What's Different About Finals?

Finals, by their nature, tend to pit more-evenly matched teams against one another, on average, than do games from the home-and-away season. It seems reasonable, therefore, to hypothesise that margins will tend to be smaller in Finals than in the home-and-away season, but what other changes in scoring behaviour might we expect to see?

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Explaining Variability in Game Margins

Some seasons are notable for the large number of blowout victories they force us to endure - a few recent seasons come immediately to mind - while others are more memorable because of their highly competitive nature. To what extent, I've often wondered, could we attribute a season full of sizable victory margins to the fact that strong teams were more often facing weak teams, making the magnitude of the defeats predictable if still lamentable, versus instead attributing them to on-the-day or random events that were genuinely unforeseeable pre-game?

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Team Ratings, Bookmaker Prices and the Recent Predictability of Finals

Last weekend saw three of four underdogs prevail in the first week of the Finals. Based on the data I have, you'd need to go back to 2006 to find a more surprising Week 1 of the Finals and, as highlighted in the previous blog, no matter how far you went back you wouldn't find a bigger upset than Port Adelaide's defeat of the Pies.
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Is Class More or Less Important In AFL Finals?

You'll hear it said about sport that class emerges when it's needed most. If that applies to football then you'd expect that better teams would be more likely to win games in the Finals than they are games in the regular home-and-away season.
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Lead Changes as a Measure of Game Competitiveness

The final victory margin is one measure of how close a contest was, but it can sometimes mislead when the team that's in front midway through the final term piles on a slew of late goals against a progressively more demoralised opponent, improving its percentage in so doing, but also erasing any trace of the fact that the game might have been a close-run thing throughout the first three-and-a-half or more quarters.
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Characterising AFL Seasons

I can think of a number of ways that an AFL season might be characterised but for today's blog I'm going to call on a modelling approach that I used back in 2010, which is based on Brownian motion and which was inspired by a JASA paper from Hal S Stern.
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Does An Extra Day's Rest Matter in the Finals?

This week Collingwood faces Sydney having played its Semi-Final only 6 day previously while Adelaide take on Hawthorn a more luxurious 8 days after their Semi-Final encounter. The gap for Sydney has been 13 days while that for the Hawks has been 15 days. In this blog we'll assess what, if any, effect these differential gaps between games for competing finalists might have on game outcome.
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Explaining More of the Variability in the Victory Margin of Finals

This morning while out walking I got to wondering about two of the results from the latest post on the Wagers & Tips blog. First that teams from higher on the ladder have won 20 of the 22 Semi Finals between 2000 and 2010, and second that the TAB bookmaker has installed the winning team as favourite in only 64% of these contests. Putting those two facts together it's apparent that, in Semi Finals at least, the bookmaker's often favoured the team that finished lower on the ladder, and these teams have rarely won.
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Divining the Bookie Mind: Singularly Difficult

It's fun this time of year to mine the posted TAB Sportsbet markets in an attempt to glean what their bookie is thinking about the relative chances of the teams in each of the four possible Grand Final pairings.

Three markets provide us with the relevant information: those for each of the two Preliminary Finals, and that for the Flag.

From these markets we can deduce the following about the TAB Sportsbet bookie's current beliefs (making my standard assumption that the overround on each competitor in a contest is the same, which should be fairly safe given the range of probabilities that we're facing with the possible exception of the Dogs in the Flag market):

  • The probability of Collingwood defeating Geelong this week is 52%
  • The probability of St Kilda defeating the Dogs this week is 75%
  • The probability of Collingwood winning the Flag is about 34%
  • The probability of Geelong winning the Flag is about 32%
  • The probability of St Kilda winning the Flag is about 27%
  • The probability of the Western Bulldogs winning the Flag is about 6%

(Strictly speaking, the last probability is redundant since it's implied by the three before it.)

What I'd like to know is what these explicit probabilities imply about the implicit probabilities that the TAB Sportsbet bookie holds for each of the four possible Grand Final matchups - that is for the probability that the Pies beat the Dogs if those two teams meet in the Grand Final; that the Pies beat the Saints if, instead, that pair meet; and so on for the two matchups involving the Cats and the Dogs, and the Cats and the Saints.

It turns out that the six probabilities listed above are insufficient to determine a unique solution for the four Grand Final probabilities I'm after - in mathematical terms, the relevant system that we need to solve is singular.

That system is (approximately) the following four equations, which we can construct on the basis of the six known probabilities and the mechanics of which team plays which other team this week and, depending on those results, in the Grand Final: 

  • 52% x Pr(Pies beat Dogs) + 48% x Pr(Cats beat Dogs) = 76%
  • 52% x Pr(Pies beat Saints) + 48% x Pr(Cats beat Saints) = 63.5%
  • 75% x Pr(Pies beat Saints) + 25% x Pr(Pies beat Dogs) = 66%
  • 75% x Pr(Cats beat Saints) + 25% x Pr(Cats beat Dogs) = 67.5%

(If you've a mathematical bent you'll readily spot the reason for the singularity in this system of equations: the coefficients in every equation sum to 1, as they must since they're complementary probabilities.)

Whilst there's not a single solution to those four equations - actually there's an infinite number of them, so you'll be relieved to know that I won't be listing them all here - the fact that probabilities must lie between 0 and 1 puts constraints on the set of feasible solutions and allows us to bound the four probabilities we're after.

So, I can assert that, as far as the TAB Sportsbet bookie is concerned:

  • The probability that Collingwood would beat St Kilda if that were the Grand Final matchup - Pr(Pies beats Saints) in the above - is between about 55% and 70%
  • The probability that Collingwood would beat the Dogs if that were the Grand Final matchup is higher than 54% and, of course, less than or equal to 100%.
  • The probability that Geelong would beat St Kilda if that were the Grand Final matchup is between 57% and 73%
  • The probability that Geelong would beat the Dogs if that were the Grand Final matchup is higher than 50.5% and less than or equal to 100%.

One straightforward implication of these assertions is that the TAB Sportsbet bookie currently believes the winner of the Pies v Cats game on Friday night will start as favourite for the Grand Final. That's an interesting conclusion when you recall that the Saints beat the Cats in week 1 of the Finals.

We can be far more definitive about the four probabilities if we're willing to set the value of any one of them, as this then uniquely defines the other three.

So, let's assume that the bookie thinks that the probability of Collingwood defeating the Dogs if those two make the Grand Final is 80%. Given that, we can say that the bookie must also believe that:

  • The probability that Collingwood would beat St Kilda if that were the Grand Final matchup is about 61%.
  • The probability that Geelong would beat St Kilda if that were the Grand Final matchup, is about 66%.
  • The probability that Geelong would beat the Dogs if that were the Grand Final matchup is higher than 72%.

Together, that forms a plausible set of probabilities, I'd suggest, although the Geelong v St Kilda probability is higher than I'd have guessed. The only way to reduce that probability though is to also reduce the probability of the Pies beating the Dogs.

If you want to come up with your own rough numbers, choose your own probability for the Pies v Dogs matchup and then adjust the other three probabilities using the four equations above or using the following approximation:

For every 5% that you add to the Pies v Dogs probability:

  • subtract 1.5% from the Pies v Saints probability
  • add 2% to the Cats v Saints probability, and
  • subtract 5.5% from the Cats v Dogs probability

If you decide to reduce rather than increase the probability for the Pies v Dogs game then move the other three probabilities in the direction opposite to that prescribed in the above. Also, remember that you can't drop the Pies v Dogs probability below 55% nor raise it above 100% (no matter how much better than the Dogs you think the Pies are, the laws of probability must still be obeyed.)

Alternatively, you can just use the table below if you're happy to deal only in 5% increments of the Pies v Dogs probability. Each row corresponds to a set of the four probabilities that is consistent with the TAB Sportsbet markets as they currently stand.

2010 - Grand Final Probabilities.png

I've highlighted the four rows in the table that I think are the ones most likely to match the actual beliefs of the TAB Sportsbet bookie. That narrows each of the four probabilities into a 5-15% range.

At the foot of the table I've then converted these probability ranges into equivalent fair-value price ranges. You should take about 5% off these prices if you want to obtain likely market prices.

A First Look at Grand Final History

In Preliminary Finals since 2000 teams finishing in ladder position 1 are now 3-0 over teams finishing 3rd, and teams finishing in ladder position 2 are 5-0 over teams finishing 4th.

Overall in Preliminary Finals, teams finishing in 1st now have a 70% record, teams finishing 2nd an 80% record, teams finishing 3rd a 38% record, and teams finishing 4th a measly 20% record. This generally poor showing by teams from 3rd and 4th has meant that we've had at least 1 of the top 2 teams in every Grand Final since 2000.


Reviewing the middle table in the diagram above we see that there have been 4 Grand Finals since 2000 involving the teams from 1st and 2nd on the ladder and these contests have been split 2 apiece. No other pairing has occurred with a greater frequency.

Two of these top-of-the-table clashes have come in the last 2 seasons, with 1st-placed Geelong defeating 2nd-placed Port Adelaide in 2007, and 2nd-placed Hawthorn toppling 1st-placed Geelong last season. Prior to that we need to go back firstly to 2004, when 1st-placed Port Adelaide defeated 2nd-placed Brisbane Lions, and then to 2001 when 1st-placed Essendon surrendered to 2nd-placed Brisbane Lions.

Ignoring the replays of 1948 and 1977 there have been 110 Grand Finals in the 113-year history of the VFL/AFL history, with Grand Finals not being used in the 1897 or 1924 seasons. The pairings and win-loss records for each are shown in the table below.


As you can see, this is the first season that St Kilda have met Geelong in the Grand Final. Neither team has been what you'd call a regular fixture at the G come Grand Final Day, though the Cats can lay claim to having been there more often (15 times to the Saints' 5) and to having a better win-loss percentage (47% to the Saints' 20%).

After next weekend the Cats will move ahead of Hawthorn into outright 7th in terms of number of GF appearances. Even if they win, however, they'll still trail the Hawks by 2 in terms of number of Flags.

A Decade of Finals

This year represents the 10th under the current system of finals, a system I think has much to recommend it. It certainly seems to - justifiably, I'd argue - favour those teams that have proven their credentials across the entire season.

The table below shows how the finals have played out over the 10 years:


This next table summarises, on a one-week-of-the-finals-at-a-time basis, how teams from each ladder position have fared:


Of particular note in relation to Week 1 of the finals is the performance of teams finishing 3rd and of those finishing 7th. Only two such teams - one from 3rd and one from 7th - have been successful in their respective Qualifying and Elimination Finals.

In the matchups of 1st v 4th and 5th v 8th the outcomes have been far more balanced. In the 1st v 4th clashes, it's been the higher ranked team that has prevailed on 6 of 10 occasions, whereas in the 5th v 8th clashes, it's been the lower ranked team that's won 60% of the time.

Turning our attention next to Week 2 of the finals, we find that the news isn't great for Adelaide or Lions fans. On both those occasions when 4th has met 5th in Week 2, the team from 4th on the ladder has emerged victorious, and on the 7 occasions that 3rd has faced 6th in Week 2, the team from 3rd on the ladder has won 5 and lost only 2.

Looking more generally at the finals, it's interesting to note that no team from ladder positions 5, 7 or 8 has made it through to the Preliminary Finals and, on the only two occasions that the team from position 6 has made it that far, none has progressed into the Grand Final.

So, teams only from positions 1 to 4 have so far contested Grand Finals, teams from 1st on 6 occasions, teams from 2nd on 7 occasions, teams from 3rd on 3 occasions, and teams from 4th only twice.

No team finishing lower than 3rd has yet won a Flag.