*Ahem*
There are two kinds of statistics, descriptive statistics and inferential statistics. What Joe is talking about is descriptive statistics. A statistic is a number that summarizes some interesting property of a collection of numbers. Joe’s average (aka arithmetic mean) describes what happened. These averages can be used to compare one skater to another, to set a bench mark for next year, etc. – or just to provide some interesting data to think about.
There are some other statistics that might also be interesting, such as standard deviation (which skaters are more consistent than others?) or progression of scores from the beginning to the end of the season (who had momentum, who peaked at the right time?)
The main use of “season’s best” is, in my opinion, to give individual skaters, especially at the lower levels, a mark to measure their individual progress by.
The other kind of statistics is inferential statistics. This is what Buttercup is talking about. In this topic we take the numbers before us as a sample of data from which we wish to infer properties of the population of data from which the sample was drawn. If we try to use these average scores to predict the results of future competitions, for instance, this is inferential statistics. The reliability of such predictions depends on many factors. Some of them have been mentioned on this thread: the sample size is too small, the variance is too big, judging may not be consistent, a skater had one bad competition that threw the average off – all of these things cause both random and systematic errors that cast doubt on the validity of our conclusions.
So IMHO there is nothing really to argue about. The average season scores have interest in their own right, but no claim is made about making predictions based on these numbers.
