This week was an especially bad one for the finals hopes of Sydney, Melbourne, and Essendon, and a good one for those of Richmond, Geelong, the Western Bulldogs, and West Coast.
Overall, this week's 50,000 simulations of the remainder of the 2017 AFL season sees:
- seven teams' Finals chances move by more than 5% points
- four teams' Finals chances move by more than 10% points
- six teams' Top 4 chances move by more than 5% points
- four teams' Top 4 chances move by more than 10% points
(For details on the methodology I've used in the simulations, please see this blog.)
The charts below summarise the distribution of ladder finishes for the 18 teams from the simulations run after the current round, Round 19, and Round 18. Note that the ordering of the teams is slightly different in the two charts, reflecting improvement or deterioration in some team's expected ladder finish.
In terms of Final 8 chances, the big winners this week were:
- Western Bulldogs: +15% points (up by 22% points now in the last two weeks)
- West Coast: +10% points
- Richmond: +7% points (up by 15% points now in the last two weeks)
The big losers were:
- Essendon: -17% points
- Melbourne: -14% points
- Sydney: -8% points
- St Kilda: -5% points (down by 24% points now in the last two weeks)
In terms of Top 4 chances, we had as winners:
- Richmond: +19% points (up by 36% points now in the last two weeks)
- Geelong: +10% points
- GWS: +5% points
... and, as losers:
- Sydney: -23% points
- Melbourne: -13% points
- Essendon: -5% points
Overall, the chart above and the latest heat map below show further narrowing in the range of most-likely finishes for each team, but a great deal of uncertainty remains, especially mid-table.
This week, inspired by a conversation I had on Twitter, I realised that the Gini measure of concentration, commonly used in economics for measuring income inequality, could also be used to quantify that uncertainty - that is, to measure the spread of each team's potential final ladder positions, and the concentration of the probabilities across all the teams vying for any given ladder position.
In the context of a team, a Gini coefficient of 1 implies that the team has only one feasible final ladder position, while a GIni coefficient of 0 implies that all 18 ladder positions are equally likely. Since no team has, as yet, mathematically locked in any ladder position, and none are capable of finishing in every one of the possible ladder positions with equal probability, no team has a Gini coefficient of exactly 0 or 1.
But, as we can see in the table at right, Adelaide and the Brisbane Lions are the teams whose Gini coefficients are highest, reflecting the fact that they have a relatively narrow set of likely final ladder positions (Adelaide is now a 70% chance for 1st and the Brisbane Lions a 64% chance for 18th).
Conversely, the Western Bulldogs, Melbourne, and West Coast, are the teams whose Gini coefficients are smallest, signalling that they have the broadest range of possible ladder finishes. The Dogs have about 10% or greater chances for every ladder position from 6th to 11th, Melbourne likewise from 6th to 10th, and West Coast likewise from 7th to 11th.
In the context of a ladder position, a Gini coefficient of 1 implies that only one team could feasibly finish in that position, while a GIni coefficient of 0 implies that all teams are equally likely to finish in that position. Again, because no ladder position has been secured by any team and because no position is capable of seeing every team occupy it with equal probability, no Gini coefficient is exactly 0 or 1.
Looking at the ladder position Gini coefficients, which appear at left, we see that 18th and 1st are the positions with the narrowest range of likely occupants at season's end, whilst 5th through 10th are the positions with the widest range of potential occupants.
For each of the ladder positions 5th through 10th there are at least five teams with about 10% or greater chances of occupying it come the end of Round 23, so, again, the Gini coefficient values seem to make practical sense.
It's interesting to note that 3rd and 4th positions on the ladder, whilst more settled than 5th through 10th, still have relatively low Gini coefficients, reflecting the fact that four teams have double-digit probabilities for those double-chance ladder spots.
Next, let's update the game importance table. It shows, you'll recall, how each team's chances of making the finals varies depending on the result of each of the remaining games. The overall Weighted Ave Importance figure tells us the average amount by which the teams' finals chances are expected to change on the basis of the outcome of a particular game. A larger figure means that the game is expected to change teams' finals chances, on average, by a larger amount and hence is a more important game.
(For more details about the methodology and the rationale for it, again please see this blog.)
Four hugely influential games are in prospect in Round 20: GWS v Melbourne, Essendon v Carlton, Brisbane Lions v Western Bulldogs, and St Kilda v West Coast. They are all capable of altering at least one team's finals chances by 30% points or more.
The Geelong v Sydney game is also moderately important but less so than the games just listed because it will have very little effect on the Cats' chances of playing Finals, which are already close to 100%.
NUMBER OF WINS REQUIRED
Next, an update on the analysis looking at how likely it is that a team will play Finals given that it finishes the home-and-away season on exactly 11, 11.5, 12, 12.5 or 13 wins.
Recall that these estimates, because they're based on a sample of simulations, are subject to error (as are all of those in this blog), which here is reflected in the width of the segment.
There's not a lot of change in this chart this week, which continues to reflect that 11 wins is unlikely to be enough for any team, and that 12 wins gives a better than even-money chance only for Port Adelaide, Sydney, Essendon and Melbourne. Thirteen wins pretty much guarantees every team a finals berth.
MOST LIKELY TOP 2s and top 4s
This week we'll again look at the team orderings most likely for the Top 2 and Top 4 spots.
Based on the latest simulations, the most likely final Top 2 is still Adelaide/ Geelong, which was the finishing order in about 38% of replicates, up another 7% points on last week's estimate.
The next most likely finish remains Adelaide/GWS, which occurred in about 14% of replicates, while the third mostly likely remains an Adelaide/Richmond pairing with about a 13% probability.
Combined, the 10 most-likely Top 2s account now for over 90% of replicates and include just five teams: Adelaide, Geelong, GWS, Port Adelaide and Richmond.
The most likely Top 4 is now Adelaide/Geelong/GWS/Richmond, which occurred in just over 5% of replicates, roughly doubling in likelihood relative to last week.
Port Adelaide slips into 3rd in the next-most likely Top 4, though the quartets ranked 2nd through 6th all carry roughly equal probabilities.
Altogether, the 10 most-likely Top 4s now account for about 35% of replicates.
SIMULATIONS OF THE FINALS SERIES
Applying the methodology as described in this blog to the 50,000 final ladders produced by our original simulations yields the following results.
One of the more striking features of the chart above is the relative frequency with which Sydney (c 6%) and Port Adelaide (c 3%) are projected to win the Flag despite finishing in the bottom half of the Top 8. In addition, Sydney makes but loses the Grand Final despite finishing in 5th to 8th in another 5% of replicates, and Port Adelaide does the same in another 3% of replicates.
Altogether, a team from outside the Top 4 wins the Flag in 19% of replicates, and a team from outside the Top 4 finishes as Runners Up in 21% of replicates. Before last year, those estimates would have felt ludicrously high.
Adelaide remain favoured by the simulations to take out both the Minor Premiership (70% chance) and the Flag (28% chance). Geelong has about a 15% chance for the Minor Premiership and a 17% chance for the Flag, while Richmond, GWS, Port Adelaide and Sydney all have about 9 to 13% chances for the Flag.
We see from the heatmap above that, if we define the season in terms of the six events listed there, the most-likely finishes for each team are estimated to be:
- Lose in a Preliminary Final: Port Adelaide, GWS, Richmond, Geelong and Adelaide
- Lose in an Elimination Final: Sydney
- Miss the Finals: all other teams
We also see that Adelaide are estimated to be about 50% chances for making the Grand Final, Geelong 34%, Richmond, GWS and Port Adelaide about 25%, and Sydney about 18%. The Dogs are now just 6% chances of playing in back-to-back Grand Finals.