This week, I've used the same methodology as I did last week, but expanded the number of simulations to 100,000, which means I've doubled the precision relative to last week's estimates (since four times the number of simulations provides twice the precision). It took about 7 hours to run the simulations, but that's a small price to pay for added precision (he offers, self-affirmingly ...)
Read MoreThis year I'm starting simulations for the Finalists a bit earlier than usual, partly as a result of a request from Twitter follower @SgtButane, who's another of the burgeoning group of AFL fans using statistical modelling techniques to forecast game outcomes. If you've an interest in this sort of modelling and you're not yet on Twitter, I'd strongly encourage you to sign up and start following like-minded people (I'm @MatterOfStats by the way). There's a tremendous amount of informed commentary and quality analysis being shared by some very talented people in this space.
Read MoreAfter Week 1 of the Finals, six teams are still capable of winning the Flag and nine Grand Final pairings are still possible.
Read MoreThis year, I think the trickiest part about forecasting the Finals series is deciding how relevant recent Finals history will be in the current season.
Read MoreThe Eagles' victory over the Dockers considerably enhanced their chances of taking out the Minor Premiership, though the Eagles' gain came at the expense not of their immediate opponents but instead of Hawthorn, whose loss to Port Adelaide all but ended their hopes of this minor honour.
Read MoreThe previous post here on the Simulations blog triggered an interesting exchange of comments with Rob that forced me to think a little harder about the appropriate interpretation of the results presented in that original blog post.
Read MoreImagine that the TAB Bookmaker was exceptionally good at his job and that his assessments of every game this season were what a statistician would label an "unbiased estimator" of the final result.
Read MoreThe ChiPS System, on whose opinions I've been basing this year's Finalist simulations, thought Fremantle would go down to the Eagles last weekend, and also that Hawthorn would win.
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Fremantle clearly increased its chances of taking out the Minor Premiership this last weekend in defeating the Saints while the Eagles went down to the Hawks. That said, the Dockers still face the Eagles as the home team at Subiaco, as well as the Roos and the Power as the away team, so they're not yet certainties, some in the popular press' views notwithstanding.
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Well that last weekend certainly changed things a bit
Read MoreThe latest round of simulations has one of Hawthorn, West Coast or Fremantle taking out the Minor Premiership in all but a handful of replicates, and Hawthorn collecting that prize about half of the time. I find it hard to imagine a time in recent history where a team 3rd on the ladder so late in a season is such an overwhelming favourite for this honour.
Read MoreLast weekend's results made the Hawks almost even-money prospects for the Minor Premiership and all but extinguished the Swans' already-slender hopes for that same title.
Read MoreI've been part of some interesting conversations this week on Twitter about definitions of "close" and "blowout" games of Australian Rules.
Read MoreEarlier in the week I posted the results for the latest set of Finals simulations and explored the interdependencies amongst team Finals fates, estimating how likely it was that Team A would make the Finals if Team B did or did not. In today's blog I'm going to analyse other dependencies, not between Team A's and Team B's Finals chances but instead between Team A's Finals chances and the results of each of the remaining games.
Read MoreAccording to the latest round of simulations using updated ChiPS Ratings seven teams' Finals' chances were materially affected by last weekend's results
Read MoreIt seems I'm projecting the likely Finalists earlier and earlier each season, but the competition is at such an interesting juncture that I thought this week might be the right time to start this year.
Read MoreAgain this week I'm providing a downloadable Excel spreadsheet so that you can make your own projections of the remainder of the season. The cells to change are the ones coloured yellow, which you should alter to reflect your opinion about the relevant probability for the listed game and winner.
The spreadsheet as downloaded includes the probabilities from the most recent update of the model I've been using to project the Finals this year. These probabilities, as you can see, suggest that Sydney are about 51% chances for the Flag, Hawthorn 37% chances, Port Adelaide 7.5% chances, and the Roos 4% rank outsiders.
Based on those probabilities and current TAB prices the only Flag market wager with a positive expectation is one on Sydney at $2.25.
This week, for the first time ever on MoS (or MAFL), you can do more than just rant at the inanity of my Finals simulations: you can download an Excel spreadsheet and make your own assumptions.
Read MoreAny statistical modeller looking to project the results for the 2014 season must address the fact that teams finishing higher on the competition ladder have won about three-quarters of the Finals played since 2000, a substantially higher proportion than home teams generally have won over that same period.
My own view is that this history represents a credible Bayesian Prior and, accordingly, the binary logit model that I've built to estimate the probability of victory of the team finishing higher on the competition ladder during the Finals series reflects this through the large value of its intercept term:
Pr(Victory by higher finishing team) = logit(6.81 + 0.0249 x MARS Rating of Higher Finishing Team - 0.0308 x MARS Rating of Lower Finishing Team)
One consequence of recognising the importance of ladder position is that the Swans' chances for the Flag are significantly bolstered, as evidenced by the following matrix, which details the team-versus-team probabilities that I've used for my Finals simulations, based on the binary logit described above.
These team-versus-team probabilities, used in 1,000,000 simulations, produce the following summary outcomes for the Finals series, especially for the last two weeks:
Based on these results, Sydney's Flag chances, currently priced at $2.75 on the TAB, represent the only value. A wager on them for the Flag carries a 30% positive expectation.
Looking next at modelled GF Quinella results we find that the most likely GF has the Swans pitted against the Hawks, an outcome eventuating in almost 37% of simulations. Barring that outcome, a Sydney v Fremantle GF is next most likely with a simulated probability of about 18%.
After that, the third-most likely GF sees the Hawks face the Cats. It turned up in about 1 simulated GF in 6, which makes its $9 TAB price tag seem quite profitable. It is, in fact, the only Grand Final Quinella with a significantly positive expectation.
A Swans v Hawks GF priced at $2.75 also carries a positive expectation, though the size of the edge is so small that it's not one I'd be willing to wager on.
(Two GF matchups are, by the way, impossible as a consequence of the Finals System that the AFL follows. These are the matchups of this weeks' Elimination Finals: Port Adelaide v Richmond and Kangaroos v Essendon.)
Normally I wouldn't bother simulating just a single round prior to the Finals, but this year it seemed like it might be an interesting exercise - even if for no other reason than to estimate just how likely it is that the Tigers will finish 9th.
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