2018 : Simulating the Final Ladder After Round 16
/Updated final home and away ladder simulations appear below.
(For details on the methodology, see this post from earlier.)
As the remaining number of rounds dwindles to just seven, only three teams gained more than half an Expected Win this week:
- Geelong (+0.7)
- Melbourne (+0.6)
- Hawthorn (+0.6)
The three teams they defeated were the only ones to see their Expected Win count drop by more than half a game:
- Sydney (-0.8)
- Fremantle (-0.6, making it -1.6 over the past two weeks)
- Western Bulldogs (-0.6)
Ten teams are expected to win 12 games or more in the regular season, with Sydney in 5th now separated from Hawthorn in 8th by only 0.5 Expected Wins.
Based on the latest replicates there's an estimated 39% chance (down 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. The chart below shows how likely it is that any pair of ladder positions will be occupied by teams equal on wins.
In terms of likelihood of making the Finals, the week's big gainers were:
- Hawthorn (+15% points)
- Geelong (+14% points)
- Melbourne (+12% points)
The week's big losers were:
- GWS (-18% points)
- Sydney (-14% points)
- Adelaide (-7% points)
- Essendon (-7% points)
Only eight teams now (down one on last week) are assessed as better than even-money chances for a spot in the Finals.
In the quest for a Top 4 spot, a number of teams made 6 to 10% point gains: Geelong +10% points; Collingwood, Melbourne and Hawthorn +7% points; and West Coast +6% points. Only two suffered significant declines: Sydney -28% points, and GWS -10% points.
Just four teams now (also down one on last week) 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, 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, Port Adelaide has a Gini coefficient of 0.653, 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 Port Adelaide is only capable of finishing in six different ladder positions (it can actually finish in any of 13 different positions), 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".)
For the average team, final ladder position certainty rose quite a bit this week, and fell only for Sydney, St Kilda, the Brisbane Lions, and (barely) the Western Bulldogs. Sydney's fell by so much that it now finds itself having the least certainty of any team in the competition. Its 0.523 coefficient is roughly equivalent to that a team equally likely of finishing in any of eight or nine ladders positions would have. Sydney are, in fact, now estimated 8% or higher chances to finish in any of the positions from 3rd to 10th.
The largest increases in certainty came for GWS, Essendon and Adelaide, though GWS still has a relatively high level of uncertainty about its final ladder position.
Carlton are now the team with the highest level of certainty about their ultimate ladder finish, with an estimated 70% chance of finishing 18th, and an estimated 22% chance of finishing 17th.
Overall, looking across all 18 teams, we saw a decrease of 4.2% in uncertainty, taking us to the lowest level of average uncertainty that we've seen since we began tracking it this season.
Looking next at each of the ladder positions, we find increases in uncertainty only for positions 15th and 16th, and only very small increases even there.
The largest decreases were for positions 11th and 12th, though these remain in the top half of positions when ordered by level of certainty.
Most uncertainty continues to be associated with 6th place, which nine teams (Port Adelaide, Collingwood, West Coast, Sydney, Geelong, Melbourne, Hawthorn, GWS, and North Melbourne) still have about 8% or higher estimated chances of filling. The five positions carrying most uncertainty are now 4th through 8th on the ladder.
Least uncertainty is associated with 18th position (which Carlton has a 71% chance of filling), and 1st (which Richmond has a 75% 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 over 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.)
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 dropping this week to about 40%. Fremantle, Essendon and the Western Bulldogs remain the teams least likely to make the Finals should they finish on just 12 wins, though all but Geelong, Melbourne and Hawthorn have estimated chances of 20% or less of doing so should they finish on that count.
Thirteen wins makes all teams except Essendon and Fremantle 75% or better chances for a finals berth.
Looking next at the analysis for Top 4 finishes, we see quite a bit of change from the situation after Round 15, with no team better than even-money chances of a Top 4 finish with only 14 wins. Melbourne and Geelong still do best, on average, with 14 wins, but even they are only about 40% chances of a Top 4 finish. A number of teams - Collingwood, West Coast, Port Adelaide, Sydney, North Melbourne, and Essendon - are less than 25% chances of a Top 4 finish with just 14 wins.
Fifteen wins now sees Collingwood, West Coast, Port Adelaide, and Sydney as the only teams with 85% or less chances of finishing Top 4.
We can, as we did last week, 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. There are still quite wide ranges of relatively plausible finishes for some teams given a specified number of wins - say Geelong, for example, with 12 or 13 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. It's quite clear from this, for example, that 13 wins is more often associated with 8th spot than is 12 wins. Similarly, 15 wins is more often associated with 4th spot than is 14 wins.
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 R15) with those in the charts on the right (post R16), we can see that Adelaide's, Geelong's and Hawthorn's fates are now less tied to other teams', while GWS's, North Melbourne's and Sydney's fates are now more tied to other teams'.
(Collingwood, Essendon and Port Adelaide have dropped off the chart because their estimated Finals chances have fallen outside the 5% to 95% range).
We can do the same analysis for positions in the Top 4, which we do below.
Here we find that most teams' fates are about as dependent on other teams' as they were last week, though Geelong has become very slightly more dependent on a few of the teams, and GWS and Sydney slightly less dependent.
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 and GWS both now have five games in the Top 10, while Sydney has two.
Games that were also on the Top 30 list last week are marked with an asterisk. Nineteen of the 26 games that were on last week's list and that weren't Round 16 games are still on the list.
We can also, using a similar methodology, estimate the importance of each remaining game to the composition of the Top 4, which we do in the table below.
Here we find that three games involving West Coast across Rounds 17 to 22 top the list.
More broadly, West Coast are involved in five of the games in the Top 10, Collingwood and Melbourne in three each, and Geelong, Port Adelaide and Sydney in two games each.
