Like many Victorians, I watched a telecast of the AFL Grand Final with some mates at a barbeque. It was slightly surreal. After about thirty seconds of stunned silence, I think we came to the only collective reaction that made any sense. Never before, and not again for a very long time, will greet a grand final result with a chorus of laughter…
The second reaction was that Andrew Demetriou, the CEO of the league, would also have been laughing – all the way to the bank. According to news reports, the replay will be worth about $20 million to the AFL. By contrast, Cycling Australia must be ruing the lost publicity for the world road cycling championships in Geelong this coming weekend.
The drawn game is of course the ultimate in close grand finals, but the last decade has featured a number of highly competitive games. The 1990s, by contrast, were a decade of grand final blowouts, with not a single close grand final in it. But is this just chance, or is there something more systematic going on? Is there something about the tactics, the rules, or the competition structure – or indeed some combination of these things – that is affecting the closeness of the big day? To analyze this, I looked at the margins in Grand Finals since 1950.
There’s very little evidence of an overall trend over that time period. The trendline is almost horizontal, and the Pearson R2 is only 0.006. That is, less than 1% of the variance in margins is explained by the year in which the grand final occurs.
But all that shows is that there’s little overall trend over the period.
I asked an alternative question. The game’s tactics, playing personnel, and so on evolve from year to year. So, if there are long-term trends in the game that push grand final margins closer or further apart, you’d expect there to be some correlation between the margin in the grand final in year x, and year x+1. So I plotted that:
Each point on this graph represents a pair of grand final margins from consecutive years. The X axis represents the margin in year x, the Y axis represents the margin in the previous year.
If there was some connection between results, you’d expect the dots to cluster round some kind of line. But they’re all over the place. There’s no pattern at all.
Calculating a correlation coefficient confirms what’s obvious from just looking at the graph. There’s no connection whatsoever. The Pearson R2 value is 0.007. Less than 1% of the variation in grand final margins can be explained in terms of last year’s margin.
This analysis, as displayed, wouldn’t exactly pass muster for peer-reviewed publication. There are a whole bunch of other things you could do to try and extract a pattern, and I’ve tried a few of them. But every way I’ve looked at the data (and all the more statistically-oriented bloggers out there are welcome to have a shot with multivariate models if they wish), there doesn’t appear to be any discernible trends pushing towards or away from close grand finals. Our recent run of gritty struggles is just glorious chance at work. Let’s hope it holds for another week and we get a grand final replay as epic as Saturday’s first effort.
UPDATE: Regular commenter sg applies a more sophisticated time series analysis. He finds, like me, that there are no linear or cyclic trends. However, he does find one relationship: “Analysis of autocorrelation and partial autocorrelation functions (not shown) suggests that the serial dependence in this model is AR(2), that is the margin of victory in any given year is related negatively to the margin of victories in the previous two years, and very strongly to the previous year.”