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.)
We’re beginning to see a wider range of expected wins in the MoSHBODS simulations now. This week they span about 8.9 games, which is up from last week’s 7.5 game span thanks to a Cats win and a Blues loss.
The week’s biggest losers in terms of Expected Wins, according to the simulations, were Richmond (down 1.0 Expected Wins), and Hawthorn and Carlton (down 0.8 games each), while the biggest gainers were the Western Bulldogs (up 0.9 games).
Looking at the simulations through the lens of making the Finals, we have:
Richmond (down 16% points)
Hawthorn (down 12% points)
Western Bulldogs (up 10% points)
Brisbane Lions (up 8% points)
Geelong now find themselves almost even-money chances for the minor premiership, and Collingwood roughly 3/1 propositions.
TEAM AND POSITION CONCENTRATION
As mentioned for a few weeks now, 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, from both a team and a position viewpoint, we find slight reductions in uncertainty, with the overall Gini coefficients now around 0.46 to 0.47.
At the team level, we saw particularly large reductions in uncertainty for the Lions, Blues, Pies, Hawks, Giants, and Swans this week, and relatively large increases for the Dogs, Tigers, and Dees.
Geelong, Carlton, Collingwood, and Sydney currently have least uncertainty about their eventual ladder finishes, while West Coast, Fremantle, St Kilda, and Essendon have the most uncertainty.
Next, adopting a ladder position viewpoint, we see that 1st and 18th remain the positions with the narrowest range of likely occupants at season's end, whilst positions 7th through 13th continue to have the widest range of applicants.
Looking more broadly, every ladder position except 14th and 15th became at least a little more certain this week about which team will occupy it come the end of the home-and-away season.
(One way of getting a feel for what a particular Gini value means is to look at the Gini coefficient that would eventuate if a team were equally-likely to finish in any of X positions and in no other, or, equivalently, if X teams were equally-likely to finish in a give ladder position and no other teams were capable of doing so.
The lookup table at right provides those numbers for all possible values of X.
With it you can say, for example, that Geelong’s current Gini of 0.8 is roughly equivalent to a situation where they were equally-likely to finish in any of 3 or 4 positions. In contrast, West Coast’s Gini of 0.3 is roughly equivalent to a situation where they were equally-likely to finish in any of 12 or 13 positions.
From the ladder position perspective, we can also say that the Gini of 0.8 for 1st spot on the ladder is roughly equivalent to a situation where they were 3 or 4 teams equally-likely to finish in that position. In reality we have one team that’s most likely (Geelong at about 48%), a second that’s about a 25% chance (Collngwood), a third that’s about a 13% chance (GWS), and then 8 teams with chances in the 1% to 4% range.
It’s a somewhat crude way of looking at the Gini values, but it gives a rough feel for at least the larger differences.)
Here are the updated assessments of the 30 most-important games between now and the end of the home-and-away season. (See this blog for details about how these are calculated.)
We’re again seeing a significant amount of stability in this list, with twenty-two of the 30 games (and 17 of the top 18) shown also having been estimated as being in the top 30 last week.
In terms of the temporal distribution of these games, we now have:
Rounds 8 to 12: 5 games
Rounds 13 to 17: 8 games
Rounds 18 to 23: 17 games
We’re continuing to see then the influence of this year’s conservative methodology regarding games further into the future.
That said, looked at by team we have:
9 games involving Essendon
8 games involving St Kilda
7 games involving Adelaide, Richmond, or West Coast
6 games involving Fremantle
5 games involving Port Adelaide
4 games involving Western Bulldogs
2 games involving Hawthorn or Brisbane Lions
1 game involving Collingwood, GWS, or Melbourne
We can see the commonsense of this list when we compare it with the simulated probabilities for teams finishing in 8th or 9th, which are:
18%: St Kilda, Adelaide, Richmond, West Coast, and Fremantle
16%: Port Adelaide
15%: Brisbane Lions
12%: Western Bulldogs
No other team has a higher than 9% estimated probability of finishing in 8th or 9th.