Last 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. They also lifted the Tigers' hopes of a Top 4 finish from about 12% to about 20%, and slashed the Swans' chances of a spot in that same elite group from 87% to 66%. In terms of Finals positions, they elevated the Crows' from 33% to 60%, lowered the Pies' from 73% to 63%, lowered Port's from 18% to 2%, lowered the Dogs' from 71% to 60%, and lifted the Giants' from 33% to 48%.

All of those assessments are from the latest set of 100,000 Finals simulations, this week using assumptions for the remaining games reflected in the matrix of probabilities at right. (See this blog entry for details of how these simulations are run).

[Ed: an earlier version of this table presented the expected wins excluding Rounds 20 and 21; Excel VLOOKUP errors - gotta love 'em. Thanks to eagle-eyed Rob for picking this up. This error has no effect on the remainder of the blog, the analysis for which was based on a far more trustworthy CSV with no formulae whatsoever.] 

Detailed assessments of each team's chances for a key ladder position and of which of those assessments represent value in the latest TAB markets, appear in the table at left. Prices shaded green in the right hand portion of the table are those where the implied edge is greater than 5%, and those shaded grey have an edge greater than zero but less than 5% (which means I'd pass on them as a wagering opportunity).

This week sees far more prices shaded green than was the case last week when only the Hawks' and Eagles' Minor Premiership prices earned this shade along with the Dogs' price to make the 8. So, either my simulations have identified a slew of lucrative wagering opportunities or my assessments of relative team strengths are poor. Only you can be the judge of that, but I would remind enthusiastic readers that my wagering Portfolio is down by 27% on the year ... 

In the next chart we see the number of times that each team finished in each position across the entirety of the 100,000 simulations. As we've seen for the past few weeks, a number of teams from around the middle of the ladder have retained a broad range of possibilities for their final ladder position, all with non-trivial probability attached. Collingwood is, perhaps, the best example of this, with ladder positions 5 through 10 all carrying roughly equal levels of likelihood. (I'll admit that, since I planted the thought in my own mid - and, I hope, in the minds of at least a couple of readers - a few weeks back, I can't look at this chart and not imagine a cavalcade of dinosaurs wandering past fences.)

Other teams' fates are more narrowly constrained, this especially the case for the Lions, Blues, Suns, Dees and Saints, and, at the happier end of the ladder, for the Dockers, Hawks and Eagles.

Specific probabilities attached to individual ladder positions for each team can be found in the following heat map.

This heat map now suggests that the competition has split, roughly speaking, into six sub-competitions:

• for positions 1 to 3 (Fremantle, West Coast, Hawthorn)
• for positions 4 and 5 (Sydney and Richmond)
• for positions 6 to 10 (Collingwood, Adelaide, Western Bulldogs, Kangaroos, GWS)
• for positions 11 and 12 (Geelong, Port Adelaide)
• for positions 13 to 15 (St Kilda, Essendon, Melbourne)
• for positions 16 to 18 (Carlton, Gold Coast, Brisbane Lions)

Whilst there is some possibility that teams will finish in positions other than those shown here, as the shading reveals, these groupings reflect the most likely finishes for each team.

MOST LIKELY ORDERING OF TOP 2, 4 AND 8 TEAMS

A Hawthorn / West Coast one-two finish has now emerged as the clear favourite based on the most recent simulations. That ordering occurred in about 28% of all replicates, about 10% more often than the next most-common ordering of Fremantle / Hawthorn.

Third most common was a reversal of the number one finish, with West Coast instead winning the Minor Premiership and Hawthorn finishing as runner up.

It's interesting to note that it's now not until you get to the seventh most-likely top two pairing that any involving the Swans appears, and further that, by then, the attached probability has shrunk to about 2%.

Hawthorn and West Coast, in that order, also appear in three of the 10 most common Top 4 finishes, and they appear in the opposite order in four more.

The most common Top 4 sees Hawthorn as Minor Premier, West Coast as runner-up, Fremantle in 3rd, and Sydney in 4th. That ordering appeared in about 1 replicate in 8.

Again we find this week no standout most-likely Top 8, with the ordering that did appear most often doing so in only about 1 replicate in 740 and appearing only 14 more times across the 100,000 replicates than the second most-common ordering. The ordering that was commonest had Fremantle, Hawthorn, West Coast, Sydney filling places 1 to 4 in that order, followed by Richmond, the Western Bulldogs, Adelaide and Collingwood rounding out the 8, also in that order.

The six next most-common Top 8s all had Hawthorn / West Coast / Fremantle / Sydney filling their first four places, and Richmond finishing fifth, this latter characteristic true of all of the 10 most-common Final 8s.

TEAM AND GAME DEPENDENCIES

As we did last week, we can also use the simulations to assess the dependencies between teams in terms of making the Final 8, and to assess the importance of each of the remaining games in terms of their ability to influence the Final 8.

On the first of those topics, the table below records the unconditional and conditional probabilities for teams to make the Final 8 contingent on whether some other team does or does not make the 8.

Looking at each of the hopeful but uncertain Finalists in order we can say that:

• Adelaide least wants to see Geelong or Port Adelaide make the Finals, and most wants to see Richmond miss
• Collingwood least wants to see Geelong make the Finals, and most wants to see Richmond miss
• Geelong least wants to see GWS make the Finals, and most wants to see Collingwood miss
• GWS least wants to see Port Adelaide make the Finals, and most wants to see Adelaide miss
• The Kangaroos least want to see Port Adelaide make the Finals, and most want to see Richmond miss
• Port Adelaide is fairly indifferent about who makes the Finals, but most wants to see the Western Bulldogs miss
• Richmond least wants to see Adelaide or the Kangaroos make the Finals, and most wants to see Adelaide miss
• The Western Bulldogs least want to see Port Adelaide make the Finals, and most want to see Collingwood miss

Lastly, as noted above, we can look at the each of the 45 contests across the five remaining rounds and estimate its likely effect on the Finals chance of each of the current aspirants (see table below) and determine that:

• This week's Giants v Cats, and Dogs v Pies games are two of the four most Finalist-determining of the remaining games this season, both having significant impact on the estimated probabilities of participation in September of the teams involved, but also non-trivial impact on the estimated probabilities of a number of non-participating aspirants.
• The Adelaide v Richmond game in two weeks' time looms as another crucial game in the context of the Finals.
• The Roos v Dogs game in Round 22 is, currently, the game with the largest assessed impact on the Finals prospects of all current aspirants.
• In Round 23, the last of the home-and-away season, two games are currently in the Top 10 of those most important in the context of the Finals: the Melbourne v GWS game (ranked 6th), and the Richmond v Kangaroos game (ranked 7th).
• None of the remaining five rounds has a game outside the top dozen in terms of influence on the Finals, and only next week's Round 18 is bereft of at least one game from the Top 10.
• Round 21 also, given current circumstances and team Ratings, appears as though it might have little impact on the teams that make and miss the Final 8, with only Crows v Lions game looming as significant. Things might, of course, change between then and now.

As always, comments and suggestions are welcomed, and if you'd like me to run simulations for different game-by-game probabilities, please let me know.