When last I considered the issue of the value of MARS Ratings across time I assessed their value in terms of a team's victory probability. Perhaps a more intuitive approach would be to, instead, value them in terms of a team's victory margin.
For this blog I'm going to use a very flexible - and highly non-linear - functional form for fitting the Home team's victory margin as a function of the MARS Ratings of the participating teams, viz
where MARSH is the MARS Rating of the Home team, MARSA is the MARS Rating of the Away team, and the other variables on the right-hand side of the equation are parameters to be optimised.
I fitted a separate model to each season's results and used R's optim function to find the optimal parameter values based on a squared-error loss function.
(For the curious, there's a thumbnail image at the end of this blog with the optimal parameters for every year. If you click on it you'll be able to view a larger version.)
Having fitted the 116 models, one for each season, I then proceeded as I did in the earlier blog, to estimate the value of Home Ground Advantage by calculating the predicted Home Team Margin for a game involving two teams with MARS Ratings of 1,000. I also calculated the value of 20 MARS Ratings points, here by calculating the predicted Home Team Margin for a game where a Home team with a MARS Rating of 1,000 meets an Away team with a MARS Rating of 980, and then subtracting from this predicted Margin the just-calculated Home Ground Advantage.
The conclusion from the previous blog that the value of MARS Ratings Points has been relatively stable across time is confirmed by this analysis. For almost the entire history of VFL/AFL, 20 Ratings Points have translated into an increased victory margin of between 10 and 20 points.
Home Ground Advantage has also been relatively stable, mostly tracking in a narrow range between 5 and 10 points.
ALL THE MODELS
Please click for a much larger version.
(If you're also curious about the efficacy of the fitted models, the mean absolute prediction errors (MAPEs) for the past 5 seasons were:
- 2008 : 30.46
- 2009 : 28.19
- 2010 : 30.08
- 2011 : 30.18
- 2012 : 30.87
The season-average MAPE for the period 1980 to 2012 is 31.32 points per game.
So, the models are clearly adequate if not stunning.)