The statistic of interest here is median absolute deviation (MAD), which is a measure of variability. In this case, we’re calculating a MAD value for each skier and each season on their percent back results. So each skier get a MAD value for each season they compete in that measures how variable their results were.
In my previous post, I just compared the distributions of these values for XC and biathlon skiers, showing of course that biathletes’ results are considerably more variable. My commenter wanted to know if these values have changed much over time.
What I actually did is to plot some quantiles of each distribution over time, and extended the time frame back to 1992 or so. What this means is that each line represents the trend for a particular quantile over time. For instance, the middle line for both XC and biathlon represents the median, or 50% quantile. The quantiles plotted are 10%, 25%, 50%, 75% and 90% (10% is the bottom line, 90% is the top line).
Graph below the fold:
Obviously, these values do bounce around a bit from year to year. However, I’d say that for the most part they’ve remained fairly stable. It looks to me like the XC men might be seeing a slight decline is variability over the last 4-5 seasons, and conversely the women may be seeing a slight increase. These changes are very minor, though.