2022 : Simulating the Final Ladder After Round 21
/At this point in the season, simulations are essentially simple mathematics, but let’s see what that mathematics reveals for one last time this season.
The latest Standard and Heretical simulations suggest the following:
Geelong: virtually assured of the Minor Premiership
Collingwood and Sydney: 70-75% chances for Top 4
Melbourne: 60% chances for Top 4
Brisbane Lions and Fremantle: 45-50% chances for Top 4
Richmond: 85% chances of playing Finals
Carlton: 80% chances of playing Finals
St Kilda and Western Bulldogs: 15-20% chances of playing 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 2.2 to 17.7, which has grown a little from last week’s range of 2.4 to 17.4. 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 Melbourne and Western Bulldogs (-0.7), while the biggest increases came for Richmond (+0.8).
In terms of Top 8 chances, there were only three double-digit changes in estimate, including Richmond’s +48% points, Western Bulldogs’ -33%, and St Kilda’s -11% points.
There were also three double-digit changes in estimates of Top 4 finishes, with big gains for Collingwood and Fremantle, and a big loss for Melbourne.
Comparing the results for the Standard and Heretical Methodologies we find:
A very similar range of Expected Wins from the Heretical approach
An identical ordering of the teams in terms of Expected Wins
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, though with some sizeable increases for Melbourne and Adelaide.
Both methods suggest that teams are, on average, effectively competing for about 3 different ladder positions now, and both have most teams competing for between 2 and 5 positions, the exceptions being Geelong, and GWS, both of whom have now effectively got only 1 spot they could occupy on the ladder at home-and-away season’s end.
standard methodology
heretical methodology
These tables also imply a further reduction in uncertainty this week, but also suggest that there are still 4 or 5 teams effectively competing for each of positions 2 through 6 on the ladder.
They also have the average ladder position with effectively around 3 teams likely to fill it, and with most ladder positions effectively expecting anywhere between 2 and 5 teams to be competing for them. The exceptions amongst the ladder positions are 1st and 16th.
WINS AND LADDER POSITION
Here’s an updated view of the distribution of team wins and final ladder position, based on the Standard Methodology
If we, again, sum across all the teams, we can see how many wins are most likely for each ladder position, as shown in the chart below.
The draw between Richmond and Fremantle has, as noted previously, brought the scenarios with half-wins more into play and means that 12 wins is now associated with the team finishing 8th in 35% of replicates, 12.5 wins in 27% of replicates, and 13 wins in 30% of replicates.
For the team finishing 4th, 15 wins is now the result in 57% of replicates, 15.5 wins in 27%, and 16 wins in 14%.
These percentages, of course, vary by team, and in the chart below we look at how likely it is that a given team plays Finals if it records a particular number of wins, and how likely that outcome is. In the first chart we use the results from the Standard Methodology, and in the second chart from the Heretical Methodology.
We have then, Carlton with just under 50% chances of playing Finals with exactly 12 wins, Richmond 80-85% (although that would require another draw), St Kilda about 10%, and Western Bulldogs about 40%.
Repeating the analysis for finishing in the Top 4.
Under both methodologies, Sydney (80%) and Melbourne (60%) are the only teams with a better than even chance of finishing Top 4 when they register 15 wins or fewer for the season. Under that same scenario, Brisbane Lions are about 40% chances, Collingwood about 15% chances, and Fremantle about 30% chances.
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 decreased the likelihood that percentages will separate 8th and 9th on the final home and away ladder to about 28%. They also slightly increased the likelihood that 4th and 5th will be decided on percentages (41%), and hugely decreased the likelihood this will be how the Minor Premiership is decided (4%).
MOST LIKELY SET OF FINALISTS AND TOP 4S
Across the 50,000 replicates from the Standard Methodology, there were 948 unique orderings of the 18 teams, and just 6 different sets of teams comprising the Top 8.
In the table at right we show those 6 sets of 8 teams that finish as the Finalists, in some order, in at least one replicate.
Three sets of 8 stand out, as you can see, and account for almost 90% of the replicates. The first of those comprises all of the teams from the current Top 8. The next swaps in the Western Bulldogs for Carlton, and the third swaps in St Kilda for Richmond.
After that, no combination appears in more than 1-in-13 replicates.
There are now 12 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 retaining 2nd spot, all of them having Melbourne or Sydney assuming that position. All of them except the ninth where Western Bulldogs replace Carlton, include the eight teams that are currently in the Top 8, but in different orders.
Note that none of these finishes is truly “likely” - even the most common one shown here occurs in only about 1-in-40 replicates.
Next, the Top 4, also taking order into account.
There remains quite a lot of uncertainty here, too, with even the most common Top 4 - which sees Sydney move from their current 4th spot into 2nd, and Brisbane Lions from 5th to 3rd, relegating Collingwood to 4th - occurring in only about 2-in-25 replicates. The current Top 4 in their current order is only the ninth-most likely final outcome and it appears in only about 1-in-33 replicates.
Altogether there are 34 Top 4 orderings that appeared in at least 1% of replicates, with Fremantle appearing in 16 (and never finishing higher than 3rd), Brisbane Lions in 18, Melbourne in 20, Collingwood in 23, Sydney in 25, and Geelong in all 34, appearing as Minor Premier on all occasions.
These 34 orderings - of which there were 102 in total across the entire simulation - together account for 94% of all replicates.
Lastly, let’s look at the Top 2s that came out of the simulations.
There were 10 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 almost 2-in-5 replicates.
The second- through fifth-most common orderings all have Geelong in 1st and swap in one of Collingwood, Melbourne, Brisbane Lions, or Fremantle for 2nd. Together, they account for another 60% of replicates.
Thereafter follow five more orderings that, together, appear in less than 1-in-200 replicates.
