Pointless v St Kilda

The Swans' 2nd and 3rd quarter performances last Saturday should not go unremarked.

In the 3rd quarter they failed to register a point, which is a phenomenon that's occurred in only 1.2% of all quarters ever played and in just 0.3% of quarters played since and including the 1980 season. Indeed, so rare is it that only one occurrence has been recorded in each of the last two seasons.

Last year, Melbourne racked up the season's duck egg in the 1st quarter of their Round 19 clash against Geelong, leaving them trailing 0.0 to 8.5 at the first change and in so doing setting a new standard for rapidity in disillusioning Heritage Fund Investors. In 2007 the Western Bulldogs were the team who failed to trouble the goal umpire for an entire quarter - the 2nd quarter of their Round 22 game against the Kangaroos.

So, let's firstly salute the rarity that is failing to score for an entire quarter.

But the Swans did more than this. They preceded their scoreless quarter with a quarter in which they kicked just two behinds. Stringing together successive quarters that, combined, yield two points or fewer is a feat that's been achieved only 175 times in the entire history of the game, and 140 of those were recorded in the period from 1897 to 1918.

Across the last 30 seasons only 12 teams have managed such frugality in front of goal. Prior to the Swans, the most recent example was back in Round 14 of 2002 when West Coast went in at half-time against Geelong having scored 4.7 and headed to the sheds a bit over an hour later having scored just two behinds in the 3rd quarter and nothing at all in the 4th. That makes it almost 6-and-a-half seasons since anyone has done what the Swans did on Saturday.

Prior to the Eagles we need to reach back to Round 4 of 1999 when Essendon - playing West Coast as it happens - finished the 1st quarter and the half stuck at 2.2 and then managed just two behinds in the 3rd term. (They went on to record only two more scoring shots in the final term but rather spoiled things by making one of them a major.)

If you saw the Swans games then, you witnessed a little piece of history.

Waiting on Line

Hmmm. (Just how many ms are there in that word?)

It's Tuesday evening around 7pm and there's still no Line market up on TAB Sportsbet. In the normal course this market would go up at noon on Monday, and that's when the first match is on Friday night. So, this week the first game is 24 hours earlier than normal and the Line market looks as though it'll be delayed by 48 hours, perhaps more.

Curiouser still is the fact that the Head-to-Head market has been up since early March (at least) and there's an historical and strong mathematical relationship between Head-to-Head prices and the Line market, as the following chart shows.

The dark line overlaid on the chart fits the empirical data very well. As you can see, the R-squared is 0.944, which is an R-squared I'd be proud to present to any client.

Using the fitted equation gives the following table of Favourite's Price and Predicted Points Start:

Anyway, back to waiting for the TAB to set the terms of our engagement for the weekend ...

Marginally Interesting

Here are a handful of facts on AFL margins:

• The largest ever victory margin was 190 points (Fitzroy over Melbourne in 1979)
• Every margin between 0 and 150 points has been achieved at least once except margins of 136, 144, 145, 148 and 149 points.
• Last season, no game finished with a victory margin of 25 points
• No game finished with a margin of 47 points in the previous 2 seasons
• No game finished with a margin of 67 points in the previous 5 seasons
• No game finished with a margin of 90, 94 or 98 points in the previous 8 seasons
• No game finished with a margin of 109 points in the previous 12 seasons
• No game finished with a margin of 120 points in the previous 17 seasons
• No game finished with a margin of 128 points in the previous 39 seasons
• No game finished with a margin of 161 points in the previous 109 seasons
• At least one game has finished with a margin of 6 points in each of the previous 48 seasons
• At least one game has finished with a margin of 26 points in each of the previous 42 seasons

Draw Doesn't Always Mean Equal

The curse of the unbalanced draw remains in the AFL this year and teams will once again finish in ladder positions that they don't deserve. As long-time MAFL readers will know, this is a topic I've returned to on a number of occasions but, in the past, I've not attempted to quantify its effects.

This week, however, a MAFL Investor sent me a copy of a paper that's been prepared by Liam Lenten of the School of Economics and Finance at La Trobe University for a Research Seminar Series to be held later this month and in which he provides a simple methodology for projecting how each team would have fared had they played the full 30-game schedule, facing every other team twice.

For once I'll spare you the details of the calculation and just provide an overview. Put simply, Lenten's method adjusts each team's actual win ratio (the proportion of games that it won across the entire season counting draws as one-half a win) based on the average win ratios of all the teams it met only once. If the teams it met only once were generally weaker teams - that is, teams with low win ratios - then its win ratio will be adjusted upwards to reflect the fact that, had these weaker teams been played a second time, the team whose ratio we're considering might reasonably have expected to win a proportion of them greater than their actual win ratio.

As ever, an example might help. So, here's the detail for last year.

Consider the row for Geelong. In the actual home and away season they won 21 from 22 games, which gives them a win ratio of 95.5%. The teams they played only once - Adelaide, Brisbane Lions, Carlton, Collingwood, Essendon, Hawthorn, St Kilda and the Western Bulldogs - had an average win ratio of 56.0%. Surprisingly, this is the highest average win ratio amongst teams played only once for any of the teams, which means that, in some sense, Geelong had the easiest draw of all the teams. (Although I do again point out that it benefited heavily from not facing itself at all during the season, a circumstance not enjoyed by any other team.)

The relatively high average win ratio of the teams that Geelong met only once serves to depress their adjusted win ratio, moving it to 92.2%, still comfortably the best in the league.

Once the calculations have been completed for all teams we can use the adjusted win ratios to rank them. Comparing this ranking with that of the end of season ladder we find that the ladder's 4th-placed St Kilda swap with the 7th-placed Roos and that the Lions and Carlton are now tied rather than being split by percentages as they were on the actual end of season ladder. So, the only significant difference is that the Saints lose the double chance and the Roos gain it.

If we look instead at the 2007 season, we find that the Lenten method produces much greater change.

In this case, eight teams' positions change - nine if we count Fremantle's tie with the Lions under the Lenten method. Within the top eight, Port Adelaide and West Coast swap 2nd and 3rd, and Collingwood and Adelaide swap 6th and 8th. In the bottom half of the ladder, Essendon and the Bulldogs swap 12th and 13th, and, perhaps most important of all, the Tigers lose the Spoon and the priority draft pick to the Blues.

In Lenten's paper he looks at the previous 12 seasons and finds that, on average, five to six teams change positions each season. Furthermore, he finds that the temporal biases in the draw have led to particular teams being regularly favoured and others being regularly handicapped. The teams that have, on average, suffered at the hands of the draw have been (in order of most affected to least) Adelaide, West Coast, Richmond, Fremantle, Western Bulldogs, Port Adelaide, Brisbane Lions, Kangaroos, Carlton. The size of these injustices range from an average 1.11% adjustment required to turn Adelaide's actual win ratio into an adjusted win ratio, to just 0.03% for Carlton.

On the other hand, teams that have benefited, on average, from the draw have been (in order of most benefited to least) Hawthorn, St Kilda, Essendon, Geelong, Collingwood, Sydney and Melbourne. Here the average benefits range from 0.94% for Hawthorn to 0.18% for Melbourne.

I don't think that the Lenten work is the last word on the topic of "unbalance", but it does provide a simple and reasonably equitable way of quantitatively dealing with its effects. It does not, however, account for any inter-seasonal variability in team strengths nor, more importantly, for the existence any home ground advantage.

Still, if it adds one more finger to the scales on the side of promoting two full home and away rounds, it can't be a bad thing can it?

Limning the Ladder

It's time to consider the grand sweep of football history once again.

This time I'm looking at the teams' finishing positions, in particular the number and proportion of times that they've each finished as Premiers, Wooden Spooners, Grand Finalists and Finalists, or that they've finished in the Top Quarter or Top Half of the draw.

Here's a table providing the All-Time data.

Note that the percentage columns are all as a percentage of opportunities. So, for a season to be included in the denominator for a team's percentage, that team needs to have played in that season and, in the case of the Grand Finalists and Finalists statistics, there needs to have been a Grand Final (which there wasn't in 1897 or 1924) or there needs to have been Finals (which, effectively, there weren't in 1898, 1899 or 1900).

Looking firstly at Premierships, in pure number terms Essendon and Carlton tie for the lead on 16, but Essendon missed the 1916 and 1917 seasons and so have the outright lead in terms of percentage. A Premiership for West Coast in any of the next 5 seasons (and none for the Dons) would see them overtake Essendon on this measure.

Moving then to Spoons, St Kilda's title of the Team Most Spooned looks safe for at least another half century as they sit 13 clear of the field, and University will surely never relinquish the less euphonius but at least equally as impressive title of the Team With the Greatest Percentage of Spooned Seasons. Adelaide, Port Adelaide and West Coast are the only teams yet to register a Spoon (once the Roos' record is merged with North Melbourne's).

Turning next to Grand Finals we find that Collingwood have participated in a remarkable 39 of them, which equates to a better than one season in three record and is almost 10 percentage points better than any other team. West Coast, in just 22 seasons, have played in as many Grand Finals as have St Kilda, though St Kilda have had an additional 81 opportunities.

The Pies also lead in terms of the number of seasons in which they've participated in the Finals, though West Coast heads them in terms of percentages for this same statistic, having missed the Finals less than one season in four across the span of their existence.

Finally, looking at finishing in the Top Half or Top Quarter of the draw we find the Pies leading on both of these measures in terms of number of seasons but finishing runner-up to the Eagles in terms of percentages.

The picture is quite different if we look just at the 1980 to 2008 period, the numbers for which appear below.

Hawthorn now dominates the Premiership, Grand Finalist and finishing in the Top Quarter statistics. St Kilda still own the Spoon market and the Dons lead in terms of being a Finalist most often and finishing in the Top Half of the draw most often.

West Coast is the team with the highest percentage of Finals appearances and highest percentage of times finishing in the Top Half of the draw.