The Decline of the Humble Behind

Last year, you might recall, a spate of deliberately rushed behinds prompted the AFL to review and ultimately change the laws relating to this form of scoring.

Has the change led to a reduction in the number of behinds recorded in each game? The evidence is fairly strong:

So far this season we've seen 22.3 behinds per game, which is 2.6 per game fewer than we saw in 2008 and puts us on track to record the lowest number of average behinds per game since 1915. Back then though goals came as much more of a surprise, so a spectator at an average game in 1915 could expect to witness only 16 goals to go along with the 22 behinds. Happy days.

This year's behind decline continues a trend during which the number of behinds per game has dropped from a high of 27.3 per game in 1991 to its current level, a full 5 behinds fewer, interrupted only by occasional upticks such as the 25.1 behinds per game recorded in 2007 and the 24.9 recorded in 2008.

While behind numbers have been falling recently, goals per game have also trended down - from 29.6 in 1991, to this season's current average of 26.8. Still, AFL followers can expect to witness more goals than behinds in most games they watch. This wasn't always the case. Not until the season of 1969 had there been a single season with more goals than behinds, and not until 1976 did such an outcome became a regular occurrence. In only one season since then, 1981, have fans endured more behinds than goals across the entire season.

On a game-by-game basis, 90 of 128 games this season, or a smidge over 70%, have produced more goals than behinds. Four more games have produced an equal number of each.

As a logical consequence of all these trends, behinds have had a significantly smaller impact on the result of games, as evidenced by the chart below which shows the percentage of scoring attributable to behinds falling from above 20% in the very early seasons to around 15% across the period 1930 to 1980, to this season's 12.2%, the second-lowest percentage of all time, surpassed only by the 11.9% of season 2000.

(There are more statistical analyses of the AFL on MAFL Online's sister site at MAFL Stats.)

Does The Favourite Have It Covered?

You've wagered on Geelong - a line bet in which you've given 46.5 points start - and they lead by 42 points at three-quarter time. What price should you accept from someone wanting to purchase your wager? They also led by 44 points at quarter time and 43 points at half time. What prices should you have accepted then?

In this blog I've analysed line betting results since 2006 and derived three models to answer questions similar the one above. These models take as inputs the handicap offered by the favourite and the favourite's margin relative to that handicap at a particular quarter break. The output they provide is the probability that the favourite will go on to cover the spread given the situation they find themselves in at the end of some quarter.

The chart below plots these probabilities against margins relative to the spread at quarter time for 8 different handicap levels.

Negative margins mean that the favourite has already covered the spread, positive margins that there's still some spread to be covered.

The top line tracks the probability that a 47.5 point favourite covers the spread given different margins relative to the spread at quarter time. So, for example, if the favourite has the spread covered by 5.5 points (ie leads by 53 points) at quarter time, there's a 90% chance that the favourite will go on to cover the spread at full time.

In comparison, the bottom line tracks the probability that a 6.5 point favourite covers the spread given different margins relative to the spread at quarter time. If a favourite such as this has the spread covered by 5.5 points (ie leads by 12 points) at quarter time, there's only a 60% chance that this team will go on to cover the spread at full time. The logic of this is that a 6.5 point favourite is, relatively, less strong than a 47.5 point favourite and so more liable to fail to cover the spread for any given margin relative to the spread at quarter time.

Another way to look at this same data is to create a table showing what margin relative to the spread is required for an X-point favourite to have a given probability of covering the spread.

So, for example, for the chances of covering the spread to be even, a 6.5 point favourite can afford to lead by only 4 or 5 (ie be 2 points short of covering) at quarter time and a 47.5 point favourite can afford to lead by only 8 or 9 (ie be 39 points short of covering).

The following diagrams provide the same chart and table for the favourite's position at half time.

Finally, these next diagrams provide the same chart and table for the favourite's position at three-quarter time.

I find this last table especially interesting as it shows how fine the difference is at three-quarter time between likely success and possible failure in terms of covering the spread. The difference between a 50% and a 75% probability of covering is only about 9 points and between a 75% and a 90% probability is only 9 points more.

To finish then, let's go back to the question with which I started this blog. A 46.5 point favourite leading by 42 points at three-quarter time is about a 69.4% chance to go on and cover. So, assuming you backed the favourite at $1.90 your expected payout for a 1 unit wager is 0.694 x 0.9 - 0.306 = +0.32 units. So, you'd want to be paid 1.32 units for your wager, given that you also want your original stake back too.

A 46.5 point favourite leading by 44 points at quarter time is about an 85.5% chance to go on and cover, and a similar favourite leading by 43 points at half time is about an 84.7% chance to go on to cover. The expected payouts for these are +0.62 and +0.61 units respectively, so you'd have wanted about 1.62 units to surrender these bets (a little more if you're a risk-taker and a little less if you're risk-averse, but that's a topic for another day ...)

Sometimes, Seven Goals Just Isn't Enough

You might think, if you'd wagers on three teams (albeit outsiders) that led by 8, 7 and 42 points at half time, that at least one of them would take home the biscuits, especially the one that led by 42 points. If you'd thought this over the last weekend, you'd be wrong.

The Dons were the first of the disappointments, leading the Dogs by 8 points at the half only to concede 11 goals in the second half to go down by 33 points. Next came Fremantle, who enjoyed a 7 point buffer at the half and who maintained legitimate hopes until late in the final term only to falter in the wet against the Lions and lose eventually by 15 points.

Then, on Sunday, the Tigers, who led by 7 straight goals (yes, 7) at the half, barely managed to cling on for a draw, which was enough to stop Investors losing a great deal on the game, but wasn't enough to provide them with a profit. In draws, head-to-head wagers pay out at half-price, so teams at prices below $2 pay back less than the amount wagered. Investors had the Tigers at $1.95.

Indeed it was a weekend littered with close finishes for many Investors. The Cats lost on line betting by half a point, Freo won on line betting by two and a half points, and Port won on line betting by a point and a half. Still, most Investors would've swapped those two favourable line betting results for a Tigers head-to-head victory.

In total, New Heritage won 4.5 of 6 wagers and fell 3.3%, Prudence won 4.5 of 7 wagers and fell 4.2%, Hope lost its only bet and fell 5.5%, Chi-squared won 0.5 of 3 wagers and fell a precipitous 33.3%, and Line Redux won 2 of 4 wagers and fell 1%.

As a result, the Recommended Portfolio fell 9.4% to leave it just 4.5% ahead for the season. Other Portfolios fell by between 3.3% and 9.5% to leave them in front for the season by amounts ranging from 7.5% to 35.4%.

On tipping, RYL had the best possible round, landing 7.5 from 8. Silhouette and Shadow bagged 6.5 and 5.5 respectively to jointly lead outright on 93.5 from 128 (73%), 5 tips ahead of BKB on 88.5 from 128 (69%) and a further tip ahead of CTL and STM II on 87.5 from 128 (68%).

Level-stake, home team only, start at Round 6 wagering on the heuristic tipsters has now been profitable for all tipsters except ELO, Chi and HSH. Shadow, Silhouette and STM II are currently up by over 11 units using such a wagering strategy - if only we'd known ...

Chi's and ELO's line betting results were once again poor this weekend, with Chi scoring 3 from 8 and ELO just 2 from 8.

All told, a weekend best forgotten.

Clutch Betting

The English language has many wondrous, often euphonious collective nouns ready to serve as descriptors for sets of objects, especially animals. So we have, for example, an exultation of larks, a murder of crows, a gaggle of geese, a cloud of bats, a flutter of butterflies, a cackle of hyenas, a smack of jellyfish, a deceit of lapwing, a richness of martens, a parliament of owls, a watch of nightingales and - a personal favourite - a prickle of porcupines.

English lacks, however, a collective noun for a group of bets, a deficiency I feel needs to be remedied. Accordingly, I'm nominating the word 'clutch' for this purpose.

Its appropriateness can be argued on a number of fronts.

Firstly, the word clutch evokes images of an anxious punter, betting slips gripped tightly in hand, attention riveted on a large screen that's beaming the performance of some two- or four-legged determiner of his or her fate. Surely such a punter can be said to be in the clutch.

The word's also evocative of the notion of 'clutching at straws', a desperate and generally futile exercise, which can seem an especially apposite metaphor some weekends.

Further and more positively, the term 'clutch' already has a sporting pedigree as an honorific applied to the exalted few who can be expected to perform when it matters - hence 'clutch' putter, 'clutch' hitter, 'clutch' pitcher and, more generally, 'clutch' player.

Clutch it it then.

This weekend Investors most certainly face a clutch of bets, 21 in all for the second weekend in a row, and 8 of them on underdogs priced as high as $3.

Chi-squared's own clutch is the scariest. Three bets totalling over 44% of the Fund, the two largest on Essendon and Fremantle both at $3 and both facing teams that are fighting for top 8 and possible top 4 positions. The remaining bet is on Richmond, also the underdogs, but they're only at $1.95 and the bet is relatively small.

New Heritage is also putting a large proportion of the Fund at risk - just under 63% of the Fund on 6 teams, all of them favourites and all but one of them home teams. The largest wager is just over 13% of the Fund on Geelong at what others might call an unbackable $1.04. The smallest wager is just over 2% on the Roos at $1.80 away to the Tigers.

Prudence, as has been its habit for most of the season, has this week nibbled on a smorgasbord of teams rather than gorging on just a few. It has 7 bets totalling a little over 30% of the Fund, 2 of them on underdogs and including a surprising 2% wager on the Dons at $3. The largest wager is for a trifle under 7% of the Fund on the Cats at $1.04.

Line Redux has four wagers representing 20% of the Fund. Two of these wagers are on favourites (Geelong and Port Adelaide) and the other 2 are on underdogs (Essendon and Fremantle).

(There is still one line market to be posted - that for the Tigers v Roos clash - but I don't expect we'll have a bet in it.)

Hope, whose selectivity has been its hallmark this season, has only 1 bet this week, its 20th of the season and its 6th on the Dons. It has 5.5% of the Fund on them at $3.

Together these bets yield the following Ready Reckoner:

The entire tenor of the weekend will be established late on Friday night for all Investors except MIN#017, though even a Dons win won't make the weekend entirely pot-hole resistant.

Next we move to tipping where we find:

* Essendon are 8-5 favourites over the Dogs. Amongst our top 5 tipsters, Silhouette, BKB and CTL have sided with the Dogs, while Shadow and STM II (along with a cadre of anxious MAFL Investors and a badly-bred Pomeranian) are riding the Don train. Chi could definitely be more convincing in his Dondom - he has them as only 1 point winners making this game one of his two Games of the Round.

* Carlton are unanimous favourites over the suddenly unpopular Swans.

* Geelong are 8-5 favourites over the Dees, the narrowness of their favouritism due mostly to the shortness of the memories of many of our heuristic-based tipsters. Amongst the cream of these tipsters, only Shadow and STM II are lining up behind the Dees in what will surely be the shortest of queues.

* Collingwood are 8-5 favourites over the Hawks. Once again it's only Shadow and STM II from the top 5 tipsters who are supporting the underdogs.

* Brisbane are 11-2 favourites over Fremantle, the sole support for the Dockers coming from HSH and Chi, who has this as his second and final Game of the Round.

* Port Adelaide are unanimous favourites over the Eagles.

* The Roos are 8-5 favourites over Richmond. The Tigers' following amongst our top tipsters is thin: only STM II is in their corner. ELO is another Tigers tipper, though only by 6 points, making this its Game of the Round.

* St Kilda are 11-2 favourites over the Crows, with EI I and II the only ornithologists amongst the MAFL tipsters.

On line betting, ELO will surely improve on its 0 from 8 record last weekend, though I'm not as certain that Chi will better his 3 from 8 performance. This week:

* Chi's on: Essendon, Sydney, Melbourne, Collingwood, Fremantle, West Coast, Richmond and Adelaide.

* ELO's on: Essendon, Sydney, Geelong, Collingwood, Brisbane Lions, West Coast, Richmond and St Kilda.

On Line Betting this year teams receiving start have fared much better than those giving it. The current tally is 69-51 in favour of the teams receiving start. The teams with the best records when receiving start are Carlton (4-0), St Kilda (3-0), Brisbane (4-1), and West Coast (8-3). Those with the poorest records when giving start are Fremantle (0-4), West Coast (0-4), Hawthorn (1-11), Port Adelaide (3-6), Adelaide (2-4), Sydney (2-4), Geelong (6-9) and Carlton (4-7).

One last statistic before I go. Which teams do you think have the best and worst win-loss records this year in games that have been decided by fewer than 12 points?

Three teams have perfect records: Essendon (2-0), St Kilda (2-0) and Adelaide (1-0). The Hawks (3-1) also have a strongly positive record. The worst, or perhaps the unluckiest, team in these situations has been Carlton (1-4), followed by 5 teams - Collingwood, Port Adelaide, Richmond, West Coast and the Western Bulldogs - all with 1-2 records.

No team has failed to register at least one result where the margin of victory or defeat has been 11 points or fewer.

Are Footy HAMs Normal?

Okay, this is probably going to be a long blog so you might want to make yourself comfortable.

For some time now I've been wondering about the statistical properties of the Handicap-Adjusted Margin (HAM). Does it, for example, follow a normal distribution with zero mean?

Well firstly we need to deal with the definition of the term HAM, for which there is - at least - two logical definitions.

The first definition, which is the one I usually use, is calculated from the Home Team perspective and is Home Team Score - Away Team Score + Home Team's Handicap (where the Handicap is negative if the Home Team is giving start and positive otherwise). Let's call this Home HAM.

As an example, if the Home Team wins 112 to 80 and was giving 20.5 points start, then Home HAM is 112-80-20.5 = +11.5 points, meaning that the Home Team won by 11.5 points on handicap.

The other approach defines HAM in terms of the Favourite Team and is Favourite Team Score - Underdog Team Score + Favourite Team's Handicap (where the Handicap is always negative as, by definition the Favourite Team is giving start). Let's call this Favourite HAM.

So, if the Favourite Team wins 82 to 75 and was giving 15.5 points start, then Favourite HAM is 82-75-15.5 = -7.5 points, meaning that the Favourite Team lost by 7.5 points on handicap.

Home HAM will be the same as Favourite HAM if the Home Team is Favourite. Otherwise Home HAM and Favourite HAM will have opposite signs.

There is one other definitional detail we need to deal with and that is which handicap to use. Each week a number of betting shops publish line markets and they often differ in the starts and the prices offered for each team. For this blog I'm going to use TAB Sportsbet's handicap markets.

TAB Sportsbet Handicap markets work by offering even money odds (less the vigorish) on both teams, with one team receiving start and the other offering that same start. The only exception to this is when the teams are fairly evenly matched in which case the start is fixed at 6.5 points and the prices varied away from even money as required. So, for example, we might see Essendon +6.5 points against Carlton but priced at $1.70 reflecting the fact that 6.5 points makes Essendon in the bookie's opinion more likely to win on handicap than to lose. Games such as this are problematic for the current analysis because the 'true' handicap is not 6.5 points but is instead something less than 6.5 points. Including these games would bias the analysis - and adjusting the start is too complex - so we'll exclude them.

So, the question now becomes is HAM Home, defined as above and using the TAB Sportsbet handicap and excluding games with 6.5 points start or fewer, normally distributed with zero mean? Similarly, is HAM Favourite so distributed?

We should expect HAM Home and HAM Favourite to have zero means because, if they don't it suggests that the Sportsbet bookie has a bias towards or against Home teams of Favourites. And, as we know, in gambling, bias is often financially exploitable.

There's no particular reason to believe that HAM Home and HAM Favourite should follow a normal distribution, however, apart from the startling ubiquity of that distribution across a range of phenomena.

Consider first the issue of zero means.

The following table provides information about Home HAMs for seasons 2006 to 2008 combined, for season 2009, and for seasons 2006 to 2009. I've isolated this season because, as we'll see, it's been a slightly unusual season for handicap betting.

Each row of this table aggregates the results for different ranges of Home Team handicaps. The first row looks at those games where the Home Team was offering start of 30.5 points or more. In these games, of which there were 53 across seasons 2006 to 2008, the average Home HAM was 1.1 and the standard deviation of the Home HAMs was 39.7. In season 2009 there have been 17 such games for which the average Home HAM has been 14.7 and the standard deviation of the Home HAMs has been 29.1.

The asterisk next to the 14.7 average denotes that this average is statistically significantly different from zero at the 10% level (using a two-tailed test). Looking at other rows you'll see there are a handful more asterisks, most notably two against the 12.5 to 17.5 points row for season 2009 denoting that the average Home HAM of 32.0 is significant at the 5% level (though it is based on only 8 games).

At the foot of the table you can see that the overall average Home HAM across seasons 2006 to 2008 was, as we expected approximately zero. Casting an eye down the column of standard deviations for these same seasons suggests that these are broadly independent of the Home Team handicap, though there is some weak evidence that larger absolute starts are associated with slightly larger standard deviations.

For season 2009, the story's a little different. The overall average is +8.4 points which, the asterisks tell us, is statistically significantly different from zero at the 5% level. The standard deviations are much smaller and, if anything, larger absolute margins seem to be associated with smaller standard deviations.

Combining all the seasons, the aberrations of 2009 are mostly washed out and we find an average Home HAM of just +1.6 points.

Next, consider Favourite HAMs, the data for which appears below:

The first thing to note about this table is the fact that none of the Favourite HAMs are significantly different from zero.

Overall, across seasons 2006 to 2008 the average Favourite HAM is just 0.1 point; in 2009 it's just -3.7 points.

In general there appears to be no systematic relationship between the start given by favourites and the standard deviation of the resulting Favourite HAMs.

Summarising:

* Across seasons 2006 to 2009, Home HAMs and Favourite HAMs average around zero, as we hoped

* With a few notable exceptions, mainly for Home HAMs in 2009, the average is also around zero if we condition on either the handicap given by the Home Team (looking at Home HAMs) or that given by the Favourite Team (looking at Favourite HAMs).

Okay then, are Home HAMs and Favourite HAMs normally distributed?

Here's a histogram of Home HAMs:

And here's a histogram of Favourite HAMs:

There's nothing in either of those that argues strongly for the negative.

More formally, Shapiro-Wilks tests fail to reject the null hypothesis that both distributions are Normal.

Using this fact, I've drawn up a couple of tables that compare the observed frequency of various results with what we'd expect if the generating distributions were Normal.

Here's the one for Home HAMs:

There is a slight over-prediction of negative Home HAMs and a corresponding under-prediction of positive Home HAMs but, overall, the fit is good and the appropriate Chi-Squared test of Goodness of Fit is passed.

And, lastly, here's the one for Home Favourites:

In this case the fit is even better.

We conclude then that it seems reasonable to treat Home HAMs as being normally distributed with zero mean and a standard deviation of 37.7 points and to treat Favourite HAMs as being normally distributed with zero mean and, curiously, the same standard deviation. I should point out for any lurking pedant that I realise neither Home HAMs nor Favourite HAMs can strictly follow a normal distribution since Home HAMs and Favourite HAMs take on only discrete values. The issue really is: practically, how good is the approximation?

This conclusion of normality has important implications for detecting possible imbalances between the line and head-to-head markets for the same game. But, for now, enough.

Favourites Stumble While (Most) Investors Profit

When you lose your first 9 wagers of the weekend and when you've a strategy built around favourites and half of them lose, you're not really entitled to expect to profit from such a weekend, especially when such profit is largely dependent on the team that's at the foot of the ladder toppling a team vying for a spot in the finals and the major wager on that team is one that's been placed by a canine whose to-do list comprises sleep, eat and beg for pats in varying orders.

So, it's with some relief that I report that the Recommended Portfolio and all but one Investor finished in the black this weekend.

Three Funds declined: New Heritage, which won 3 of 5 bets but declined by just under 10%; Prudence, which landed 4 from 6 bets but fell by 1%; and Line Redux, which was right only 1 time in 3 and consequently fell 5.5%. The two successful funds were Hope, which was right 2 times in 3 and rose almost 8%, and Chi-squared, which picked 2 from 4 but rose almost 19%, ensuring that Chi gets fed for another week.

In total that left the Recommended Fund up about another 1.5% and other portfolios up by amounts ranging from 1% to 8%, the only exception being the portfolio of MIN #017, which is down by almost 10% this week though still up almost 35% across the season.

On tipping, Shadow led the way with 6 from 8, propelling it to outright lead on 88 from 120 (73%), now one tip ahead of Silhouette in 2nd and a remarkable 6 tips ahead of BKB on 82 in 4th. Never have the bookies seemed so fallible.

On level-stake, home team only, starting in Round 6 wagering (one day I'll come up with a neat shorthand for that), all but one tipster, ELO, remain profitable.

Indeed, ELO posted something of a record this weekend, landing no line bets at all, three fewer than even Chi managed. Still, line betting based on ELO margin predictions would have been profitable across the entire season, albeit now only by 2.57 units. ELO still has an impressive MAPE of 28.2 points per game, just 0.3 points behind BKB and 2.3 points ahead of Chi.

Fremantle's capitulation to the Crows on Saturday shouldn't go unremarked. Freo recorded just 8 scoring shots (7 of them behinds) to Adelaide's 35, meaning that Freo registered only 19% of the scoring shots in the same. In the entire history of VFL/AFL, spanning more than 13,500 games, only 76 teams have kicked a smaller proportion of scoring shots, and only 3 have done so in the seasons from 1980 onwards. Oddly enough, the most recent of these was this season - in Round 5 when Geelong thumped the Lions 18.18 to 5.3. Prior to that, you need to hark back to Round 13 of 1996 when Geelong beat Fitzroy 25.16 to 6.3. Before that you need to return to Round 14 of 1981 when a wayward Carlton thumped Footscray 15.25 to 5.4. So, truly an historic occasion, though not one you'd expect Dockers fans to commit to memory.

A Blackjack of Wagers

What is it they say again about old dogs and new tricks?

Buoyed - or perhaps blinded - by recent successes, the Funds have launched a record-equalling 21-bet salvo at the very much suspecting TAB Sportsbet bookie, amongst these wagers another fur-raiser from Chi. He's made 4 wagers this week totalling about 27.5% of the Fund, 3 of them on favourites, but the fourth on Melbourne at $2.80. Such is his faith on the Dees' going back-to-back he's put 16% of the Fund at risk.

Chi's faith in the Dees is mirrored, though with considerably less conviction, by Prudence and Hope, as odd a pairing in wagering as they are in life. Prudence has about 1.5% on the Dees as one of its 6 wagers for the weekend, which total around 20% of the Fund. Its other wagers are on teams ranging in price from $1.12 (Adelaide, 5.6%) to $1.60 (Sydney 3.3%).

Hope has 5.3% on the Dees and two other wagers: 2% on Sydney at $1.60, and 0.3% on Hawthorn at $1.45. In total Hope has put about 7.5% of the Fund at risk.

New Heritage has nothing on the Dees but has 54% of the Fund on 5 other teams. The largest wager is 12.7% on Adelaide at $1.12 and the most improbable is 9.2% on Sydney at $1.60. New Heritage's aggregate wagering of 54% in this round is its third-highest aggregate for the season, trailing only the 64% of Round 13 and the 60% of Round 7.

Line Redux has found 3 acceptable risks for the weekend: the Dogs giving the Pies 12.5 points start, Sydney giving Essendon 8.5 points start, and West Coast receiving 32.5 points start from the Saints.

Looking at the wagers across the Funds I note that Sydney, for the second time this season, finds itself with a wager from every Fund. No other team has enjoyed such unanimous support even once, let alone twice, from our 5 Funds this season.

In total, those Investors with the Recommended Portfolio have about 24% of their Initial Funds at risk, which is the second highest aggregate this season, behind only the proportion that was at risk in Round 13, which was 0.6% higher.

Here's the week's Ready Reckoner:

On tipping:
* The Dogs are 12-1 favourites over the Pies, with FTS the only Pie-eyed tipster.
* Sydney are 8-5 favourites over the Dons, though the Dons have the support of 4 of our top 5 tipsters, excluding only BKB. ELO is tipping an 11-point Sydney win and has this as its Game of the Round.
* Carlton are unanimous favourites over the Tigers.
* Geelong are 12-1 favourites over the Lions. HSH, as has often been the case this season, finds itself the lone tipster supporting the underdogs. Chi, though siding with the Cats, predicts only a 5-point margin making this one of his two Games of the Round [he's trying to cut back to just a couple a week].
* Adelaide are unanimous favourites over Fremantle.
* Hawthorn are 11-2 favourites over the Roos. The Roos' 2 supporters include the highly-ranked STM II and the lesser-ranked EI I.
* Port Adelaide are 9-4 favourites over the Dees. Amongst the Dee-favourers are Shadow and STM II. Chi also tips the Dees but by only 5 points, making this his Alternative Game of the Round.
* St Kilda are 12-1 favourites over West Coast and it's once again HSH that is the outlier.

On line betting:
* Chi favours: the Dogs, Sydney, Carlton, Brisbane, Fremantle, Hawthorn, Melbourne and West Coast
* ELO favours: the Dogs, Sydney, Carlton, Geelong, Fremantle, Hawthorn, Port Adelaide and St Kilda

I was reviewing the extended ladder (which can be downloaded from the MAFL Stats site each week) and noticed how strong the Saints' defence has been this season. While their attack has been more than acceptable - they rank 3rd overall in terms of points scored - their defence has been 250 points better than any other team in the league. That's almost 3 goals better per game.

Adelaide, 5th on the ladder, are another team whose success has been based more on defence than attack. They're ranked 9th on Points For and 4th on Points Against. Carlton, who sit 7th on the ladder, have instead relied on attack. The opposite of the Crows, the Blues are ranked 4th on Points For and 9th on Points Against.

In general, defence has had a larger bearing on teams' competition points so far this season than has attack, as evidenced by the slightly higher (in absolute terms) correlation between Competition Points and Points Against (-0.92) than between Competition Points and Points For (+0.85). Put another way, variation in Points Against explains about 12% more (ie 0.92 squared vs 0.85 squared) of the variation in Competition Points than does Points For.