The first task for this week was to create a model to estimate the probability that one finalist should beat another using only the knowledge of which team was at home and the competing teams' MARS Ratings. Fitting a binary logistic to historical data produced the following model:
Prob(Home Team Wins) = logistic(0.446518 + 0.034125 * Home Team MARS Rating - 0.034161 * Away Team MARS Rating)
Applying that model to the most recent team MARS Ratings yields the following team-versus-team probability matrix:
(Note that, using the fitted model, the probability that Team A defeats Team B when Team A is at home is not the complement of the probability that Team B defeats Team A when Team B is at home.)
Based on the early head-to-head prices for the weekend's Finals, it would seem that MARS rates the chances of the Hawks, Swans and Roos more highly, or rates the chances of the Crows, Pies and Eagles less highly (or both) than does the TAB Bookmaker. It also appears to rate the Cats' and Freo's chances about the same as does the TAB Bookmaker.
Using this probability matrix to simulate the 2012 Finals series 1,000,000 times yields the following team-by-team probabilities:
Comparing the probabilities in this table with the prices on offer at TAB Sportsbet suggests that the only wagers currently offering a positive expectation are for Hawthorn to win the Flag (28% edge) or to make the GF (11% edge), and for Sydney to win the Flag (5% edge) or to make the GF (24% edge). No other wagers on the Flag or Make the GF markets are worthwhile.
Based on these simulated results the only TAB GF Quinella prices offering value are Hawthorn v Sydney at $5.50 (54% edge), Sydney v Geelong at $26 (40% edge), Hawthorn v Kangaroos at $67 (26% edge) and Geelong v Kangaroos at $501 (58% edge). No other pairing has a positive expectation.
The top half dozen most common simulated GF pairings combined represent around 80% of total probability, which means that the remaining 20 potential pairings amongst them account for only 20% of total probability.
(Note that there are only 26 possible GF pairings not 28, because two possible pairings, those reflecting the Elimination Finals, cannot occur in the GF.)
As an interesting exercise, this week I decided to investigate the importance of teams' final ladder positions on their Finals aspirations. To do this I imagined that the teams in the top 8 had finished in a randomised order but with the same MARS' Ratings and hence probabilities of victory against any specified opponent.
I then simulated 1,000,000 Finals series, randomising the order for the top 8 teams for each simulation, and determined that, with randomised team order but with preserved team Ratings, the Flag probabilities would become Hawthorn 39% (down from 57%), Adelaide 6% (no change), Sydney 18% (no change), Collingwood 8% (no change), West Coast 8% (up from 2%), Geelong 13% (up from 8%), Fremantle 3% (up from 1%), and the Kangaroos 4% (up from 1%). Randomisation, it seems. serves mainly to redistribute probability from Hawthorn to the teams that finished in ladder positions 5 through 8.
The summary of this exercise if that, no matter where the Hawks had finished in the eight, on the basis of their MARS Rating superiority they'd still have been Flag favourites. Similarly, the Swans would have been 2nd-favourites regardless of their ladder finish, with Geelong, Collingwood, West Coast and Adelaide all forming the next tier of the market, Geelong foremost amongst them because of its superior MARS Rating. Not even randomisation of ladder finishes could substantially elevate the Flag potential of Fremantle and the Roos however.