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Crunch the probabilities and predict the AFL finals

15th August, 2017
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Mitch McGovern of the Adelaide Crows. (AAP Image/David Mariuz)
Roar Guru
15th August, 2017
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There are only two rounds left of the 2017 AFL season, and it’s time to put my maths degree to use!

With just a few variables left to deal with, we can take the punters odds and some basic probability calculations to figure out what the (relatively) precise probabilities are for each team to earn a finals berth, a home final or whichever appropriate goal is in sight.

Adelaide
Adelaide has a top-two seed nailed down as Geelong cannot realistically make up 410 points of differential. In order to not take the top seed, the Crows would have to lose both games in R22 and R23 while the Giants would have to win both games. We, by the way, are not considering the possibility of draws in our calculations because, frankly, we’re just sick of draws this year!

The translation of the decimal odds into percentage chances are as follows.

31% x 37% x 92% x 57% = 0.31 x 0.37 x 0.92 x 0.57 = 0.0582 – Adelaide, therefore, has a 5.82 per cent chance of the second seed, which means their chance of claiming the top seed is 94.18 per cent.

Greater Western Sydney
The Giants have that 5.82 per cent chance of the top seed as described above, and they have a (92% x 57%) 52.44 per cent chance of winning both games. If they do win the next two, they’ll have at least the second seed, which means they have (52.44% – 5.82%) a 46.62 per cent chance of winning both games and keeping the second seed.

What if they don’t win both games?

If they lose to West Coast (an 8 per cent chance) but defeat Geelong (a 57 per cent chance), they’ll still be second because Richmond can’t catch them even with two wins and 129 points to make up the percentage. Geelong will also have lost a game as well.

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If they defeat West Coast (a 92 per cent chance) but lose to Geelong (a 43 per cent), they’ll still be ahead of Richmond but be passed by Geelong if they also defeat Collingwood (a 74 per cent chance). All that multiplies to a 29.27 per cent chance of falling to third. No-one else can catch a 60-point GWS team.

Without going through all the possibilities here, if the Giants does lose both games, they could land anywhere from third to sixth.

Greater Western Sydney’s likely finishing position
First place: 5.82 per cent.
Second place: 58.62 per cent.
Third place: 31.36 per cent.
Fourth place: 2.59 per cent.
Fifth place: 1.61 per cent.
Sixth place: 1.61 per cent.

(Image: AAP Image/Mick Tsikas)

Geelong
The Cats can finish in second position with a double home chance if they win both games because they’ll pass GWS in round 23 by defeating them. They can also win just R23 if the Giants and Cats both lose this week, as long as the Tigers don’t go two-for-two.

If they lose to GWS, Geelong cannot finish higher than third, and Richmond has a 56 per cent percent chance of passing them should the Cats lose either game. Finally, if Geelong loses both games, they can finish anywhere from third to sixth.

Geelong’s likely finishing position
First place: 35.08 per cent.
Fourth place: 41.38 per cent.
Fourth place: 15.41 per cent.
Fifth place: 8.13 per cent.
Sixth place: 8.13 per cent.

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Richmond
Believe it or not, it is still possible for Richmond to finish ninth! THe permutations, however, are strict.

They must lose both games (a 6.24 per cent chance), Sydney must win at least one game (a 99.3 per cent chance), Port Adelaide must win at least one (a 98.7 per cent chance), Melbourne must win both games and make up 59 points or so on percentage (a 6 per cent chance), West Coast must win both games and make up 65 points or so on percentage (against Adelaide and GWS; less than 0.1 per cent chance), and the Western Bulldogs must win both games and make-up about 193 points of percentage (a 0.00012% per cent chance).

So, yes, the Tigers are pretty much guaranteed a spot in the finals. They do have a slim but realistic chance at the second seed if they win both games, GWS loses both games and Geelong loses in R22, but that comes out to be a 0.48 per cent chance – not great, but much better than their shot at ninth.

More likely is that the Tigers win both games, which puts them in third or fourth. Winning one of two puts them somewhere between third and sixth dependent mostly on whether or not the Swans or Power lose a game or not. Losing both games puts the Tigers somewhere between fourth and eighth, as the ninth caluclation hints.

Richmond’s likely finishing position
Second place: 0.48 per cent.
Third place: 27.26 per cent.
Fourth place: 41.75 per cent.
Fifth place: 30.03 per cent.
Sixth place: 30.03 per cent.
Seventh place: 0.48 per cent.
Eighth place: 0.48 per cent.

(Image: AAP Image/Julian Smith)

Sydney and Port Adelaide
Despite the Swans’ slight percentage advantage, the Power have slightly better odds of success because they don’t have to play Adelaide this week. Neither can place any higher than fourth, and while ninth is still a possibility for each team, it’s going to take the following combination of events to happen:
They must lose both games (a 0.69 per cent chance for Sydney, a 1.325 per cent chance for Port Adelaide), their opposite number must win at least once and Melbourne, West Coast, and the Bulldogs must all win both their games.

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The total chance of this happening is 0.004 per cent for Sydney and 0.007 per cent for Port Adelaide, so it’s no major concern for either team. Two wins guarantees a top-six finish for either team, although neither can place higher than fourth because either GWS or Geelong will win at least once more in R23.

Richmond has to win at least as many as Sydney or Port Adelaide to stay ahead of either because of their percentage deficit to their non-Victorian rivals. For the same reason, none of the 11-win teams can catch Sydney or Port Adelaide unless they surpass their win total, so as long as the Swans or Power win at least once, they’re guaranteed a top-six finish.

Sydney’s likely finishing position
Fourth place: Sydney 16.51 per cent.
Fifth place: Sydney 83.01 per cent.
Sixth place: Sydney 83.01 per cent.
Seventh place: Sydney 0. 476 per cent.
Eighth place: Sydney 0. 476 per cent.
Ninth place: Sydney 0.004 per cent.

Port Adelaide’s likely finishing position
Fourth place: Port 23.74 per cent.
Fifth place: Port 75.32 per cent.
Sixth place: Port 75.32 per cent.
Seventh place: Port 0.934 per cent.
Eighth place: Port 0.934 per cent.
Ninth place: Port 0.006 per cent.

Melbourne, West Coast and Western Bulldogs
The less-than-two per cent chance of the top six not staying put doles out small chances to these three teams making it to a home elimination final game. The Demons have the best shot because of their easier fixture, claiming a 1.45 per cent chance of a top six finish. The Bulldogs have the next best shot at 0.37 per cent and the gargantuan task of facing the top two teams in the competition makes the Eagles’ shot at a top six finish a negligible 0.08 per cent chance.

But as for the more likely seventh or eighth-place finish, here’s what these three teams are looking at. First, Melbourne has a 56.2 per cent chance of winning both games and, if they do, they’re playing in September for the first time since 2006. If they win once, they still go to the finals if no more than one of the following happens: West Coast gets two wins (a 3.0 per cent chance), the Bulldogs get two wins (a 33 per cent chance) or Essendon gets two wins and makes up a few points of percentage (a 64 per cent chance).

West Coast has only a 3.0 per cent chance of beating both the Crows and Giants, but they’re in if they do. If they win once, they need no more than one of the following to happen: Melbourne gets two wins (a 56 per cent chance), the Western Bulldogs get two wins (a 33 per cent chance) or Essendon wins two and makes up the percentage difference (a 64 per cent chance).

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The Western Bulldogs have to win twice and hope that the Demons and Eagles don’t both also win twice, which is a 32.3 per cent chance. If they win once, they’re going to be hoping for no more than one of the following to happen: Melbourne wins once (a 98.5 per cent chance), West Coast wins once (a 42 per cent chance) or Essendon wins twice (a 72 per cent chance). This is where that low percentage will very likely squeeze them out of a title defence.

Composite likely finishing positions for Melbourne, Western Bulldogs and West Coast
Melbourne – Top 6: 1.45 per cent; seventh or eighth place: 84.05 per cent; miss finals: 14.50 per cent.

Western Bulldogs – Top 6: 0.37 per cent; seventh or eighth place: 39.29 per cent; miss finals: 60.34 per cent.

West Coast – Top 6: 0.08 per cent; seventh or eighth place: 20.68 per cent; miss finals: 79.24 per cent.

(Image: AAP Image/Tony McDonough)

Essendon
Despite being a game behind, their easy fixture against Gold Coast in R22 (a 84 per cent chance of victory) and Fremantle in R23 (an 86 per cent chance of victory) actually makes them the favourite for eighth spot. Although they need an extra win and a bit of percentage to pass either Melbourne or West Coast, the difficulty of the Eagles’ schedule makes this more likely than not.

If the 72 per cent chance of winning both games comes to fruition, at least two of the following things will have to happen to prevent a Bomber appearance in finals next month: Melbourne must either win both games or win one game with a superior percentage (together a 65 per cent chance), West Coast must either win both games or win one game with a superior final percentage (only an approximately 6 per cent chance) and the Bulldogs must win twice (a 33.3 per cent chance).

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What are the odds? Overall, better than a coin-flip: Essendon have a 52.07 per cent chance of making the finals.

St Kilda and Hawthorn
In theory the Saints and Hawks could make the finals thanks to the miracles of modern upset technology: Essendon has to lose at least once, Melbourne twice, the Eagles twice and the Bulldogs twice – although it’s conceivable they could win one and have the Saints still overtake them on percentage – in addition to one of the two teams winning both of their remaining games.

For the Saints there’s only a 1.12 per cent chance of all of that happening, and for the Hawks it’s a mere 0.90 per cent chance.

Finally, if you’re looking for a most likely outcome, here’s what the first week of finals should look like according to probability.

Qualifying Final 1
Adelaide (1) versus Richmond (4)

Qualifying Final 2
Greater Western Sydney (2) versus Geelong (3)

Elimination Final 1
Port Adelaide* (5) versus Essendon (8)

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Elimination Final 2
Sydney* (6) versus Melbourne (7)

*Port Adelaide are more likely to win twice than Sydney is, but it’s a virtual toss-up for fifth right now.

That’s right: four Victorian teams travelling out of state to compete in Adelaide and Sydney while the MCG stands silent for a week – this is not your father’s footy league!

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