Updated final home and away ladder simulations appear below.

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

With a number of upsets this week, five teams gained more than half an Expected Win, the combined bounty from the unexpected win itself and slightly elevated expectations for the remainder of the season:

• Brisbane Lions (+0.9)
• St Kilda (+0.8)
• Western Bulldogs (+0.7)
• Adelaide (+0.7)
• Essendon (+0.6, making it +1.5 over the past two weeks)

Five more teams saw their Expected Win count drop by more than half a game:

• Fremantle (-1.0)
• Melbourne (-0.8, making it -1.4 over the past two weeks)
• Geelong (-0.7)
• North Melbourne (-0.7)
• West Coast (-0.7, making it -1.6 over the past two weeks)

Ten teams are expected to win 12 games or more in the regular season, with GWS in 6th now separated from North Melbourne in 10th by only 0.6 Expected Wins. Based on the latest replicates there's an estimated 43% chance (up 4% 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. Expect a lot more talk in commentary about "percentage boosting wins" in the weeks to come.

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

• GWS (+22% points, which makes it +30% across the last two weeks)
• Adelaide (+8% points)

The week's big losers were:

• Melbourne (-13% points, which makes it -23% across the last two weeks)
• North Melbourne (-12% points)

Only nine teams are now assessed as better than even-money chances for a spot in the Finals.

In the quest for a Top 4 spot, Port Adelaide again made the biggest gains (+15% points, which makes it +31% across the last two weeks), while Collingwood (+12% points) and GWS (+9% points) also enjoyed significant increases. The biggest losers were Melbourne (-11% points, which makes it -25% across the last two weeks), West Coast (-11% points, which makes it -28% across the last two weeks), and Geelong (-9% points).

Five teams have better than even-money chances for a place in the Top 4.

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, see this blog.)

For the average team, we are this week slightly more certain about their most likely ladder finish, but that's not the case for Adelaide, Essendon, West Coast, and GWS whose final positions each became less certain. For West Coast, that's five weeks in a row where their final ladder position has become murkier rather than clearer.

The largest increases in certainty came for Port Adelaide and Collingwood, with both now roughly even-money chances to finish 2nd, 3rd or 4th.

In absolute terms, Richmond are the team most certain about their ladder finish, they being 86% chances to finish 1st or 2nd, while Carlton are next-most certain, they being 86% chances to finish 17th or 18th - a stunning example of why greater certainty is not always a positive thing.

Melbourne remain the team with the most uncertain future, with 8% or higher chances of finishing anywhere from 4th to 10th. GWS, whose future is next-least certain, has a similar spread of possibilities with similar numbers - it has 7.5% or higher chances also of finishing anywhere from 4th to 10th.  

Overall, looking across all 18 teams, we saw a decrease of 1.9% in uncertainty, taking us to the lowest level of average uncertainty that we've seen since we've began tracking it this season.

Looking next at each of the ladder positions, we find increases in uncertainty only for positions 6th, 8th, 11th and 12th, and decreases everywhere else, most notably for 1st.

Most uncertainty continues to be associated with 6th place, which nine teams (Port Adelaide, Collingwood, Sydney, West Coast, GWS, Geelong, Melbourne, Hawthorn, and North Melbourne) have 8% or higher chances of filling. Next-most uncertainty is associated with the last spot in the Finals for which 11 teams have about 5% or higher chances. In fact, we are now less certain about the likely occupants of each of the positions 6th through 10th than we were at the end of Round 11.

Least uncertainty is associated with 18th (which Carlton has a 61% chance of filling), and 1st (which Richmond has a 71% chance of filling).

Across all 18 ladder positions, the average decrease in uncertainty this week is similar to that we saw for the team-based view (viz just under a 2% 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.)

Geelong and Melbourne remain the teams most likely to make the Finals should they finish on only 12 wins, with the estimated conditional probability of them doing this rising to nearly 50% this week. Fremantle, Essendon and the Western Bulldogs remain the teams least likely to make the Finals should they finish on just 12 wins.

Thirteen wins makes all teams now 75% or better chances for a finals berth, with Essendon least likely to finish Top 8 should they win "only" six of their remaining eight games.

Looking next at the analysis for Top 4 finishes, we see quite a bit of change from the situation after Round 14, with Richmond, Melbourne and Geelong now better than 50% chances of finishing Top 4 with only 14 wins, and with every team that is mathematically capable of registering 14 wins now better than 25% chances of finishing Top 4 if they do so.

Fifteen wins now gives every team at least about an estimated 90% chance of a spot in the Top 4.

We can also look for each team at the relationship between every possible ladder finish and the number of wins that team records by creating a heat map from the simulation results, which we do in the chart below. 

In this chart, darker areas relate to higher probability, so we can see, for example, the high likelihood of Richmond finishing 1st if they finish on 16, 17 or 18 wins. It's interesting to note the wide range of relatively plausible finishes for some teams given a specified number of wins - say Geelong, for example, with 12 wins.

A similar analysis, aggregating across teams, gives us an idea of the overall spread of likely ladder finishes for teams with a specified number of wins. 

We can see, for example, that 12 wins is most heavily associated with ladder finishes of 8th, 9th, and 10th, but most often of all with 9th.

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.)

By comparing the arrow lengths in the charts on the left (post R14) with those in the charts on the right (post R15), we can see that Collingwood's fate is now less tied to other teams', while Essendon's, Geelong's, Melbourne's and Port Adelaide's fates are now more tied to other teams'.

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

Here we find that Collingwood's, GWS's, Port Adelaide's, Sydney's and West Coast's Top 4 fates are now more intertwined with those of other teams that have genuine Top 4 aspirations.

GAME IMPORTANCE

Lastly, here's the updated list of the 30 most important games remaining in the fixture on the basis of their expected impact on all 18 teams' finals chances. North Melbourne now has five games in the Top 10, Geelong has three, while Hawthorn and Melbourne have two each.

Games that were also on the Top 30 list last week are marked with an asterisk. Nineteen of the 27 games that were on last week's list and that weren't Round 15 games are still on the list. Seven of the new games on the list involve North Melbourne. 

Looking just at the next few rounds, we have the following counts of Top 30 games:

• Round 16: 4 
• Round 17: 5 
• Round 18: 4