Updated final home and away ladder simulations (and quite a bit more this week) appear below.
(For details on the methodology, see this post from earlier.)
In terms of expected wins, the week's big gainers were four of the weekend's winners:
- Brisbane Lions (+1.1)
- Essendon (+1.1)
- West Coast (+0.9)
- Melbourne (+0.8)
while the big losers were the teams they beat plus GWS:
- Geelong (-1.0)
- Hawthorn (-1.0)
- Richmond (-0.8)
- GWS (-0.7)
- Carlton (-0.7)
The teams ranked 3rd to 10th now are separated by less than 2 Expected Wins.
TEAM AND POSITION CONCENTRATION
As mentioned last week, one way of measuring how much uncertainty there is in the competition is to use the Gini measure of concentration to quantify the spread of each team's estimated final ladder positions across the 50,000 simulation replicates, and to quantify the concentration in the probabilities across all the teams vying for any given ladder position. Gini coefficients range between 0 and 1, with 0 implying minimal concentration (ie a team could finish anywhere with equal probability, or a ladder position could be filled by any of the teams with equal probability) and 1 maximal concentration (ie a team finishes in a single ladder position in every replicate, or a particular ladder position is occupied by the same team in every replicate).
This week, we'll show the new coefficients for each team and compare them with what they were after Round 8. Teams with a positive change now have less uncertainty than they did last week about the range of their final ladder positions, while teams with a negative change have more uncertainty.
So, for example, West Coast enjoyed a considerable reduction in uncertainty and is now about 77% likely to finish in the Top 3. Conversely, the Brisbane Lions saw an increase in their uncertainty after they considerably (and surprisingly) enhanced their chances of avoiding the Spoon.
In absolute terms, Carlton, Richmond and West Coast have least uncertainty now about the range of their likely final ladder positions, while North Melbourne have the most uncertainty. The Roos have a better than 8% chance of finishing in any of the positions 5th through 11th.
Doing the same thing for ladder positions rather than teams, we find that there was the greatest reduction in uncertainty about 2nd place on the final ladder this week, with there now being an almost 80% chance that either Richmond or West Coast will fill it.
The largest increase in uncertainty was associated with 1st on the ladder after Richmond's loss to West Coast enhanced the Eagles' chances and diminished the Tigers'
Nonetheless, 1st place still has associated with it a relatively low level of uncertainty, greater only than that associated with 18th position. It remains the case that the highest levels of uncertainty are associated with ladder positions 4th through 12th.
Below are the updated estimates of teams' likelihood of making the Finals depending on the number of wins that they record. (Recall that, because we're working with a sample of simulated final ladders, our estimates have sampling error, so we show them as 95% confidence intervals here with the mean estimate shown as a point. In some cases, our sample is so large that the interval essentially collapses to a point, at least to the resolution show here.)
It's still the case that 12 wins would give Geelong about a 65% chance of making the Finals. It's also still the case that the Western Bulldogs have the lowest chance of making the Finals with just 12 wins, but the estimated probability has risen from about 30% to 35%. Two other teams, Fremantle and Gold Coast, are less than even money odds to make the Finals with only 12 wins, and West Coast is close to even money.
Thirteen wins still makes every team near certainties for a spot in the Finals.
Turning next to the analysis for a Top 4 finish we find that Richmond's chances remain high with just 14 wins, though not quite as high as they were last week. Five teams have a less than 50% chance of a Top 4 finish with 14 wins: Port Adelaide, Hawthorn, Collingwood, Fremantle and the Western Bulldogs.
Fifteen wins still virtually guarantees any team a spot in the top 4.
Next, we can again explore the inter-team dependencies in the composition of the final 8 by estimating the probability that a particular teams makes the 8 conditioned on some other team making or missing the 8.
These are shown in the chart below, as they were last week, as arrows with the base of an arrow marking the estimated probability that a team makes the 8 conditioned on a nominated team missing the 8, and the arrow head marking the estimated probability that a team makes the 8 conditioned on a nominated team making the 8.
Adelaide's Finals chances remain strongly linked to GWS' (and vice versa), as do Collingwood's to North Melbourne and Fremantle (though the latter are relatively unlikely to make the Finals, as reflected in the proximity of the arrow head for Fremantle in the Colingwood box to Collingwood's unconditional probability, which is denoted by the vertical black line).
Lastly, here's the updated list of the 30 most important games remaining in the fixture on the basis of their expected impact of all 18 teams' finals chances.
Games that were also on the Top 30 list last week are marked with an asterisk. Twenty of the 29 games that were on last week's list and that weren't Round 9 games are still on the list. (To be honest, I've been quite surprised at how stable this list has been from week to week).
Looking just at the next few rounds, we have the following counts of Top 30 games:
- Round 10: 1 (of 8 games)
- Round 11: 3 (of 9 games)
- Round 12: 2 (of 7 games)