# 2018 : Simulating the Final Ladder After Round 17

/Updated final home and away ladder simulations appear below.

(For details on the methodology, see this post from earlier.)

With a number of surprise wins this week, five teams gained more than half an Expected Win:

**Fremantle**(+0.8)**Brisbane Lions**(+0.8)**GWS**(+0.7)**Adelaide**(+0.7)**West Coast**(+0.6)

Six more saw their Expected Win count drop by more than half a game:

**Hawthorn**(-0.8)**Port Adelaide**(-0.8)**Richmond**(-0.7)**Collingwood**(-0.7)**Geelong**(-0.6)**North Melbourne**(-0.6)

Only nine teams are now expected to win 12 games or more in the regular season, with Port Adelaide in 3rd now separated from Melbourne in 6th by only 0.76 Expected Wins.

In terms of likelihood of making the Finals, the week's big gainers were:

**GWS**(+25% points)**Sydney**(+12% points)**Melbourne**(+10% points, making it +22% points over the past two weeks)

The week's big losers were:

**Hawthorn**(-23% points)**North Melbourne**(-15% points)**Geelong**(-12% points)

Eight teams are still assessed as better than even-money chances for a spot in the Finals.

In the quest for a Top 4 spot there were a number of large changes this week, the largest among them:

**West Coast**+23% points (making it +29% points over the past two weeks)**Sydney**+18% points**Melbourne**+12% points (making it +19% points over the past two weeks)**GWS**+12% points**Port Adelaide**-17% points**Collingwood**-16% points**Geelong**-14% points**Hawthorn**-13% points

Just two teams now (half as many as last week) have better than even-money chances for a place in the Top 4. Four teams have between 37% and 48% chances.

Percentages still seem likely to be important for separating teams in a number of key ladder positions. The chart below shows how likely it is that any pair of ladder positions will be occupied by teams equal on wins at the end of the home-and-away season. It shows that there's an estimated 43% chance (up 4% points from last week) that the team in 9th will be separated only on percentage from the team in 8th.

It also shows that there is about a 46% chance that the teams in 4th and 5th will finish equal on wins, and about a 30% chance that the Minor Premiership will be determined by percentage.

### TEAM AND POSITION CONCENTRATION

This week's Gini concentration measures appear below, and reflect the level of certainty in our knowledge about which teams will finish where at the end of the home and away season.

For information about how to interpret these measures, you can see this blog, but the table at right might also help. It shows the Gini coefficient that a team would have if it were equally likely to finish in any of a specified number of ladder positions (and in no other position).

So, for example, a team that was equally likely to finish in any of six ladder positions would have a Gini coefficient of 0.667. This week, as we'll see in a moment, North Melbourne has a Gini coefficient of 0.643, so we can think of the level of uncertainty it has about its final home-and-away ladder position as roughly equivalent to that for a notional team that found itself equally likely to finish in any of six ladder positions. Note that we're not saying that North Melbourne is only capable of finishing in six different ladder positions (it can actually finish in any of 15 different positions, 11 of them with an estimated probability of 1% or more), just that the uncertainty it faces it roughly equivalent to a team in that situation.

You'll note that a team equally likely of finishing in any of the 18 ladder positions will have a Gini coefficient of 0, but one that is absolutely certain of its final ladder position will have a Gini coefficient of 0.944, not 1. There's a technical reason for this - and a 'bias correction' we could apply to all coefficients to force the range to be (0,1) - but for our purposes, the uncorrected coefficients are fine.

(Note that, when we're looking at the Gini coefficients for ladder finishes rather than teams, we can substitute "Number of Equally-Likely Finishes" for a team with "Number of Teams Equally-Likely to Finish in the Position".)

For the average team, final ladder position certainty rose only slightly this week, but it fell for Richmond, Essendon, Adelaide, Collingwood, Port Adelaide, and GWS.

Melbourne are the team whose final position is now least certain. They have a 7% or greater estimated chance of finishing in any of the positions from 2nd to 9th.

The largest increase in certainty came for West Coast, who are now roughly as certain about their final ladder position as they were at the end of Round 13, the intervening rounds having muddied the waters for them in this regard.

Carlton remain the team with the highest level of certainty about their ultimate ladder finish, with an estimated 77% chance of finishing 18th, and an estimated 22% chance of finishing 17th.

Overall, looking across all 18 teams, we saw a decrease of only 0.9% in uncertainty.

Looking next at each of the ladder positions, we find increases in uncertainty for 1st, 7th, 8th, 9th, 11th and 12th, with 8th now the ladder position about which there is most uncertainty.

The largest decreases in certainty were for 2nd, 5th, 15th and 17th, although 5th remains one of the positions still with relatively high levels of uncertainty.

Least uncertainty is associated with 18th position (which Carlton has a 77% chance of filling), 17th position (which Gold Coast has a 65% chance of filling), and 1st (which Richmond has a 66% chance of filling).

Across all 18 ladder positions, the average decrease in uncertainty this week is similar to that we saw for the team-based view (viz just under a 1% increase in the average Gini coefficient).

### WINS REQUIRED

Below are the updated estimates of teams' likelihood of making the Finals depending on the number of wins that they record.

*(Recall that, because we're working with a sample of simulated final ladders, our estimates have sampling error, so we show them as 95% confidence intervals here with the mean estimate shown as a point. In some cases, our sample is so large that the interval essentially collapses to a point, at least to the resolution shown here.)*

Geelong and Melbourne remain the teams most likely to make the Finals should they finish on only 12 wins, with the estimated conditional probability of them doing this still under 50%. Adelaide, Fremantle, and Essendon are the teams least likely to make the Finals should they finish on just 12 wins, though most teams' conditional probabilities are under 25%.

Thirteen wins makes all teams except Essendon and Fremantle 75% or better chances for a finals berth.

Looking next at the analysis for Top 4 finishes, we find that Richmond and Melbourne are now both better than even-money chances of finishing in the Top 4 with only 14 wins. Geelong's chances are assessed as being only slightly below 50%.

West Coast, Collingwood, Sydney, and Port Adelaide - who currently fill 2nd to 5th on the competition ladder - are all only about 25% chances of finishing Top 4 with only 14 wins.

Fifteen wins now sees every team capable of reaching that tally with 90% or better chances of finishing Top 4 should they do this.

Looking at the relationship between every possible ladder finish for a team and the number of wins that team records we still see still quite wide ranges of relatively plausible finishes for a number of teams given a specified number of wins - say Geelong or North Melbourne, for example, with 12 or 13 wins.

A similar analysis, aggregating across teams, gives us an idea of the overall spread of likely ladder finishes for teams with a specified number of wins. It's quite clear from this, for example, that, as was the case last week, 13 wins is more often associated with 8th spot than is 12 wins. However, 14 wins is now marginally more often associated with 4th spot than is 15 wins.

Next, we explore the inter-team dependencies in the composition of the final 8 by estimating the probability that a particular teams makes the 8 conditioned on some other team making or missing the 8.

These are shown in the charts below, as usual, as arrows with the base of an arrow marking the estimated probability that a team makes the 8 conditioned on a nominated team missing the 8, and the arrow head marking the estimated probability that a team makes the 8 conditioned on a nominated team making the 8.

(Note that these images can be clicked on to access larger versions.)

The magnitude of the arrow lengths in the chart denotes the extent to which one team's chances are linked to another's, and reveals that, for example:

- Geelong's fate is highly associated with Hawthorn's
- Hawthorn's fate is highly associated with Geelong's, Sydney's, and Essendon's (although Sydney are unlikely to miss the 8, and Essendon unlikely to make the 8, as reflected in the extent to which the relevant arrows protrude above or below the black line, which denotes Hawthorn's unconditional probability of making the 8).
- GWS's fate is highly associated with Adelaide's
- North Melbourne's fate is highly associated with Collingwood's and West Coast's (although neither are likely to miss the 8).

We can do the same analysis for positions in the Top 4, which we do below.

Here we find the highest levels of dependence across a range of teams for Collingwood, Melbourne, Port Adelaide, and Sydney, which are the teams currently filling 3rd to 6th on the competition ladder.

### GAME IMPORTANCE

Below is the updated list of the 30 most important games remaining in the fixture on the basis of their expected impact on all 18 teams' finals chances.

Five of Hawthorn's six remaining games are in the Top 10, as are three of North Melbourne's, and two of Geelong's.

There are two of the Round 18 games in the Top 10: Collingwood v North Melbourne, and Geelong v Melbourne.

In the next and final table we have the estimated importance of each remaining game to the composition of the Top 4.

Here we find that Melbourne and Sydney both have four games in the Top 10, while GWS and Port Adelaide have three each, and Collingwood and West Coast two.

Next weekend's Port Adelaide v GWS, and Geelong v Melbourne games are both amongst the Top 10.