP, suggests this is a poor way to predict or explain sporting success.

In the end and irrespective of the ways we measure success at the Olympics, I am enjoying the gold-medals we've been accumulating. We're doing well :)