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.

Another Look At Quarter-by-Quarter Performance

It's been a while since we looked at teams' quarter-by-quarter performances. This blog looks to redress this deficiency.

(By the way, the Alternative Premierships data is available as a PDF download on the MAFL Stats website .)

The table below includes each teams' percentage by quarter and its win-draw-lose record by quarter as at the end of the 14th round:

(The comments in the right-hand column in some cases make comparisons to a team's performance after Round 7. This was the subject of an earlier blog.)

Geelong, St Kilda and, to a lesser extent, Adelaide, are the kings/queens of the 1st quarter. The Cats and the Saints have both won 11 of 14 first terms, whereas the Crows, despite recording an impressive 133 percentage, have won just 8 of 14, a record that surprisingly has been matched by the 11th-placed Hawks. The Hawks however, when bad have been very, very bad, and so have a 1st quarter percentage of just 89.

Second quarters have been the province of the ladder's top 3 teams. The Saints have the best percentage (176) but the Cats have the best win-draw-lose record (10-1-3). Carlton, though 7th on the ladder, have the 5th best percentage in 2nd quarters and the equal-2nd best win-draw-lose record.

St Kilda have also dominated in the 3rd quarter racking up a league-best percentage of 186 and a 10-0-4 win-draw-lose record. Geelong and Collingwood have also established 10-0-4 records in this quarter. The Lions, though managing only a 9-1-4 win-draw-lose record, have racked up the second-best percentage in the league for this quarter (160).

Final terms, which have been far less important this year than in seasons past, have been most dominated by St Kilda and the Bulldogs in terms of percentage, and by the Dogs and Carlton in terms of win-draw-lose records.

As you'd expect, the poorer teams have tended to do poorly across all terms, though some better-positioned teams have also had troublesome quarters.

For example, amongst those teams in the ladder's top 8 or thereabouts, the Lions, the Dons and Port have all generally failed to start well, recording sub-90 percentages and 50% or worse win-draw-lose performances.

The Dons and Sydney have both struggled in 2nd terms, winning no more than 5 of them and, in the Dons' case, also drawing one.

Adelaide and Port have found 3rd terms most disagreeable, winning only, respectively, 6 and 5 of them and in so doing producing percentages of around 75.

No top-ranked team has truly flopped in the final term, though the Lions' performance is conspicuous because it has resulted in a sub-100 percentage and a 6-0-8 win-draw-lose record.

Finally, in terms of quarters won, Geelong leads on 39 followed by the Saints on 38. There's then a gap back to the Dogs and the Pies on 32.5, and then Carlton, somewhat surprisingly given its ladder position, on 32. Melbourne have only the 3rd worst performance in terms of total quarters won. They're on 19.5, ahead of Richmond on 19 and the Roos on just 16.5. That means, in an average game, the Roos can be expected to win just 1.2 quarters. Eleven of the 16.5 quarters won have come in the first half of games so, to date anyway, Roos supporters could comfortably leave at the main change without much risk of missing a winning Roos quarter or half.

More Green Shoots

This weekend we learned a great deal.

We learned - if we didn't already know - that the Saints are genuine contenders for the flag this year and aren't at all intimidated by the Cats' incredible win-loss record since 2007. We learned that it is possible to make money without relying on occasional improbable victories by rank outsiders and that last weekend's profit wasn't merely a statistical anomaly. We learned that the Hawks aren't good enough to go back-to-back and that the Dees aren't yet focussed on priority draft picks. And we learned that dogs of dubious breeding shouldn't be entrusted with large sums of cash.

Still, it was another glorious weekend's wagering. Combined, across this weekend and last, Investors have landed 31 winners from 33 bets, missing only a line bet on the Cats last weekend and a highly speculative head-to-head bet on the Tigers at $3.75 this weekend. Even then, neither of these bets lost by more than 3 goals.

New Heritage has so far this season won 38 from 49 bets and is up about 45%. Prudence has won 35 from 44 bets and is up about 19%. Hope, inactive this week, has won 7 from 16 bets across the season and is up by about 33%. Line Redux has won 20 from 39 bets and is finally back in the black, although only by about 1%. Chi-squared is what could politely be called the 'outlier'. It's won 7 from 14 bets and is down by around 33%, over one-half of that loss attributable to this weekend's (obvious in hindsight) folly.

For most Investors, the weekend's successes added between about 8c and 9c to their share price. The two exceptions were MIN #002, who was betless this weekend and so marked time, and MIN #017, whose Heritage-only portfolio leapt over 27c.

These increases leave most Investors up by between about 12% and 15% on the season, the exceptions yet again being MIN #002, who's up 33%, and MIN #017, who's up nearly 45%.

Here's a chart showing each Investor's triumphal march:



On tipping, this week's best performance was HSH's 7 from 8. Most other top tipsters scored 6 from 8, though BKB managed just 5, dropping it into joint 3rd place with STM II on 78 from 112 (70%). Shadow and Silhouette remain joint leaders, now on 82 from 112 (73%). CTL fills out the top 5 places with 76 from 112 (68%).

Only one tipster, ELO, is now showing a loss on level-stake, home team only wagering, commencing in Round 6. Applying this same wagering strategy to the tips of our top 3 tipsters would have yielded profits of over 11 units, which represents an ROI of over 10%.

Whilst ELO might not be performing well on head-to-head wagering, it continues to excel on line betting, recording 6 from 8 this weekend to move to 65 and 47 for the season and a profit to level-staking of 10.57 units. Chi had a good line-betting week too, picking 7 from 8 this week, but he's still at less than 50% (he's 54 and 58) for the season.

In running down the Dockers in the final term on Sunday night, Carlton became only the 8th team this season to come from behind at three-quarter time to win and the 1st team to do so when trailing by 2 goals or more at the last change.

As I've commented before, this has not been a season for winning after trailing. About 68% of teams who've led at the first change (ignoring games that were tied at this change) have gone on to win. This is about 1% point higher than the all-time average. Teams leading at the half (again ignoring games tied at the half) have won 81% of the time, up 2% points on the all-time average, and teams leading at the final change (ignoring games tied at this point) have won 93% of the time, up a startling 7% points on the all-time average.

This latter statistic is not, as you might suspect, the result of teams tending to lead by more at the final change this season compared to previous seasons. In fact, even teams with quite slender leads have been hanging on to win at historically high rates. For example, teams leading by between 6 and 11 points have won 85% of the time (up 13% points on the all-time average), and those leading by between 12 and 17 points have won 100% of the time (up 18% points on the all-time average).

The only three-quarter time lead range that has proved more vulnerable this season than has been the case historically is a lead of between 1 and 5 points, which has been defended only 55% of the time this season, 3% points under the all-time average.

AFL Players Don't Shave

In a famous - some might say, infamous - paper by Wolfers he analysed the results of 44,120 NCAA Division I basketball games on which public betting was possible, looking for signs of "point shaving".

Point shaving occurs when a favoured team plays well enough to win, but deliberately not quite well enough to cover the spread. In his first paragraph he states: "Initial evidence suggests that point shaving may be quite widespread". Unsurprisingly, such a conclusion created considerable alarm and led, amongst a slew of furious rebuttals, to a paper by sabermetrician Phil Birnbaum refuting Wolfers' claim. This, in turn, led to a counter-rebuttal by Wolfers.

Wolfers' claim is based on a simple finding: in the games that he looked at, strong favourites - which he defines as those giving more than 12 points start - narrowly fail to cover the spread significantly more often than they narrowly cover the spread. The "significance" of the difference is in a statistical sense and relies on the assumption that the handicap-adjusted victory margin for favourites has a zero mean, normal distribution.

He excludes narrow favourites from his analysis on the basis that, since they give relatively little start, there's too great a risk that an attempt at point-shaving will cascade into a loss not just on handicap but outright. Point-shavers, he contends, are happy to facilitate a loss on handicap but not at the risk of missing out on the competition points altogether and of heightening the levels of suspicion about the outcome generally.

I have collected over three-and-a-half seasons of TAB Sporsbet handicapping data and results, so I thought I'd perform a Wolfers style analysis on it. From the outset I should note that one major drawback of performing this analysis on the AFL is that there are multiple line markets on AFL games and they regularly offer different points start. So, any conclusions we draw will be relevant only in the context of the starts offered by TAB Sportsbet. A "narrow shaving" if you will.

In adapting Wolfers' approach to AFL I have defined a "strong favourite" as a team giving more than 2 goals start though, from a point-shaving perspective, the conclusion is the same if we define it more restrictively. Also, I've defined "narrow victory" with respect to the handicap as one by less than 6 points. With these definitions, the key numbers in the table below are those in the box shaded grey.

These numbers tell us that there have been 27(13+4+10) games in which the favourite has given 12.5 points or more start and has won, by has won narrowly by enough to cover the spread. As well, there have been 24(11+7+6) games in which the favourite has given 12.5 points or more start and has won, but has narrowly not won by enough to cover the spread. In this admittedly small sample of just 51 games, there is then no statistical evidence at all of any point-shaving going on. In truth if there was any such behaviour occurring it would need to be near-endemic to show up in a sample this small lest it be washed out by the underlying variability.

So, no smoking gun there - not even a faint whiff of gunpowder ...

The table does, however, offer one intriguing insight, albeit that it only whispers it.

The final column contains the percentage of the time that favourites have managed to cover the spread for the given range of handicaps. So, for example, favourites giving 6.5 points start have covered the spread 53% of the time. Bear in mind that these percentages should be about 50%, give or take some statistically variability, lest they be financially exploitable.

It's the next percentage down that's the tantalising one. Favourites giving 7.5 to 11.5 points start have, over the period 2006 to Round 13 of 2009, covered the spread only 41% of the time. That percentage is statistically significantly different from 50% at roughly the 5% level (using a two-tailed test in case you were wondering). If this failure to cover continues at this rate into the future, that's a seriously exploitable discrepancy.

To check if what we've found is merely a single-year phenomenon, let's take a look at the year-by-year data. In 2006, 7.5-to 11.5-point favourites covered on only 12 of 35 occasions (34%). In 2007, they covered in 17 of 38 (45%), while in 2008 they covered in 12 of 28 (43%). This year, to date they've covered in 6 of 15 (40%). So there's a thread of consistency there. Worth keeping an eye on, I'd say.

Another striking feature of this final column is how the percentage of time that the favourites cover tends to increase with the size of the start offered and only crosses 50% for the uppermost category, suggesting perhaps a reticence on the part of TAB Sportsbet to offer appropriately large starts for very strong favourites. Note though that the discrepancy for the 24.5 points or more category is not statistically significant.

Chi Returns As Hope Fades

Chi, as a dog (which he is, so I guess that's a little redundant, but bear with me) is prone to inexplicable bursts of canine euphoria during which times he's apt to bound around like a dog a fraction of his age.

Whatever it is that transports him into these displays of friskiness clearly struck sometime this week just as he was contemplating his weekly wagers. Why else would he have decided to put 17.7% of the Fund on the Tigers at $3.75? His other wager is a much more sedate one: 4.6% of the Fund on the Pies at $1.55.

Prudence has sipped from the same chalice - dog slobber and all - as evidenced by its two most extreme wagers of 1.9% on St Kilda at $2.35, and 1.5% on the Dees at $2.10. As well as these it has three other wagers on teams at prices ranging from $1.30 to $1.55, the largest on being 4.9% on the Swans at $1.30.

New Heritage has also found a lot to like, with wagers in all but the Richmond v Adelaide game. These wagers include almost 12% of the Fund risked on teams priced above $2: Melbourne (5.4% @ $2.10), Port (3.1% @ $2.35) and St Kilda (3.1% @ $2.35). The four other bets range in size from 11.4% on Sydney @ $1.30 to a neither-here-nor-there 0.1% on Carlton @ $1.55.

Line Redux, the only other active Fund this weekend as we are again Hope-less, has found four wagers, three on teams receiving start and one on the Pies, giving start.

Together these produce a Ready Reckoner that looks a lot like this:



Unusually, due mainly to Chi's Richmond wager, all Investors except MIN #017 have roughly equal upside and downside risk this weekend.

On tipping we have:
* Collingwood the unanimous favourites over the Dons.
* West Coast 9-4 favourites over the Dees. Amongst the top six tipsters, the Dees have Shadow, Silhouette and STM II as supporters and the Eagles have BKB, ELO and CTL. Chi has this as one of his four - yes, four - one point margin predictions and hence Games of the Round.
* Brisbane are 12-1 favourites over Port. Only HSH is tipping Port.
* Adelaide are 12-1 favourites over the Tigers. Chi is the sole Tigers fan (hence the wager) but here too is prediction a single point margin making this another of his Games of the Round.
* The Dogs and unanimous favourites over the Hawks.
* Sydney are 8-5 favourites over the Roos. The top six tipsters are split as for the Eagles v Dees clash. This time Shadow, Silhouette and STM II are siding with the Roos and BKB, ELO and CTL are on the Swans.
* St Kilda are 10-3 favourites over the Cats. Geelong have, amongst the top six tipsters, only BKB and ELO in their corner. Chi and ELO are tipping just one point margins and so have this as a/the Game of the Round.
* Carlton are 11-2 favourites over Freo. Only HSH and EI II have tipped Fremantle. Chi though has this as another one pointer, which makes this his fourth and final Game of the Round.

So close are many of the games expected to be this weekend, anyone who tips the card deserves double points in their tipping competition. One measure of this expected closeness is the average points start per game on line betting.This week that statistic is 14.6 points per game, more than two points lower than the next-lowest this season, which was 16.9 points per game in Round 5.

Another measure is the combined probability of all underdogs winning in the round. The probability of that happening this week is about 3,800 to 1, which is roughly 12 surprisal bits. Previously, the lowest this has been this season was about 7,950 to 1, or approximately 13 surprisal bits, which it was in Round 1. In other words, the probability of all 8 underdogs winning this week is roughly twice what it's been for any other round this season.

For Line Betting:
* Chi's on Collingwood, Melbourne, Port, Richmond, the Dogs, the Roos, the Saints and Fremantle.
* ELO agrees except for swapping West Coast in for Melbourne.