How equal is equal? Discuss (in ten thousand articles or fewer)

Everyone seems to love writing about equalisation in the AFL. That’s the only explanation that I can find for the articles here (vague speculation), here (AFL corporate line), here (AFL corporate line, part two) here (inflammatory rhetoric), here (inflammatory rhetoric, part two), here (my club has worked bloody hard to get where we are you bludgers), here (no actual news), here (a discussion of the goals of equalisation!), here (finances), here (excellent, excellent, excellent article… also the author has a black belt in karate), here, here, here, and, although the author seems a little confused re what his actual topic is, here.

And in all this writing, no-one seems prepared to take a stab at proving that a lack of equality actually exists. There’s plenty of discussion of money, but no evidence is provided that financial disparity creates on-field disparity (it seems likely that it does – but no-one challenges the assumption).

There are all sorts of potential measures for this, and I suspect I may be a little distracted until I’ve tried quite a few of them. This first graph shows confidence intervals (all intervals in this post are for 95% confidence) for the average game margin for the last 10 seasons. (Note that season 2013 data in the below and all following graphs excludes the last month – this has been on the backburner for a while.) Some evidence there, perhaps, of recent instability?

1 - confidence intervals 2004-2013

The second graph broadens the study out (by quite a bit, really), showing margin confidence intervals by decade going back to 1914. Did we miss a whole lot of great football in the nineteen-teens? Maybe great-granddad wasn’t lying when he said it was better back then. And the zenith of inequality / nadir of equality / thing that sticks out is 1994-2003, just after the dawn of the national competition.

2 - confidence intervals decades 1914-2013

But hold on. Football was a different game a hundred years ago. When commentators go on about the speed of scoring in “modern day football” (well, not commentators, mostly just Brian Taylor), the corollary is the slowness of and lack of scoring in “olden day football”. The average team score in 2012 was 92; in 1914 it was 60. Obviously, lower scoring overall will depress the average margin; the graph below adjusts all the data to take that into account. The 2012 data is used as the benchmark; for example, the 1914 data is multiplied by approx 1.55 to bring it into line with 2012. This paints a slightly different picture – inequality is at the upper end of where it has historically been.

4 - adjusted confidence intervals decades 1914-2013

Finally, a graph of the same data, but compiled into ten-year rolling confidence intervals. An imaginary horizontal line through the data around 34.5 stays within the intervals until the mid-1970s – meaning, no ten-year period in the last forty years can be differentiated with 95% confidence from any other ten-year period, with respect to adjusted margin.

4 - adjusted ten year moving average

So, if the game on the field is as competitive as it’s ever been, what’s the problem? The assumption built into that question, though, is that this is actually a useful measure – there are any number of other metrics that could be used, such as shares of finals appearances and premierships, overall proportion of “close” games (defined however you like – under 30 points? under 20 points?) or the Noll-Scully measure, of which more in another post.

Obviously, the really large beltings that happen from time to time put a significant skew on this data – or do they? A study using median margins, or excluding a proportion of the data at the extremes, may tell a different story – but, as 10:30pm approaches, it will need to be a story for another time.

h/t to AFL Tables, the most accessible site for AFL data that I’ve found.

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