2019 : Simulating the Final Ladder After Round 22
/Often, there’s little point in simulating the final ladder with only one round to be played, but this year is different, as there are four teams with some hope - but no certainty - of playing Finals.
So, the results of the latest 50,000 simulations appear below.
(If you’re curious about the methodology used to create them, you can start here.)
RESULTS
According to these latest results, the Western Bulldogs are by far the team most likely to join the seven that already have a guaranteed spot in the Top 8. Their estimated chances of progressing are 3 in 4, while Hawthorn’s are about 1 in 9, Port Adelaide’s 1 in 11, and Adelaide’s 1 in 20.
In the race for the Top 4, the Lions and Cats are locked in, and Richmond and West Coast are both about 75 to 80% chances of filling one of the two other spots. Collingwood are about a 9 in 20 chance.
Geelong are now estimated to be 45% chances for the Minor Premiership, and the Brisbane Lions 52% chances.
In terms of estimated probability of making the Finals, the largest moves this week were increases of around 50% points for Essendon and the Western Bulldogs, and decreases of 61% points for Port Adelaide, and 32% points for Adelaide.
The biggest changes in teams’ Top 4 prospects came for Collingwood (up 16% points), and West Coast (down 12% points).
DETAILED LADDER FINISH ESTIMATES
The detailed view of each team’s estimated probability of finishing in each of the 18 possible ladder positions appears below. Blank cells represent ladder finishes that did not occur even once in the 50,000 simulations, while cells showing a value of 0 represent estimated probabilities below 0.05%.
No team now has more than six possible ladder finishes, and most have four or fewer.
The most-likely tally of wins for teams in various final home-and-away ladder positions are now:
1st to 3rd: 16 wins
4th and 5th: 15 wins
6th: 13 wins
7th and 8th: 12 wins
9th: 11 wins
10th: 10 or 11 wins
11th and 12th: 10 wins
13th and 14th: 9 wins
15th: 8 wins
16th: 7 wins
17th: 5 wins
18th: 3 wins
FINAL 8S
This week, for the first (and only) time, we’ll look at what the simulations are suggesting are the most-likely orderings for the Final 8.
In total, there were 191 different orderings this week across the 50,000 simulations, 23 of which occurred in at least 1% of replicates. Those 23 appear below. Combined, they represent just over three-quarters of the simulation replicates.
We can see that even the most likely final ordering has less than a 1 in 10 chance of occurring.
The simulations also give us estimates of the likelihood of each possible matchup for week 1 of the Finals.
For the 1st v 4th clash we have the estimates as shown at right, which show that a Geelong v Richmond matchup is most likely, and occurs in just over 1 in 4 replicates.
A Brisbane Lions v Collingwood clash is next-most likely, and occurs in just under 1 in 5 replicates. Three other pairings occur in at least 1 replicate in 10: Geelong v Collingwood, Brisbane Lions v Richmond, and Brisbane Lions v West Coast.
The Lions face the Cats in about 1 replicate in 11, but do so away on less than half of those occasions.
West Coast, should they make it, play this Final interstate in all but the very few cases where they finish as Minor Premiers.
For the 2nd v 3rd clash we have exactly the same number of possibilities as we have for the 1st v 4th clash, but we’ve three almost equally-likely possibilities in Geelong v West Coast, Brisbane Lions v West Coast, and Brisbane Lions v Richmond clashes. They each occur in about 1 replicate in 5.
If we combine the two possible orderings for each pair of teams, we have the Cats/Eagles pairing at 26%, Lions/Eagles at 27%, and Lions/Tigers at 23%. Together, these three pairings represent over three-quarters of all replicates.
Richmond play interstate in over 1 replicate in 4, West Coast in about 1 replicate in 4, Brisbane Lions about 1 replicate in 10, and Geelong in about 1 in 20.
Next, 5th v 8th, where we find more possibilities, but a number of them with only very remote chances of occurring.
The most likely matchup is Collingwood v Western Bulldogs, which crops up in about 1 replicate in 4 and slightly more often than Collingwood v Essendon, and Richmond v Essendon matchups. Together, these three matchups account for about 3 replicates in 5.
The only other pairing with an estimated probability greater than 1 in 10 in West Coast v Essendon.
Essendon play interstate in about 1 replicate in 8, Port Adelaide in about 1 in 12, Hawthorn 1 in 20, and Adelaide also about 1 in 20.
Collingwood faces a team travelling from interstate in over 1 replicate in 3, West Coast about 1 in 5, and Richmond 1 in 20.
Finally, 6th v 7th, where the set of possibilities is very small and where two of them - GWS v Western Bulldogs, and GWS v Essendon - account for over 9 in 10 replicates.
The only other pairing with a better than 1 in 100 estimated chance of occurring is Essendon v GWS, which appears in 1 in 20 replicates.
LIKELIHOOD OF PERCENTAGE DETERMINING POSITIONS
This week’s results altered considerably the likelihood that certain key positions on the final home-and-away ladder will be determined by percentage because the teams in those positions finish tied on competition points.
In the latest simulations, 4th and 5th are separated by percentage in about 48% of the simulations (up 18% points), and 8th and 9th are separated by percentage in about 30% of the simulations (down 31% points). As well, 8th and 10th are separated by percentage in about 37% of the simulations, and 8th from 11th in about 9%.
Also, in almost two-thirds of the simulation replicates, 1st and 2nd are separated only by percentage.
TEAM AND POSITION CONCENTRATION
One way of measuring how much uncertainty there is in the competition is to use the Gini measure of concentration commonly used in economics for measuring income inequality to quantify the spread of each team's estimated final ladder positions across the 50,000 simulation replicates, and to quantify the concentration in the probabilities across all the teams vying for any given ladder position.
This week, as we’d again expect, we saw the uncertainty about the final ordering of the teams decrease quite significantly, with the Gini coefficients rising now to around 0.88. (For purely mathematical reasons, the actual maximum they can reach is just over 0.94, so we’re getting close to complete certainty.)
At the team level, most uncertainty remains for West Coast, Adelaide, Richmond, and Hawthorn, while Gold Coast, Melbourne, Sydney, Carlton, and GWS have the most certainty about their eventual ladder finishes.
If we adopt a ladder position viewpoint instead, we see that 6th, and 15th to 18th are the positions with the narrowest ranges of likely occupants, while 2nd to 4th, 8th, 10th and 11th have the widest ranges.
Roughly speaking, we have slightly more certainty this year after 22 rounds than we did last year at the same point about the final ordering of the teams at the end of the home-and-away season (the Gini coefficient then was about 0.89).
GAME IMPORTANCE
Here are the assessments of importance for the remaining 9 games of the home-and-away season. (See this blog for details about how these are calculated.)
In reality, only three games will have any affect on which teams do and don’t play Finals, the non-zero results for the six games at the bottom of the list being attributable purely to sampling variation.
And, finally, here are the assessments of the importance of the remaining games in terms of their estimated likely impact on the Top 4 (using an equivalent methodology to that we used for assessing the likely impact on the Top 8).
Here, too, only three games will have any impact in practice, sampling variation again the cause of the non-zero results for the six other games.
Note that the West Coast v Hawthorn game is the only one that will affect membership of both the Top 4 and the Top 8.
