Updated final home and away ladder simulations appear below.

(For details on the methodology, see this post from earlier.)

Five teams gained one half of an Expected Win or more this week:

• Western Bulldogs (+0.7)
• North Melbourne (+0.6, making it +1.2 over the past two weeks)
• Hawthorn (+0.5, making it +1.0 over the past two weeks))
• Adelaide (+0.5)
• Sydney (+0.5)

Four more saw their Expected Win count drop by half a game or more:

• St Kilda (-0.7)
• Port Adelaide (-0.6)
• Brisbane Lions (-0.6)
• Collingwood (-0.5)

In terms of likelihood of making the Finals, the week's big gainers were:

• Hawthorn (+10% points, making it +36% points over the past three weeks)
• North Melbourne (+10% points, making it +17% points over the past three weeks)

The week's big losers were:

• Port Adelaide (-15% points)
• Essendon (-10% points)

Just eight teams are assessed as better than even-money chances for a spot in the Finals.

In the quest for a Top 4 spot, the largest changes were:

• GWS (+15% points)
• Melbourne (+11% points, making it +20% points over the past three weeks)
• West Coast (+10% points)
• Hawthorn (+9% points, making it +16% points over the past three weeks)
• Port Adelaide (-15% points)
• Essendon (-10% points)

Three teams have estimated better than even-money chances for a place in the Top 4. Five other teams have between 15% and 46% chances.

The weekend's results made percentage far more likely to be required as a tie-breaker for a number of key ladder positions. There's now an estimated 68% chance (up 15% 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.

There's also about an 18% chance that 6th and 9th will all be equal on wins, and about a 54% chance that the teams in 4th and 5th will finish equal on wins.

TEAM AND POSITION CONCENTRATION

This week's Gini concentration measures appear below, and reflect the level of certainty in our knowledge about which teams will finish where at the end of the home and away season.

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".)

Five teams became less certain about their final ladder positions this weekend, most significantly Collingwood and North Melbourne who suffered greater uncertainty for the second successive week.

Port Adelaide are still the team with most uncertainty. They have an estimated 6% or greater chance of finishing in any of the positions 3rd through 10th, and an estimated 10% or greater chance of finishing in any of the positions 5th through 9th

Overall though, certainty increased substantially this, with the average Gini coefficient rising by 3.5%.

The largest increases in certainty came for Essendon, Western Bulldogs, West Coast and GWS, but Richmond and Carlton remain most certain about their final ladder finishes. Richmond are 95% chances to finish 1st, and Carlton 89% chances to finish last.

Again this week, no ladder position saw a significantly large increase in the uncertainty associated with, though there were small increases for 6th and 10th.

That small increase for 6th was enough to make it now the position with least certainty. Seven teams now have 10% or greater chances of occupying 6th at the end of the home-and-away season. Next-most uncertain is 8th spot where eight teams have estimated chances of about 5% or higher. More broadly, positions 3rd through 10th remain the seven most-uncertain ladder positions of all.

Least uncertainty is associated with 1st position, which, as just noted, Richmond has a very high chance of occupying. 

Across all 18 ladder positions, the average decrease in uncertainty this week is similar to that we saw for the team-based view (viz about a 4% increase in the average Gini coefficient).

WINS REQUIRED

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 shown here.)

Thirteen wins is now all but certain to be the minimum to play Finals this season, with only Geelong and Melbourne having greater than 10% chances of finishing in the Top 8 with just 12 wins.

Even 13 wins is no guarantee for most teams, however, and each of Sydney, North Melbourne, Essendon and Adelaide have estimated chances of only about even-money or less should they finish the season on 13 and 9.

Fourteen wins, however, guarantees all teams a spot in the Finals.

Looking next at the analysis for Top 4 finishes, we find that Melbourne and Geelong are the only teams with a roughly better than even-money chance of finishing in the Top 4 with only 14 wins. All other teams have estimated chances of 30% or lower - lowest of all for West Coast, Port Adelaide, Sydney and North Melbourne.

Fifteen wins, however, virtually assures all teams of a Top 4 finish.

The uncertainties associated with exactly 13 and 15 wins are reflected in the chart below, manifested in the broad range of feasible ladder outcomes for some teams when they record exactly those number of wins.

A similar analysis, aggregating across teams, gives us an idea of the overall spread of likely ladder finishes for a generic teams with a specified number of wins. We see that 13 wins is most associated with 8th spot, but also with 7th and 9th, and that 14 wins is most associated with 4th, but also with 5th and 6th.

As we noted earlier, percentage seems very likely to play a role in separating 8th from 9th, and 4th from 5th this season.

Next, we 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 charts below, as usual, 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.

(Note that these images can be clicked on to access larger versions.)

The magnitude of the arrow lengths in the chart denotes the extent to which one team's chances are linked to another's, and the number of relatively long arrows reflects the general level of dependence. We see this week that Geelong, North Melbourne, Port Adelaide, and Sydney are the teams with the highest levels of dependency on other teams' fates. Between them, they fill positions 7th through 10th on the competition ladder.

We can do the same analysis for positions in the Top 4, which we do below.

Here we find the highest levels of dependence across a range of teams for Collingwood, GWS, Hawthorn and Melbourne.

GAME IMPORTANCE

Below are the updated estimates of game importance for all remaining games in the fixture, and calculated on the basis of the game's expected impact on all 18 teams' finals chances.

The top three games all involve Sydney, and three of the top six come from the final round. 

Just six games have no bearing on the set of teams that will play Finals (note that the Estimated Weighted Average Importance is not exactly zero for these game because sampling variation means that, by chance, some teams will make the Finals slightly more or less often in those simulation replicates where, say, Fremantle defeats Carlton than in those replicates where Carlton defeats Fremantle).

In the next and final table we have the estimated importance of each remaining game to the composition of the Top 4.

Here we find that GWS are involved in three of the top six most important games and that three of the top nine games are from Round 23.