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 five of the weekend's winners:
- Port Adelaide (+0.8)
- West Coast (+0.7)
- Geelong (+0.6)
- Melbourne (+0.6)
- Carlton (+0.6)
while the big losers were three of the teams they beat:
- GWS (-0.7)
- Adelaide (-0.7)
- Collingwood (-0.6)
The teams ranked 3rd to 10th now are separated by less than 1.5 Expected Wins.
(Interestingly, Adelaide, whilst having a fractionally smaller Expected Win count than Melbourne, have slightly higher estimated probabilities for making and for positions in the final 8.)
TEAM AND POSITION CONCENTRATION
One way of measuring how much uncertainty there is in the competition is to use the Gini measure of concentration commonly used in economics for measuring income inequality 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.
In the context of a team, a Gini coefficient of 1 implies that the team has only one feasible final ladder position, while a Gini coefficient of 0 implies that all 18 ladder positions are equally likely. Since no team has, as yet, mathematically locked in any ladder position, and none are capable of finishing in every one of the possible ladder positions with equal probability, no team has a Gini coefficient of exactly 0 or 1.
But, as we can see in the table at right, Richmond and the Brisbane Lions are the teams whose Gini coefficients are highest, reflecting the fact that they have a relatively narrow set of likely final ladder positions (Richmond is now a 67% chance for 1st and the Brisbane Lions a 41% chance for 18th).
Conversely, Melbourne, Adelaide and GWS are the teams whose Gini coefficients are smallest, signalling that they have the broadest range of possible ladder finishes. Melbourne have an 8% or greater chances for every ladder position from 3rd to 10th, Adelaide likewise from 3rd to 10th, and GWS likewise from 6th to 12th.
Similarly, Hawthorn and Port Adelaide have relatively low Gini values and both have estimated probabilities of about 8% or more for positions 3rd to 10th.
We'll continue to calculate each team's Gini coefficient over the course of the remainder of the season to track the speed at which potential ladder finishes narrow or widen.
In the context of a ladder position, a Gini coefficient of 1 implies that only one team could feasibly finish in that position, while a GIni coefficient of 0 implies that all teams are equally likely to finish in that position. Again, because no ladder position has been secured by any team and because no position is capable of seeing every team occupy it with equal probability, no Gini coefficient is exactly 0 or 1.
Looking at the ladder position Gini coefficients, which appear at left, we see that 1st and 18th are the positions with the narrowest range of likely occupants at season's end (as we just saw, Richmond and the Brisbane Lions have already left a deposit on these positions with the landlord), whilst positions 4th through 12th have the widest range of potential occupants.
For each of the ladder positions 4th through 12th there are at least five - and usually seven or even eight - teams with 8% or greater chances of occupying it come the end of Round 23, so, her too, the Gini coefficient values seem to make practical sense.
In summary, it's the bottom six and top three ladder positions that are most determined, and the positions from 4th to 12th that are least determined.
We'll also take a first look this week at estimates of teams' likelihood of making the Finals depending on the number of wins that they record. These appear below.
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.)
We see, for example, that 12 wins would give Geelong about a 65% chance of making the Finals, but would give the Western Bulldogs only about a 30% chance. Other teams' estimated chances with 12 wins fall somewhere within that range. The differences come because of teams' remaining schedules and current percentages.
It's really only once we get to 13 wins that every team has roughly the same chance (viz, near certainty) of playing in the Finals.
A similar analysis can be done focussing on a top 4 finish, which shows that 14 wins would give Richmond almost a 75% chance of such a finish, but would give Port Adelaide, Fremantle and the Western Bulldogs less than 50% chances. Fifteen wins would virtually guarantee any team a spot in the top 4.
We can also 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 arrows, with the base of the arrow showing the estimated probability that a team makes the 8 conditioned on a nominated team missing the 8, and the arrow head showing the estimated probability that a team makes the 8 conditioned on a nominated team making the 8.
So, for example, Adelaide are about a 59% chance of making the 8 if GWS make the 8, but about a 74% chance if GWS miss the 8.
Broadly speaking, the longer the arrow the more a team's finals chances depend on the nominated team associated with that arrow (although the probability estimates for both ends of every arrow are subject to some sampling error, which could affect the length disproportionately in some cases).
The black vertical line for each team shows its unconditional estimated probability of making the 8, and the nearer is the tail or head of an arrow to that line, the smaller or larger is the unconditional probability of the nominated team to make the 8.
For example, Adelaide's arrow when the Western Bulldogs is the nominated team has its head near the black vertical line, reflecting the fact that the Dogs have a low estimated probability of making the 8. Conversely, Adelaide's arrow when Richmond is the nominated team has its base near the black vertical line, reflecting the fact that the Tigers have a high estimated probability of making the 8.
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-one of the 28 games that were on last week's list and that weren't Round 8 games are still on the list.
Looking just at the next few rounds, we have the following counts of Top 30 games:
- Round 9: 1 (of 9 games)
- Round 10: 2 (of 8 games)
- Round 11: 3 (of 9 games)
- Round 12: 3 (of 7 games)