Why have winning times improved?
The most commonly held explanation for the improvement in gold medal performances is that training programmes for athletes have themselves improved and intensified.
However there is a second reason why the gold medal performances have improved. In the first dozen or so modern Olympic Games, there was a small pool of people who were wealthy enough to train and compete, whereas in more recent games a far greater proportion of the world's population would be trained and sent if they exhibited potential in their sport.
A model for the improvement in winning times
The consequence of the increasing pool of potential competitors for the winning performance is demonstrated below. We assume that a characteristic in the world population has a normal distribution with mean 12 and standard deviation 2.
The diagram shows the abilities of a sample of 100 people from this population. The ability of the best person in the sample (the winner!) is shown at the bottom.
Click Accumulate then click Take sample a few times to build up the distribution of the winner's ability.
Now repeat with sample sizes of 1,000 and 10,000 and observe that the 'winner' usually has a lower value when the sample size is higher.
We therefore expect that the winning time in the 1500 metres at the Olympics will decrease as the population from which the competitors are chosen increases, even if the underlying population distribution of 'abilities' remains the same.