Projecting the Final Ladder for 2010 (After Round 16)

It's late July and normally it'd be time for the first whispers of tanking to emerge, but the rejigging of the draft process next year to accommodate the introduction of Gold Coast and GWS has significantly reduced the reward to sustained ineptitude so effectively that, this year, I doubt there'll be much talk of it (or, come to that, much compelling evidence of its existence). Another popular late-July activity is speculating about the finals and I think it's time we did a little of that.

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Simulating The Last Round

I was curious, as I imagine were many of you but to a less obsessive extent, to understand how next weekend's results will affect the make up and ordering of the final 8. So, in a fashion similar to that which I used last week, I simulated the last round of the competition, this time using the opening head-to-head TAB Sportsbet markets to set the win probabilities for each game.

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Simulating What's Left of the Season

We've just 2 rounds to go now until teams start creating the history that fans will remember - fondly or otherwise - and neither the top 4 nor the top 8 positions are all locked in. Surely the practical science of statistics can help us to determine the chances for each team that is still in the running.

To simulate the possible outcomes for the season's remaining games we need to:

• Estimate the probability of victory for each team and each game
• Use these probabilities to simulate the outcome of all remaining games
• Repeat these simulations a large number of times and aggregate the data about where teams finish in each simulation

(For anyone who's curious, in the second step I use the fact that I've determined empirically - as chronicled over on MAFL Stats - that there's a direct link between a team's probability of victory and the handicap it can expect to receive on line betting, and that handicap-adjusted margins seem to roughly follow a Normal distribution with a mean on 0 and a standard deviation of 37.7 points.)

I've completed the steps above using 3 different sets of probabilities, as set down in the table below:

The three scenarios are labelled Base Case, Stronger Favourites and Weaker Favourites, with the probabilities for the first 8 games in each scenario based on the opening head-to-head market prices on TAB Sportsbet and the remaining probabilities set to be broadly consistently with the scenario name.

So, for example, in the Base Case scenario, West Coast are slight favourites over Richmond in Round 22, as they have an assigned probability of 55% (ie 0.55). This rises to 65% in the Stronger Favourites scenario and 50% - that is, equal favouritism - in the Weaker Favourites scenario.

Okay, now to the interesting part: what outcomes do we get for each of these scenarios?

Here's the summary detail for each team of the probability of Top 4 and Top 8 finishes and the most likely ladder position under each of the scenarios:

Across the scenarios, we find that:

• The Saints and the Cats almost always finish 1st and 2nd, in that order. Looking at the actual simulation results (not shown here), in a tiny number of instances - less than 1 time in 100,000 - the Saints and the Cats swap places, but not often enough for this to be considered a serious possibility. So, the Saints' most likely finish is 1st and the Cats' is 2nd, both with probabilities close to 100%.
• Collingwood finishes in the top 4 in all but about 1-2% of the simulations, regardless of the scenario. The more detailed simulation results reveal that Collingwood finishes 3rd about 75-85% of the time, 4th 10-20% of the time, and 5th about 1-2% of the time. Their most likely finish is 3rd.
• The Western Bulldogs finish in the Top 4 about 56% of the time under the Stronger Favourites scenario and 70% of the time under the Weaker Favourites scenario. They always finish in the Top 8 under any scenario. They could finish anywhere from 3rd (with probability ranging from 15 to 25%) to 7th, though a finish this low is very unlikely. Their most likely finish is 4th, for which the probability is about 40-45%.
• Carlton finishes in the Top 4 about 17% of the time under the Weaker Favourites scenario and 32% of the time under the Stronger Favourites scenario. They too always finish in the Top 8 regardless of scenario. They could finish as high as 3rd, though this is very unlikely (probability less than 1%), or as low as 7th (with probability around 20%). Their most likely finish is 5th, for which the probability is about 35%.
• Adelaide is another team that always makes the Top 8 under any scenario. They also make the Top 4 about 10% of the time under any scenario. They could finish as high as 3rd, though this is very unlikely for them, or as low as 7th (with probability of 30-50% depending on scenario), which is their most likely finish.
• Brisbane Lions are also a simulated certainty to make the Top 8, but they've only a 2-3% chance of making the Top 4. Their best possible finish is 4th and their worst is 8th (with only about a 1% probability). Their most likely finish is 6th or 7th depending on the scenario, and the combined probability for such these two positions is about 70-80%.
• Essendon are no chance for a Top 4 spot and a 72-78% chance of a Top 8 spot, depending on the scenario. Their best possible finish is 7th and their worst is 11th. Both have associated probabilities of around 1%. Their most likely finish is 8th, for which the probability is 70-80%.
• Port Adelaide are also no chance for a Top 4 spot, but are a 13% chance of a Top 8 spot, regardless of the scenario. Their best possible finish is 8th, and their worst is 12th, though this carries only a 1% probability. Their most likely finish is 9th, for which the probability is 45-65%, depending on the scenario.
• Sydney are also no chance for a Top 4 spot and virtually no chance for a Top 8 spot. The probability of them making the 8 ranges between about 0.5% to 1.5% depending on the scenario. Their best possible finish is 8th, and their worst is 12th, with a probability of 15-30%. Their most likely finish is 11th, for which the probability is about 40%.
• Hawthorn are another team with no chance for a Top 4 spot, but the probability of them making the 8 ranges between about 8% and 14% depending on the scenario. Their best possible finish is 8th, and their worst is 12th, with a probability of 10-15%. Their most likely finish is 10th, for which the probability is about 30-35%.

No other team finished in the Top 8 in any of the simulations for any of the scenarios.

All of which means that, if you believe the probabilities I've used for the scenarios:

• For the Top 4, the Dogs are a good bet at $1.80, Carlton at $6, Adelaide at $10, and the Lions at $50
• For the Top 8, Essendon are a good bet at $1.50, Port at $8, Sydney at $250, and Hawthorn at $12.50
• The Dees are a 90-95% chance for the Spoon, though the Roos, Richmond and Fremantle all have non-zero probability of finishing last. Fremantle is a 5-10% chance, while the Roos and the Tigers both have probabilities less than 0.5% under any scenario.

Which is probably why, on TAB Sportsbet, there is no longer a Spoon market.

And Then There Were Eleven ...

Well last weekend's results certainly altered the finals landscape, leaving all of the teams currently in ladder positions 1 through 11 with legitimate dreams of playing in September and all of the teams in positions 1 through 7 with hopes for a top 4 finish and the double chance.

With the aid of the latest ELO projections, let's take a look at what's left for the teams in contention.

St Kilda have probably the easiest run home of all the teams in the competition. They face 9th placed Essendon away (hence the '9', the 'Ess' and the 'A' in the entry for St Kilda for Round 20, which is coloured green because ELO predicts the Saints will win this game), 13th placed Kangaroos at home, and then last placed Melbourne away. So, give them three wins and 1st place, with only the Dons as a realistic threat to a 22 and 0 home-and-away season.

Geelong have a slightly more challenging finish, starting with faint-hope finalists Sydney away this weekend, followed by the Dogs away, and then Fremantle at home. They should win all three of these games; regardless, they finish 2nd.

Collingwood face the in-form but out-of-contention Richmond this weekend, before matching up with the Swans in a game that'll matter much more to the Swans if they've knocked off the Cats in Round 20. In the final round the Pies take on the Dogs, but by that point they will most likely have secured 3rd place.

The Western Bulldogs have an horrendous last 3 weeks of the home-and-away season comprising contests with teams no lower than 5th on the ladder. First up is an away game with the Lions, then a home game against the Cats, and, finally, another home game, this one against the Pies. ELO has them winning 2 of these 3 contests and therefore securing 4th spot on percentages, but it's easy to see them dropping another 1 or even 2 of these games and missing a top 4 spot.

Carlton have what could be described as an awkward finish to the season, including as it does two teams that are in finals contention: Port Adelaide, who they play away this week, and Adelaide, who they play at home in the final round. In the middle they have the 4-point insurance that comes from playing the Dees. ELO has the Blues winning 3 and they should at least manage 2, making them a possible top 4 finisher.

Adelaide also have an awkward finish, starting with the 'surprised to still be in it' Hawks away this weekend, followed by the Eagles at home, and rounding out with a tricky away contest against the Blues. ELO's credited them with 2 wins, though you could make a good case for 1 or for 3 wins. The Crows should comfortably make the 8 and might yet surprise and jag a top 4 spot, but I'd treat this as unlikely.

If awkwardity is quantifiable (or, indeed, even a word) then the Brisbane Lions have more of it in their run home than any other team. This weekend they face the Dogs at home, then Port again at home, and, lastly, Sydney away, who might still have a sniff at that point but probably won't. ELO's giving the Lions just 1 win from that lot, but 2 is conceivable, even 3 if the gods of oblate spheroids are smiling on them. They'll make the 8 but almost certainly not the top 4.

Hawthorn can, amazingly, lose again this week - to the Crows at home - but still sneak into the finals with back-to-back wins against Richmond away and Essendon at home to complete a 10-12 season and pip Port on percentages. One possibility is that the Hawks will face the Dons in Round 22 with a place in the finals at stake for both of them.

Port Adelaide could also slip into the 8 with just 40 points and having lost 2 of their last 3 games. They face Carlton at home this week, then the Lions away and the Roos at home. If they can win 2 of these then the Hawks will need to win all 3 of theirs to deny Port a finals berth.

Essendon will probably finish just 1 win short of the finals. They play Saints at home this week, then Freo away and then the Hawks also away. It might, as I noted above, all come down to the Round 22 clash with the Hawks.

Sydney have the faintest of finals hopes, but would need to topple the Cats at home, Collingwood away, and then the Lions at home to realise that dream. Frankly I think I'm more likely to win Lotto - and I don't even buy tickets.

For the rest of the teams it's all about draft picks and dealing with tanking speculation.

The Ladder's Still Full of Opportunities

The top 8 of the MARS Projected Final Table after Round 18 differs from the current ladder only in that Adelaide and Collingwood trade places. MARS predicts that Adelaide will grab 4th spot on the back of four straight wins over the remainder of the season, skipping them past the Pies, who win only two more, beating Richmond and Sydney but losing to Adelaide and the Dogs.

Under the MARS scenario, 4th place will still be undecided as we move into Round 22.

Here's MARS' current projected final table and the predicted results that will produce it:

The key clash for Adelaide looms as the Round 20 matchup with the Hawks, which MARS has the Crows winning by a point. Assuming that Hawthorn lose in Round 19 to the Saints and beat Richmond and Essendon in Rounds 21 and 22, Hawthorn will need to down the Crows to have a chance at securing 8th spot, knocking Port out of the eight and relegating the Crows to 5th, behind the Pies.

Collingwood might otherwise grab a spot in the top 4 if they defeat the Bulldogs, as might the Lions if they, instead, beat the Dogs.

Essendon are projected to miss the 8 by two games, as MARS forecasts them to lose to the Lions, St Kilda and Hawthorn, securing a solitary victory over a floundering Fremantle in Round 21.

Sydney, though still a mathematical chance to reach 44 points and therefore press for a finals spot, would need to topple Richmond, Geelong, Collingwood and the Lions in successive weeks to do so, which seems about as likely at the moment as the AFL relenting and changing the rules for the draft.