Updated final home and away ladder simulations appear below.
(For details on the methodology, see this post from earlier, but note that we've effectively left the team ratings unperturbed this week instead of applying the usual standard deviation of 24 points to the offensive and defensive ratings of teams, in recognition of the fact that, with only one week to go, we're more certain about MoSHBODS' team ratings.)
The simulation this week suggests that the Finalists are all but certain, but that Hawthorn and Sydney are most likely to be fighting for the last spot in the Top 4, with Richmond, West Coast and Collingwood all but locked-in there.
A look at the detail reveals that there is an estimated 0.4% chance that Port Adelaide does enough to somehow knock Geelong (or, less likely, Melbourne) into 9th. They're currently priced at $26 to make the Final 8 on the TAB ...
The weekend's results made percentage less likely to be required as a tie-breaker for a number of key ladder positions. There's now an estimated 50% chance (down 11% points from last week) that the team in 9th will be separated only on percentage from the team in 8th at the end of the home-and-away season, and only an 8% chance (down 34% points) that the teams in 4th and 5th will finish equal on wins.
MOST LIKELY TOp EIGHT
According to the latest simulations, there are still 83 possible final Top 8s, 17 of which occurred in at least 1% of the replicates.
The 20 most common, and their estimated probability of occurrence, appear at right.
Richmond, of course, finish 1st in all of them, and West Coast finish 2nd in four of the Top 6, with Collingwood 2nd in the other two. Hawthorn grab 2nd in only three of the Top 20.
Sydney finishes as high as 3rd, with West Coast in 2nd in all instances shown here.
Melbourne makes the Top 4 in only four of the Top 20 combinations shown here and always, of course, facing Richmond in Week 1 of the Finals.
TEAM AND POSITION CONCENTRATION
Just so we continue to get a feel about the Gini concentration measures, I thought it'd be useful to calculate them again this week.
For information about how to interpret these measures, you can see this blog, but the table at right might also help. It shows the Gini coefficient that a team would have if it were equally likely to finish in any of a specified number of ladder positions (and in no other position).
So, for example, a team that was equally likely to finish in any of six ladder positions would have a Gini coefficient of 0.667. This week, as we'll see in a moment, North Melbourne has a Gini coefficient of 0.643, so we can think of the level of uncertainty it has about its final home-and-away ladder position as roughly equivalent to that for a notional team that found itself equally likely to finish in any of six ladder positions. Note that we're not saying that North Melbourne is only capable of finishing in six different ladder positions (it can actually finish in any of 15 different positions, 11 of them with an estimated probability of 1% or more), just that the uncertainty it faces it roughly equivalent to a team in that situation.
You'll note that a team equally likely of finishing in any of the 18 ladder positions will have a Gini coefficient of 0, but one that is absolutely certain of its final ladder position will have a Gini coefficient of 0.944, not 1. There's a technical reason for this - and a 'bias correction' we could apply to all coefficients to force the range to be (0,1) - but for our purposes, the uncorrected coefficients are fine.
(Note that, when we're looking at the Gini coefficients for ladder finishes rather than teams, we can substitute "Number of Equally-Likely Finishes" for a team with "Number of Teams Equally-Likely to Finish in the Position".)
Only three teams became less certain of their final ladder position this week - Fremantle, Western Bulldogs, and West Coast - while the average team enjoyed an increase in certainty of about 9% measured using the Gini coefficient.
North Melbourne has least certainty and a Gini coefficient roughly equivalent to that which a team with 3 or 4 equally likely ladder finishes would have. As you can see from the earlier chart, that's a fairly apt description of their situation. They have four potential finishes with estimated probabilities ranging from 19% to 36%.
Looking next from the ladder positions' perspective we find that only 13th and 14th positions find themselves less certain about their likely occupants this week compared to last week. They have Gini coefficients equivalent to that which a position with 2 equally likely occupants would have and, indeed are both about 50% likely to have the Western Bulldogs or Fremantle occupying them come the end of Round 23.
The position with least certainty is 10th. It will be occupied by any of four teams with probabilities ranging from 19% to 36%.
Let's finish by looking at the profile of wins by ladder finish, which shows, as we flagged some weeks ago, that it's quite likely the team finishing 9th (Port Adelaide) will have had a 13 and 9 season. That's extraordinary by historical standards.