2022 : Simulating the Final Ladder After Round 22
/The Standard and Heretical simulations are now just conditional probability calculations, and they reveal the following:
Geelong: Minor Premiers
Sydney: 85% chances for Top 4
Collingwood, Melbourne, and Brisbane Lions: 55-60% chances for Top 4
Fremantle: 40-50% chances for Top 4
Richmond: Play Finals
Carlton: 70% chances of playing Finals
Western Bulldogs: 30% chances of playing Finals
St Kilda: huge longshot to play Finals
(For details about the methodologies I’ve used, see this earlier blog).
LADDER FINISHES
The ladder projections using the Standard methodology (aka “cold” sims) appear on the left, and those using the Heretical methodology (aka “hot” sims) appear on the right.
Looking first just at the Standard Methodology, we see that the range of Expected Wins now runs from 2 to 18, which has grown a little from last week’s range of 2.2 to 17.7. We also see that only 10 teams are expected to finish with a win percentage above 50%.
The biggest declines in Expected Win tally came this week for Essendon (-0.7), while the biggest increases came for Port Adelaide (+0.7).
In terms of Top 8 chances, there were four double-digit changes in estimate, including Richmond’s +15% points, Western Bulldogs’ +14% points, St Kilda’s -19% points, and Carlton’s -11% points. There were also two double-digit changes in estimates of Top 4 finishes, with Sydney +10% points and Collingwood -20% points.
Comparing the results for the Standard and Heretical Methodologies we find:
A virtually identical range of Expected Wins from the Heretical approach
A near identical ordering of the teams in terms of Expected Wins with only Brisbane Lions finishing higher than Collingwood and Melbourne probably because of sampling variation.
Broadly similar estimates for the changes in teams’ Finals chances
TEAM AND POSITION CONCENTRATION
The HHI figures for the most recent simulation replicates appear below, with those from the Standard methodology on the top, and those from the Heretical methodology on the bottom. (For information about the HHI, also see that previous blog linked to earlier).
STANDARD METHODOLOGY
heretical methodology
Yet another reduction in average uncertainty this week, with GWS the only team registering other than a decline or trivial increase. Melbourne, remarkably, having been the team with least uncertainty for most of the season, now find themselves with the most uncertainty and effectively competing for 4 or 5 positions. Under the Standard Methodology, they’re assessed as about 20-30% chances to finish 2nd. 3rd, 5th, or 6th, and 7% chances to finish 4th.
Both methods suggest that teams are, on average, effectively competing for about 2 different ladder positions now, and both have most teams competing for between 1,5 and 4.5 positions, the exception being Geelong.
standard methodology
heretical methodology
These tables also imply a further reduction in uncertainty this week, but also suggest that there are still 3.5 to 4.5 teams effectively competing for each of positions 3 through 6 on the ladder.
They also have the average ladder position with effectively around 2 teams likely to fill it, and with most ladder positions effectively expecting anywhere between 1.5 and 4.5 teams to be competing for them. The exception amongst the ladder positions are 1st.
LIKELY IMPORTANCE OF PERCENTAGE
Next, we’ll use the Standard simulations to again investigate the estimated likelihood that any given pair of ladder positions be determined after Round 23 based on percentage.
Last week’s results slightly increased the likelihood that percentages will separate 8th and 9th on the final home and away ladder to about 38%. They also slightly increased the likelihood that 4th and 5th will be decided on percentages (50%), and hugely decreased the likelihood this will be how the Minor Premiership is decided (0%).
MOST LIKELY SET OF FINALISTS AND TOP 4S
Across the 50,000 replicates from the Standard Methodology, there were 1,143 unique orderings of the 18 teams, and just 3 different sets of teams comprising the Top 8.
In the table at right we show those 3 sets of 8 teams that finish as the Finalists, in some order, in at least one replicate.
The first of these, which accounts for almost 70% of the replicates, is the set of teams currently in the Top 8. The next, which accounts for just over 30%, sees the Western Bulldogs supplant Carlton, and the final list, which accounts for less than 1-in-1000 replicates, sees St Kilda supplant Carlton.
There are now 29 unique orderings of the Top 8 that appear in more than 1% of replicates, and they are shown in the table below.
None of them sees Collingwood finishing in 2nd spot, all of them having Melbourne, Sydney, or Brisbane Lions filling that position. Three of the Top 10 have the Western Bulldogs replacing Carlton, while the other seven have the current Top 8 on the competition ladder in some order.
Note that none of these orderings accounts for more than 1-in-12 replicates. Together they account for about 86% of all replicates, the remaining 14% being spread across another 73 orderings.
Next, the Top 4, also taking order into account.
There remains some uncertainty here, too, with even the most common Top 4 - which sees Melbourne lose to Brisbane Lions, and Collingwood defeat Carlton - occurring in only about 1-in-6 replicates. The current Top 4 in their current order is only the twelfth-most likely final outcome and appears in only about 1-in-33 replicates.
Altogether there are 17 Top 4 orderings that appeared in at least 1% of replicates, with Collingwood appearing in 7 (and never finishing higher than 3rd), Fremantle in 8, Brisbane Lions in 10, Melbourne in 12, and Geelong in all 17, appearing as Minor Premier on all occasions.
These 17 orderings - of which there were 30 in total across the entire simulation - together account for 97% of all replicates.
Lastly, let’s look at the Top 2s that came out of the simulations.
There were only 4 in all that appeared in at least 1 replicate and they are shown at left.
Geelong and Sydney is the most common ordering, that one appearing in about 5-in-9 replicates. Next comes Geelong and Melbourne, which appeared in about 3-in-11 replicates, then Geelong and Brisbane Lions in about 1-in-6 replicates and, finally, Geelong and Collingwood in about 1-in-500 replicates.
