With six rounds remaining in the regular home-and-away season, I thought it was time to start projecting the likely finalists and searching for value in the TAB's AFL "Futures" Markets (as it likes to call them).
For this purpose, first of all we need a model to predict the victory margin for all remaining games.
This year I've enlisted the help of Eureqa to come up with this model by using it to fit the victory margins of every game from the start of the 2008 season to the end of Round 17 of this year, using as predictors the competing teams' MARS Ratings and Venue Experience, as well as the Interstate Status of the clash. I opted for one of the simplest equations that Eureqa offered:
Predicted Margin = 0.7676 x Home Team MARS Rating - 0.7594 x Away Team MARS Rating
This equation, parsimony personified, explained over one-third of the variability in game margins over the period on a hold-out sample created automatically by Eureqa. It manages to incorporate a small home ground advantage by providing a slightly larger coefficient for the Home team's MARS Rating than for the Away team's, equal to a little over 8 points for a game involving two teams Rated 1,000.
Applying this model to the remaining games using teams' current MARS Ratings yields predicted margins as per the following table (please click the image for a larger view).
To simulate the outcome of each of these games we need to introduce some variability, which we do by assuming that the result of every game is distributed as a random Normal variate with mean equal to the predicted margin shown here and a standard deviation of 36 points per game.
(If you perform a few site searches here on MAFLOnline you can find posts where I've discussed the reasonableness of the Normal assumption and variously estimated empirical values for standard deviation.)
All that's left to do then is to simulate the outcome of all remaining games in the season, tot up what this means for each team's final ladder position and then repeat this 10,000 times. Because I'm simulating margins and not actual team scores in each game I can't determine each team's final percentage, which we'll need of course when teams finish tied on competition points.
What I've done instead is to use teams' points for and against difference (a la Rugby League) instead of their percentage to break ties. Almost always both methods will provide the same ranking for teams tied on competition points. On a very technical point, in those rare instances where teams in a simulation finish tied on competition points and tied on the points for and against differential, I've broken the tie at random.
Here then are the results, firstly in graphical form:
For a few teams - namely GWS, Melbourne, St Kilda and the Dogs - simulated final ladder positions fall into a narrow range. GWS has the narrowest range of all, and is assessed by the simulations as having virtually no chance of doing anything but collecting the Wooden Spoon. That opinion is shared by the TAB Bookmaker as evidenced by his unwillingness now to frame a market for this particular outcome.
Other teams' futures are full of opportunity, most notably Adelaide, Port Adelaide and West Coast, all of which have three almost equally-likely potential final ladder positions.
Here's another way of presenting that same data, here as a heatmap where the deeper the red, the larger the proportion of simulations that wound up with that team finishing in that ladder position. White cells indicate combinations of team and ladder position that occurred relatively infrequently.
From a wagering perspective, the probabilities that matter are those for a team's coming 1st, somewhere in the Top 4, or somewhere in the Top 8. The following table contains these probabilities.
Combined, based on the simulations, the probability of one of Hawthorn, Geelong or Sydney taking the Minor Premiership is about 97%. Only three other teams finished 1st in at least one of the 10,000 simulations, Essendon most often at about 3% of the time. Based on current TAB prices none of those teams represents value in the Minor Premiership market.
In the market for Top 4 positions, however, Essendon offers value at its current $2 price. They are one of eight teams that finished somewhere in the Top 4 in at least one of the simulations, though Carlton and Collingwood did so only very rarely, and Richmond did so only about 1 time in 16. Essentially, the simulations suggest, therefore, that the Cats, Hawks and Swans are virtual certainties for Top 4 finishes, and that the Dons and Freo will fight for the remaining place, with Freo currently the narrow favourite.
Adelaide, who are priced at $8, are the only team offering value in the market for places in the Finals. They are one of 14 teams that finished with a Finals berth in at least one simulated season. Here the simulations suggest that seven teams - Collingwood, Essendon, Fremantle, Geelong, Hawthorn, Richmond and Sydney - are all 90% or better chances to participate in September activity, and that only three other teams - Adelaide, Carlton and Port Adelaide - are anything but remote chances to take the remaining spot. Amongst those three teams, Carlton is the overwhelming favourite to snatch the final ticket to the Ball.
As I did last year, I'll track the performance of the wagers I highlight in these blog posts as representing value, on the assumption that each is level-staked.