In the Wooden Finger Depot’s AFL Power Rankings, the more recent a game is the more weight it carries. But some might think that recent games do not carry enough weight; for example, it took a while for the rankings to recognise that Port Adelaide and Essendon (until recently) had stepped up this season, and that St. Kilda, Adelaide, and West Coast had taken a step back. What would happen then if recent games were given even more weight – what if an exponential function was used to assign weightings instead?
In the rankings, each of a team’s past 22 games is given a weight. Currently, the weight is a linear function of how recent the game is, as shown in the graph above (most recent games are on the right). To derive an exponential function, I made the arbitrary choice to reduce the weight on the least recent game by a quarter, and then found the multiplicative factor that got the weights to add up to 1, give or take .0005.
What happens to the rankings after I do this? Well, essentially, what you get is an indication of which teams have hit form over the past few weeks. In general, and not surprisingly, the teams that have been in form over the past few weeks are also the teams that have been in form over the entirety of the season; that is, the exponential rankings are not too different from the ordinary linear rankings. But there are some big changes; the Western Bulldogs have been a much better team recently than they have been over the long haul (up in Carlton/Adelaide/Port Adelaide territory), while Essendon has been much worse (essentially not too much better than St. Kilda).
I’m going to stick with the good old linear weights, but what do people think? Do the exponential weightings look like they give a better indication of where teams are at?