Second-Placed Cats Spoil the Symmetry (Not That They Care)

Ah well, the better side on the day and all that. Congrats to the Cats but they can count themselves very lucky indeed as a gracious coach admitted in his post-game address.

The Saints' lack of finish in front of goal cost Investors dearly this weekend, the undefended goal-after-the-siren merely making their frustration complete as it consigned their line bet to the same fate as their multitudinous head-to-head bets.

Those with the Recommended Portfolio wound up losing 6.1% on the GF to finish the season up by about 1.4%. MIN#001 lost 6.3% to finish up 5.9% for the season, MIN#015 lost 5.9% to finish up 5.2% on the season, and MIN#017 lost just 4% to finish up 33.4% on the season. So, as we knew before the Granny started, profit for everybody. Just not as much as I'd hoped.

Investors: please advise me by e-mail what you'd like done with your Funds.

We now enter the chart and table section of this blog. Prepare to scroll.

Here's a chart showing the game-by-game performance of every Investor's Portfolio:



As you can see by those dips on the far right, Investors lost money over the course of the Finals this year, in stark contrast with years past.

Next, here's a chart giving the round-by-round summary:



Turning our attention to the individual Funds, we start with a table showing each Fund's performance with every team across the entire season:



And we follow this with a table summarising this data by team:



Lastly, we finish with a round-by-round summary:



On tipping BKB finishes the year with 125 from 185 (68%), ELO with 124 from 185 (67%), and Chi with 118 from 185 (64%). If offered these stats at the start of the season I'd have accepted Chi's and leapt at ELO's.

On line betting, ELO and Chi both finish with a loss, leaving Chi on 85 from 185 for the season (and 1 from 9 in the finals), and ELO on 103 from 185. Level-stake wagering on ELO's line bets would have yielded 9.49 units of profit across the season. Level-stake wagering on Chi's line bets would have yielded a peptic ulcer.

Chi's final Mean APE is 30.6 points per game, beaten by ELO's 28.7 points per game, in turn edged out by BKB's 28.0 points per game. On Median APE ELO is the best of the three. Its 23 points beats BKB's 23.5 points. Chi's 26 points places him third.

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Grand Final Typology

Today's blog looks at the typology of AFL Grand Finals.

There are five basic types of Grand Finals:

(1) The Coast-to-Coast Coasting victory

The key characteristic of this Grand Final type is that the winning team tends to lead at every change, but not by much.

There have been 31 Grand Finals of this type in history, the most recent in 2006 when West Coast led against the Swans at every change and clung on to win by a point. The Grand Final of the previous year is another example of this type; in that case the Swans led at every change over the Eagles.

(2) The Come-From-Behind victory

The key characteristic of this Grand Final type is that the winning team tends to trail at every change.

There have been only 7 instances of this type of Grand Final, the most recent in 1984 when Hawthorn led at every change before Essendon swamped them win a 9.6 to 2.1 final term.

The famous 1970 GF when Carlton kicked 5.4 to Collingwood's 1.1 in the final term to complete a stunning victory is another example of this type.

(3) The Game-of-Two-Halves Victory

The key characteristic of this Grand Final type is that the winning team tends to lead at quarter time, trails at half time but wrests the lead by three-quarter time and doesn't surrender it.

There have been 20 Grand Finals of this type in history. The GF of 2004 is an example of this type. In that year Port Adelaide led Brisbane 4.5 to 2.2 at quarter time, trailed 6.6 to 6.7 at half time, led 12.8 to 9.9 at three-quarter time, and went on to win 17.11 to 10.13.

(4) The Coast-to-Coast Blowout Victory

The key characteristic of this Grand Final type is that the winning team leads going away at every quarter.

History has produced 33 of these GF types, probably none of them good to watch for any except the fans of the winning team.

2007 leaps immediately to mind and is, unsurprisingly a GF of this type. In that year Geelong led by 23 points at quarter time, 52 points at half time, 90 points at three-quarter time, and 119 points at the final siren.

(5) The Nervous Start Victory

The key characteristic of this Grand Final type is that the winning team trails at quarter time but generally at none of the changes thereafter.

There have been 19 GFs of this type, including last year's fare. In that game the Hawks trailed the Cats by 1 point at the first change then steadied to lead by 3 points and then 17 points at the second and third changes. They won, eventually, by 26 points.

Where, you might ask, did I come up with all this?

Well, I didn't make this typology up. It came as a result of an analysis of Grand Final data using a technique called cluster analysis which, in essence, is a statistical technique that allows you to group things based on how similar they are.

To use the technique you need to decide the data on which you'll assess similarity and you need to choose what's called a "distance metric", which is the mathematical way by which you'll convert differences in the raw data into measures of similarity.

The data I used to come with these clusters was fairly simple: which team - the eventual winner or loser - led at each change, and what the eventual winning team's margin was at half time and at full time. If you want to read up on the technical details, I used pam clustering and the gower distance metric.

Now not every Grand Final fits one of these 5 descriptions perfectly, but each Grand Final is, in a mathematical sense, closer to one of these 5 types than to any of the others. That allows me to classify each of the 110 Grand Finals we've had so far.

The summary of that classification appears in this next table:

Scanning the rightmost 4 columns you can see how the mix of GF types has varied across the four epochs I've used: 1897-1919, 1920-1949, 1950-1979, and 1980-2008.

The period 1897-1919 was the heyday of the Coast-to-Coast Coasting Victory. Ten examples of this GF type came in that era.

Subsequently, the 1920-1949 era was dominated by the Coast-to-Coast Coasting Victory and the Coast-to-Coast Blowout Victory types. Combined these accounted for 18 of the 29 GFs in that period.

The 1950-1979 era was fairly similar to the 1920-1949 era though with a slightly higher proportion of Coast-to-Coast Coasting Victory types and a slightly lower proportion of Coast-to-Coast Blowout Victory types.

But, unfortunately, the Coast-to-Coast Blowout Victory wasn't really going away. It has dominated the GFs since 1980, providing 12 of the 29 results. This period has also produced 7 Nervous Start Victory type GFs, which represents the largest proportion of this type for any era.

The technique I use also spits out what it considers to be the 'best' example of each type of GF, a summary of which appears below:

As soon as I have time I'll be providing a graphic showing the typology of every Grand Final so far including the 2009 GF (so I guess you won't be getting it before Sunday at least) ...

... Okay, as it turned out I had a little time this evening so I created the table showing the classification of every Grand Final a little earlier than I expected. It's available as a download here

The Grand Finals are sorted firstly by type and then, within type, by their similarity to the archetypical Grand Final of that type. The rightmost column provides a measure of this similarity - the smaller the number the closer that Grand Final is to the archetypical Grand Final. I've colour-coded the archetypical Grand Finals grey and those Grand Finals that are relatively 'close to' the relevant archetypical Grand Final in green.

So, for example, consider the second GF block in Coast-to-Coast Coasting. It's for the 1912 GF and shows Essendon defeating South Melbourne, leading 10-9 at QT, 27-16 at HT, 38-18 at 3QT and 47-33 at FT. It's very similar to the 1910 GF, which is the archetypical Coast-to-Coast Coasting GF.

Enjoy.

Read more on "Grand Final Typology" ...

This Week We're All Saints

After 341 wagers across 184 games Investors with the Recommended Portfolio have effectively offered the TAB Sportsbet bookie a double-or-quits proposition.


If the Saints win on Saturday, their profit will lift from about 7.5% of Initial Funds to about 15.1%; if the Saints lose the entire year's effort will amount to a profit of about 1.4%.

The story for other Investors is different but they too are now all guaranteed a profit for season 2009 ranging in size from 5% to 33%.

Head-to-head bets on the Saints range from Chi-squared's 14.1% to Prudence's 3.2%, and Line Redux has its customary 5% on the Saints +8.5 points.

The bookies' re-estimation of the relative chances of the Saints and the Cats on the basis of just one game each has been quite dramatic and, in my view, excessive. This time last week I calculated that we should expect a Saints price of $1.80 to $1.95 if they were to take on the Cats in the GF. We got them at $2.30.

Our Ready Reckoner is as follows:



Those are fairly dramatic swings for just a single game. Still, it is the Granny ...

On tipping this week, a little explanation is required.

Not for Chi, who's on the Saints by 3, nor for BKB, who's on the Cats, but for ELO, who's on the Saints by 31 despite the fact that Geelong have a marginally better MARS rating (1,043.3 to the Saints' 1,043.1) and there's no true home team this week.

All year I've been selecting ELO's tips using a model, fitted to the results for seasons 2000 to 2008, that converts MARS ratings into predicted margins and takes into account true and notional home team status. This model, in the finals especially, places a great deal of weight on the home team even if that team is only the notional home team. The logic behind this is that, in the absence of a true home team, the notional home team - such as the Saints this week - finished higher on the competition ladder.

So, for ELO, the Saints by 31 points it is.

On Line Betting this means that Chi and ELO are also both on the Saints.

(Incidentally Chi's Mean APE is 30.7 points per game and his Median APE is 26.5 points. Any hopes of a sub-30 point Mean APE are long-gone, but around 30.5 points per game - which is possible if the Saints do win by around 3 points - is still a respectable outcome, unlike say his wagering performance.

ELO's Mean APE is 28.6 points per game and its Median APE is 23.0 points, respectable results both. With a Saints victory of the optimum magnitude - 31 points - the Mean APE could even finish below 28.5 points per game.

BKB's Mean APE is 28.1 points per game and its Median APE is 23.5 points, remarkably still trailing ELO's.)

Read more on "This Week We're All Saints" ...

Grand Finals: Points Scoring and Margins

How would you characterise the Grand Finals that you've witnessed? As low-scoring, closely fought games; as high-scoring games with regular blow-out finishes; or as something else?

First let's look at the total points scored in Grand Finals relative to the average points scored per game in the season that immediately preceded them.

Apart from a period spanning about the first 25 years of the competition, during which Grand Finals tended to be lower-scoring affairs than the matches that took place leading up to them, Grand Finals have been about as likely to produce more points than the season average as to produce fewer points.

One way to demonstrate this is to group and summarise the Grand Finals and non-Grand Finals by the decade in which they occurred.

There's no real justification then, it seems, in characterising them as dour affairs.

That said, there have been a number of Grand Finals that failed to produce more than 150 points between the two sides - 49 overall, but only 3 of the last 30. The most recent of these was the 2005 Grand Final in which Sydney's 8.10 (58) was just good enough to trump the Eagles' 7.12 (54). Low-scoring, sure, but the sort of game for which the cliche "modern-day classic" was coined.

To find the lowest-scoring Grand Final of all time you'd need to wander back to 1927 when Collingwood 2.13 (25) out-yawned Richmond 1.7 (13). Collingwood, with efficiency in mind, got all of its goal-scoring out of the way by the main break, kicking 2.6 (20) in the first half. Richmond, instead, left something in the tank, going into the main break at 0.4 (4) before unleashing a devastating but ultimately unsuccessful 1.3 (9) scoring flurry in the second half.

That's 23 scoring shots combined, only 3 of them goals, comprising 12 scoring shots in the first half and 11 in the second. You could see that many in an under 10s soccer game most weekends.

Forty-five years later, in 1972, Carlton and Richmond produced the highest-scoring Grand Final so far. In that game, Carlton 28.9 (177) held off a fast-finishing Richmond 22.18 (150), with Richmond kicking 7.3 (45) to Carlton's 3.0 (18) in the final term.

Just a few weeks earlier these same teams had played out an 8.13 (63) to 8.13 (63) draw in their Semi Final. In the replay Richmond prevailed 15.20 (110) to Carlton's 9.15 (69) meaning that, combined, the two Semi Finals they played generated 22 points fewer than did the Grand Final.

From total points we turn to victory margins.

Here too, again save for a period spanning about the first 35 years of the competition during which GFs tended to be closer fought than the average games that had gone before them, Grand Finals have been about as likely to be won by a margin smaller than the season average as to be won by a greater margin.

Of the 10 most recent Grand Finals, 5 have produced margins smaller than the season average and 5 have produced greater margins.

Perhaps a better view of the history of Grand Final margins is produced by looking at the actual margins rather than the margins relative to the season average. This next table looks at the actual margins of victory in Grand Finals summarised by decade.

One feature of this table is the scarcity of close finishes in Grand Finals of the 1980s, 1990s and 2000s. Only 4 of these Grand Finals have produced a victory margin of less than 3 goals. In fact, 19 of the 29 Grand Finals have been won by 5 goals or more.

An interesting way to put this period of generally one-sided Grand Finals into historical perspective is provided by this, the final graphic for today.

They just don't make close Grand Finals like they used to.

Read more on "Grand Finals: Points Scoring and Margins" ...

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.

Read more on "A First Look at Grand Final History" ...

Cold Pies Disappoint Investors

The neatness of the 2009 AFL Finals series continues, as the teams finishing 3rd and 4th on the home and away season ladder depart in the Prelims as scripted, leaving 1st to play 2nd in the GF.

A shame then that we wagered against such a tidy outcome.

St Kilda's head-to-head win and line betting loss, coupled with head-to-head and line betting losses for the Pies, left most Funds and Portfolios in red ink for the weekend.

New Heritage was the only Fund to increase in value, rising about 3.5% on 1 successful wager from 2. It's now made 99 bets during the season, 74% of which have been winners. Prudence was the only other Fund to land a winning wager, notching 1 from 2, but nonetheless shed a little under 2% in value. It's made 93 bets this season, winning 73% of them.

Chi-squared dropped furthest this weekend, frittering almost 16% on the Pies. It's made 42 bets this season, winning just 48%. Hope, another Pie-eyed Fund (gotta get these puns out now - time's running out this season), dropped a little over 5%. It's made 34 bets this season, winning exactly half.

Line Redux contrived to finish on the wrong side of both line markets this weekend (as did Chi and ELO), causing it to drop 10% of its initial value. It's made 73 bets this season and won 52% of them.

So, the Recommended Portfolio drops a little under 6%, leaving it up about 7.5% for the season. In other Portfolio news, MIN#001 and MIN#015 both dropped around 5-6% leaving them up about 11-12% on the season, and MIN#017 recorded the weekend's only Portfolio increase, rising about 3.5% to be up 37% on the season.

On tipping, Chi and ELO scored 1 from 2 and BKB scored 2 from 2. BKB and ELO are now tied on 124 from 184 (67%), 6 tips ahead of Chi on 118 (64%).

Read more on "Cold Pies Disappoint Investors" ...

What Price the Saints to Beat the Cats in the GF?

If the Grand Final were to be played this weekend, what prices would be on offer?

We can answer this question for the TAB Sportsbet bookie using his prices for this week's games, his prices for the Flag market and a little knowledge of probability.

Consider, for example, what must happen for the Saints to win the flag. They must beat the Dogs this weekend and then beat whichever of the Cats or the Pies wins the other Preliminary Final. So, there are two mutually exclusive ways for them to win the Flag.

In terms of probabilities, we can write this as:

Prob(St Kilda Wins Flag) =

Prob(St Kilda Beats Bulldogs) x Prob (Geelong Beats Collingwood) x Prob(St Kilda Beats Geelong) +

Prob(St Kilda Beats Bulldogs) x Prob (Collingwood Beats Geelong) x Prob(St Kilda Beats Collingwood)

We can write three more equations like this, one for each of the other three Preliminary Finalists.

Now if we assume that the bookie's overround has been applied to each team equally then we can, firstly, calculate the bookie's probability of each team winning the Flag based on the current Flag market prices which are St Kilda $2.40; Geelong $2.50; Collingwood $5.50; and Bulldogs $7.50.

If we do this, we obtain:

Prob(St Kilda Wins Flag) = 36.8%

Prob(Geelong Wins Flag) = 35.3%

Prob(Collingwood Wins Flag) = 16.1%

Prob(Bulldogs Win Flag) = 11.8%

Next, from the current head-to-head prices for this week's games, again assuming equally applied overround, we can calculate the following probabilities:

Prob(St Kilda Beats Bulldogs) = 70.3%

Prob(Geelong Beats Collingwood) = 67.8%

Armed with those probabilities and the four equations of the form of the one above in bold we come up with a set of four equations in four unknowns, the unknowns being the implicit bookie probabilities for all the possible Grand Final matchups.

To lapse into the technical side of things for a second, we have a system of equations Ax = b that we want to solve for x. But, it turns out, the A matrix is rank-deficient. Mathematically this means that there are an infinite number of solutions for x; practically it means that we need to define one of the probabilities in x and we can then solve for the remainder.

Which probability should we choose?

I feel most confident about setting a probability - or a range of probabilities - for a St Kilda v Geelong Grand Final. St Kilda surely would be slight favourites, so let's solve the equations for Prob(St Kilda Beats Geelong) equal to 51% to 57%.

Each column of the table above provides a different solution and is obtained by setting the probability in the top row and then solving the equations to obtain the remaining probabilities.

The solutions in the first 5 columns all have the same characteristic, namely that the Saints are considered more likely to beat the Cats than they are to beat the Pies. To steal a line from Get Smart, I find that hard to believe, Max.

Inevitably then we're drawn to the last two columns of the table, which I've shaded in gray. Either of these solutions, I'd contend, are valid possibilities for the TAB Sportsbet bookie's true current Grand Final matchup probabilities.

If we turn these probabilities into prices, add a 6.5% overround to each, and then round up or down as appropriate, this gives us the following Grand Final matchup prices.

St Kilda v Geelong

$1.80/$1.95 or $1.85/$1.90

St Kilda v Collingwood

$1.75/$2.00 or $1.70/$2.10

Geelong v Bulldogs

$1.50/$2.45 or $1.60/$2.30

Collingwood v Bulldogs

$1.65/$2.20 or $1.50/$2.45

Read more on "What Price the Saints to Beat the Cats in the GF?" ...