Well that last weekend certainly changed things a bit: the Hawks are upset by a determined Tigers unit, the Eagles stumble to a draw with the Suns, Sydney put a 50-point gap on Adelaide, and Collingwood make it six post-bye losses on the trot by going down to the Dees.

Those results, understandably, had some significant impacts on the projected probabilities and margins for the remaining games, details of which appear at right.

Despite its Round 18 hiccup though, Hawthorn, with the apparent luxury of the Lions, Blues and Port in their future, are slated for 4.4 more wins, the largest expected number for any team, almost a full game ahead of the team that beat them, Richmond, which the simulations have inked in for 3.5 more wins.

Other teams with expected win counts exceeding 3 are West Coast (3.3), the Kangaroos (3.2). and Sydney (3.2).

When we use the margins implied by these fresh probabilities in our regular suite of 100,000 simulations (for the methodology, please see this blog) we discover some significant changes in team probabilities in the major wagering markets this week. 

In the Minor Premiership race, Hawthorn's loss was devastating for their chances, dropping them from about 1-in-2 to 3-in-20 propositions. Nonetheless, at their new TAB price of $11, there still appears to be some value in the Hawks for this title.

One team's probability loss is, as a matter of mathematical certainty, other teams' probability gain, and this week it was Fremantle who crumbed the majority of the Hawks' dropped chest mark. Freo's probability for the Minor Premiership shot up from about 24% to 54%, but their price shortened far too much into $1.50.

In the race for the Top 4, Richmond were this week's huge winners, more than doubling their prospects for such a finish to about 32%. The probability donors in this market were, mostly, the Roos (5%), Crows (5%), Eagles (3%), and Pies (2%). Only the Tigers at $4 and the Dogs at $13 represent value in this market now, according to the simulations.

Richmond also significantly bolstered their chances of a spot in the 8, lifting them much closer to certainty with a now 98% probability of playing in September. Other teams enjoying significant increases were the Dogs (+13%), Cats (+7%) and Roos (+6%), while those suffering significant decreases were the Pies (-30%) and the Crows (-13%). In the market for the Final 8, only the Dogs at $1.20 and GWS at $4.25 appear to offer any non-trivial value at present. Geelong, on the other hand, offer value at $1.80 in the market to miss the Final 8.

The Spoon still seems most likely to finish in the Lions' cabinet, though Carlton marginally enhanced their prospects for it this weekend in going down to the Roos and doing it so emphatically, while the Suns made it less likely they'd need to find cupboard-space by playing out their draw against such highly-fancied opposition.

Looking next at all the teams and all the ladder positions, this week's Dinosaur Chart, as expected, reveals a continued decline in the average scales per dinosaur metric, with most teams now having only 3 or 4 finishes that are far more likely than any others.

The teams in mid-table though do still have a wider range of possibilities, which is made even clearer by this week's heat map. 

Broadly speaking, the competition now seems to have split into six groups (though some of the group boundaries, especially in mid-table, are less distinct than others):

1. Vying for positions 1-3: Fremantle, West Coast and Hawthorn
2. Vying for positions 4-7: Sydney, Richmond, Western Bulldogs, Kangaroos
3. Vying for positions 8-10: Adelaide, Geelong, GWS
4. Vying for positions 11-12: Collingwood, Port Adelaide
5. Vying for positions 13-15: St Kilda, Melbourne, Essendon
6. Vying for positions 16-18: Gold Coast, Carlton, Brisbane Lions

TOP 2s, 4s AND 8s

Hawthorn no longer features in the most common Top 2 pairing, that duo now being Fremantle plus West Coast, which cropped up in about 27% of replicates, just slightly more often than did a Fremantle plus Hawthorn pairing.

The six most-common pairings are the various possible permutations of pairs selected from Fremantle, West Coast and Hawthorn, and they together account for about 95% of all replicates.

Sydney lands as Runners-Up in the three next-most common pairings and then as Minor Premier in the tenth most-common pairing, which occurred in only about 1 replicate in 300.

The three most-common Top 4s all see Fremantle finishing as Minor Premiers and account for almost 30% of all replicates.

After that follow a number of quartets each with probabilities in the 3.5% to 6.5% range, reflecting the fact that there is still uncertainty about the precise makeup of this group, particularly in positions 3 and 4. 

One notable change from last week is that it's not now until we get to the ninth-most common Top 4 that we find one with Hawthorn as its Minor Premier. Last week, Hawthorn was Minor Premier in two of the three most-common Top 4s.

Moving next to Top 8s, we find that Fremantle finishes 1st in all 10 of the most common sets of Finalists, and that West Coast finishes 2nd in seven of them (the Hawks taking 2nd in the other three). Adelaide, Geelong and GWS, when they do appear in an 8, do so only in 8th spot.

Again though, please note that even the most-common Top 8 shown here came up in only about 1 replicate in 140 and so is very unlikely to transpire in reality.

TEAM FINALS DEPENDENCIES

In this next analysis we review all 100,000 simulation replicates to determine the proportion of them in which Team A makes the Final 8 conditional on Team B either making or not making the Final 8. This gives us a rough measure of how intertwined are the Finals fates of any two particular Finals aspirants. 

Adelaide's fate is most influenced by that of Geelong, its prospects altering by 41% points depending on whether the Cats do or don't make the 8. Geelong's fate, similarly, is most influenced by Adelaide's, the swing for it when the Crows make versus miss the 8 estimated at about 40% points. These large estimated impacts of each team's fate on the other's reflect the fact that the pair will most likely be fighting over the same spot, 8th.

Collingwood's fate is most tied to Richmond's, because Richmond play both the Roos and Adelaide, either of whose spot in the 8 the Pies might take, and also because Richmond and the Pies meet directly in Round 21.

GWS' prospects are most influenced by, about equally, Adelaide's, Geelong's and the Roos', while the Roos' are influenced almost equally by all the Finals aspirants listed.

Port Adelaide's prospects are remote regardless of the fates of the other teams, while Richmond's and the Western Bulldogs' are excellent, also regardless of the fates of their peers.

IMPORTANCE OF THE REMAINING CONTESTS ON THE COMPOSITION OF THE FINAL 8

The final piece of analysis for the week is to assess the relative importance of each of the remaining contests on the prospects of all the current Finals aspirants.

As last week, we'll use two measures of a game's importance:

• Raw Impact Index, which is the sum of the absolute differences in each Final aspirant's prospects, for each subtracting the probability that the team makes the Finals if the game ends as a home team win from the probability that the team makes the Finals if the game ends as a home team loss
• Weighted Impact Index, which is calculated in a similar manner to the Raw Impact Index except that we account for the relative likelihood of a home team win or loss (for a little more discussion, see last week's blog)

We can think of the Raw Impact Index as a measure of a game's maximum ability to change the composition of the eight when we change it from a home win to a home loss (however unlikely such a change might be), whereas the Weighted Impact Index measures a game's likely or "expected" impact on the composition of the eight.

Both measures are interesting, but I think the Weighted Impact Index is the more useful as it requires that a game both be capable of generating large swings in the prospects of the Finals aspirants contingent on its outcome, and that this outcome be relatively uncertain. My commentary below then will refer only to this measure and not the Raw Impact Index.

Using this measure, the five most important remaining games are:

1. Geelong v Collingwood (Round 22), assessed as being capable of changing the Cats' Finals chances by 36% and the Pies' by 20%, but also Adelaide's by 9% and GWS' by 6%.
2. Adelaide v Richmond (Round 19), important mainly for Adelaide's prospects, capable of changing them by about 37%, but also somewhat important for Geelong (11%), GWS (8%), and, of course, Richmond (5%).
3. Geelong v Adelaide (Round 23), also very important for Adelaide's prospects, here capable of changing them by about 43%, but also important for Geelong's (37%). What reduces this game's Weighted Impact is the fact that it carries a 75% probability of a Cats win with the game scheduled to be played at Kardinia Park.
4. GWS v Sydney (Round 21), particularly important for GWS's prospects, with a 34% swing potential, but also important for Geelong (11%) and Adelaide (10%). Its Weighted Impact is reduced a little by the fact that Sydney is assessed as enjoying a victory probability of about 60%.
5. St Kilda v Geelong (Round 21), represents a potential 32% swing for Geelong, but also a 10% swing for Adelaide and a 9% swing for GWS. The fact that it's assessed as about a 50:50 proposition lifts its Weighted Impact relative to other games.

I'll finish by noting that:

• Round 19 has two of the 10 most influential games in the context of the Final 8
• Round 20 has three
• Round 21 has three
• Round 22 has two
• Round 23 has one

No doubt it'll all change again next week ...