MAFL 2010 : Round 27 Results (GF 2.0)

If MARS Ratings are to be believed, the right team won on Saturday.

In winning so emphatically, Collingwood lifted its MARS Rating by 3.7 points to finish the season rated 1,055.4, which rates it above the Geelong of 2009 (1,044.5) but below the Geelongs of 2008 (1,065.9) and 2007 (1,058.3). Prior to that, the only teams with a higher end-of-season MARS Rating since 1999 were the Lions of 2002 (1,056.2) and the Dons of 2000 (1,072.7).

Grand Final Margins Through History and a Last Look at the 2010 Home-and-Away Season

A couple of final charts before GF 2.0.

The first chart looks at the history of Grand Finals, again. Each point in the chart reflects four things about the Grand Final to which it pertains:

• The margin of victory (indicated by the point's height)
• The year of the victory (indicated by the vertical displacement of the point)
• The decade of the victory (indicated by the colour of the point)
• Whether the winner was the team from higher or lower on the home-and-away season ladder (indicated by the point's shape, with triangles indicating a victory by the higher-placed team and circles a victory by the lower-placed team)

MAFL 2010 : Round 27 (or GF 2.0)

Every so often things crop up that unexpectedly test the statistical models I've constructed. For example a client will ask for a model to be used for a practical purpose such as forecasting, or they'll ask me to rerun a set of scenarios that I've created using a model, but this time with slightly different inputs.

Drawing On Hindsight

When sports journos wait until after a contest has been decided before declaring a group of winning punters to be "savvy", I find it hard not to be at least a little cynical about the aptness of the label.

The Bias in Line Betting Revisited

Some blogs almost write themselves. This hasn't been one of them.

It all started when I read a journal article - to which I'd now link if I could find the darned thing again - that suggested a bias in NFL (or maybe it was College Football) spread betting markets arising from bookmakers' tendency to over-correct when a team won on line betting. The authors found that after a team won on line betting one week it was less likely to win on line betting next week because it was forced to overcome too large a handicap.

MAFL 2010 : Round 26 Results (of a fashion)

After that it all feels a little flat.

I just assumed there'd be extra time on Saturday and at least an attempt to find a winner on the day; making 44 players, 2 coaching staffs, 100,000 spectators and countless fans go through that all again seems cruel, unusual and frankly unnecessary.

Grand Final History: A Look at Ladder Positions

Across the 111 Grand Finals in VFL/AFL history - excluding the two replays - only 18 of them, or about 1-in-6, has seen the team finishing 1st on the home-and-away ladder play the team finishing 3rd.

This year, of course, with be the nineteenth.

MAFL 2010 : Round 26 (Week 4 of the Finals a.k.a The GF)

There'll be no dramatic last game plunge into profitability for any Investor this season.

The best that Investors with the Recommended Portfolio can hope for is to end the season down by about 4.5%, and it'll take a Pies victory in the GF by 17 points or more to deliver them that result.

Adding Some Spline to Your Models

Creating the recent blog on predicting the Grand Final margin based on the difference in the teams' MARS Ratings set me off once again down the path of building simple models to predict game margin.

It usually doesn't take much.

Pies v Saints: An Initial Prediction

During the week I'm sure I'll have a number of attempts at predicting the result of the Grand Final - after all, the more predictions you make about the same event, the better your chances of generating at least one that's remembered for its accuracy, long after the remainder have faded from memory.

MAFL 2010 : Round 25 Results (Week 3 of the Finals)

As predicted, the haloed and the winged triumphed over the furry this weekend, leaving us with a Pies v Saints Grand Final for only the second time in VFL/AFL history.

Presumably there are supernatural consequences of cursing saints, but it was difficult to avoid risking them on Saturday night if you were a MAFL Investor watching the game as the Saints went marching off and allowed the Dogs to tack on just enough late points to win on line betting by half a point.

That cost the Recommended Portfolio almost 1% and meant that it increased by only 2.2% over the two games. This leaves the Recommended Portfolio down by 6.4% on the season on the back of three straights weeks of profitability during the Finals.

Visualising AFL Grand Final History

I'm getting in early with the Grand Final postings.

The diagram below summarises the results of all 111 Grand Finals in history, excluding the drawn Grand Finals of 1948 and 1977, and encodes information in the following ways:

• Each circle represents a team. Teams can appear once or twice (or not at all) - as a red circle as Grand Final losers and as a green circle as Grand Final winners.
• Circle size if proportional to frequency. So, for example, a big red circle, such as Collingwood's denotes a team that has lost a lot of Grand Finals.
• Arrows join Grand Finalists and emanate from the winning team and terminate at the losing team. The wider the arrow, the more common the result.

No information is encoded in the fact that some lines are solid and some are dashed. I've just done that in an attempt to improve legibility. (You can get a PDF of this diagram here, which should be a little easier to read.)

A Proposition Bet on the Game Margin

We've not had a proposition bet for a while, so here's the bet and a spiel to go with it:
"If the margin at quarter time is a multiple of 6 points I'll pay you $5; if it's not, you pay me a $1. If the two teams are level at quarter-time it's a wash and neither of us pay the other anything.

Now quarter-time margins are unpredictable, so the probability of the margin being a multiple of 6 is 1-in-6, so my offering you odds of 5/1 makes it a fair bet, right? Actually, since goals are worth six points, you've probably got the better of the deal, since you'll collect if both teams kick the same number of behinds in the quarter.

Deal?"

MAFL 2010 : Round 25 (Week 3 of the Finals)

If you've been following the story so far and I were to tell you that there are two home-team favourites this weekend, one of them short-priced, you should be able to guess the behaviour of at least two of the Funds that are still trading.

All You Ever Wanted to Know About Favourite-Longshot Bias ...

Previously, on at least a few occasions, I've looked at the topic of the Favourite-Longshot Bias and whether or not it exists in the TAB Sportsbet wagering markets for AFL.

Divining the Bookie Mind: Singularly Difficult

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

Simulating the Finals (After Week 2 of the Finals)

Another week, another 1,000,000 simulations.

This week it's a relatively brief summary, since there are only four teams remaining and because TAB Sportsbet no longer has markets for teams' chances of making the Grand Final nor for the possible Grand Final pairings.

MAFL 2010 : Round 24 Results (Week 2 of the Finals)

Maybe MAFL should only operate during the Finals.

The Cats and the Dogs delivered almost to order for MAFL Investors in their respective Semis, the only losing bet coming as a consequence of the Dogs falling just two points short of covering their 6.5 points spread.

This meant that the Recommended Portfolio rose by 2.2c to 91.49c and MIN#017's Portfolio jumped 7.65c to 48.46c. With no action this weekend MIN#002's Portfolio remained unchanged at 72c.

Just Because You're Stable, Doesn't Mean You're Normal

As so many traders discovered to their individual and often, regrettably, our collective cost over the past few years, betting against longshots, deliberately or implicitly, can be a very lucrative gig until an event you thought was a once-in-a-virtually-never affair crops up a couple of times in a week. And then a few more times again after that.

MAFL 2010 : Round 24 (Week 2 of the Finals)

Each season as we enter the Finals and games take on heightened historical relevance, a part of me wishes that the MAFL Funds would sense the occasion and respond accordingly by doing something dramatic and memorable.

They never do, of course, partly because they're not sentient and partly because the opportunity for winning large sums of money on huge home-team underdogs rarely arises during the Finals. As far as the Funds are concerned, the Finals are just another round offering a few more opportunities to spot and exploit mispricing in the head-to-head and line markets.

Which Teams Are Most Likely to Make Next Year's Finals?

I had a little time on a flight back to Sydney from Melbourne last Friday night to contemplate life's abiding truths. So naturally I wondered: how likely is it that a team finishing in ladder position X at the end of one season makes the finals in the subsequent season?

Simulating the Finals (After Week 1 of the Finals)

Okay, six teams left, and you know the drill.

Here's the probability matrix I'm using this week (and again we're ignoring any home ground benefits):

Running the now customary 1,000,000 simulations using this matrix gives us the probabilities shown in the tables below. The rows labelled "Fair" contain fair value prices and those labelled "Offer" contain the most-recent TAB Sportsbet prices.

Double-asterisks denote those wagers that the simulations suggest represent value. As has been the case for a while now, the simulations suggest that the Dogs represent value in both the Flag and the Plays-in-the-GF market.

As well, the Cats are a value bet at $4 for the Flag; the simulations suggest that any price over about $3.30 for them represents value.

In contrast, Sydney and Freo represent appalling value at only $13 and $41 respectively. You'd instead want about $30 and $125 respectively to feel as though you were obtaining fair value for this pair.

Lastly, a look at the GF Quinellas, where you'll notice that only 9 possible Grand Final pairings remain possible:

Here, the value combinations are indicated by green shading, and all of the value bets involve the Dogs.

Whether the Dogs are value bets or not all still comes down to the extent to which you believe that the Dogs' recent performances are the best indicators of their likely performance next week and, if they survive, in the weeks that follow.

MAFL 2010 : Round 23 Results (Week 1 of the Finals)

MAFL's generally done well during the Finals and, while it could have been better had the Cats' final goal been allowed to stand and had the Swans managed more than 3 behinds in the 3rd term, this year's September has at least started in the black.

Coast-to-Coast Blowouts: Who's Responsible and When Do They Strike?

Previously, I created a Game Typology for home-and-away fixtures and then went on to use that typology to characterise whole seasons and eras.

In this blog we'll use that typology to investigate the winning and losing tendencies of individual teams and to consider how the mix of different game types varies as the home-and-away season progresses.

2010: Just How Different Was It?

Last season I looked at Grand Final Typology. In this blog I'll start by presenting a similar typology for home-and-away games.

MAFL 2010 : Round 23 (Week 1 of the Finals)

The importance of the weekend's fixtures should have all of us curious about their outcomes. If you're a Recommended Portfolio holder, though, and you're a bit concerned that one or two contests might drift into dullness, be comforted by the fact that you've wagers in all four.

MAFL 2010 : Team Dashboard for Round 22

The final MAFL Team Dashboard for Season 2010 follows:

Season 2010: An Assessment of Competitiveness

For many, the allure of sport lies in its uncertainty. It's this instinct, surely, that motivated the creation of the annual player drafts and salary caps - the desire to ensure that teams don't become unbeatable, that "either team can win on the day".

A Competition of Two Halves

In the previous blog I suggested that, based on winning percentages when facing finalists, the top 8 teams (well, actually the top 7) were of a different class to the other teams in the competition.

The Eight We Had To Have?

This blog addresses a single topic: amongst the eight teams that won't be taking part in the weekend's festivities, are there any that can legitimately claim that they should be?

Simulating the Finals (After Round 22)

I've just run a quick 1 million simulations of the finals using the following probability matrix, which is based on each team's current MARS Rating and assumes that there is no home ground advantage in the finals:

MAFL 2010 : Round 22 Results

*Sigh*

Entering into Sunday with wagers on both favourites and a cumulative 3.7% profit on the weekend so far for the Recommended Portfolio, I had what I thought were reasonable hopes that this Portfolio would end the weekend having erased some of the loss it had accumulated over the preceding 6 months.

Finalist v Finalist: Who Has the Best Record in 2010?

Twenty-three weeks of footy is over and the AFL's binary division has begun, with the sixteen teams now cleaved in two.

Let's take a look at how the finalists have performed when they've met one of their own.

MAFL 2010 : Round 22

So we've reached the end of the home-and-away season with much still to do if Investors are to finish the season showing a nett gain. A perfect set of results this weekend would drag the Recommended Portfolio narrowly into profit, but similar good fortune would not be enough to do the same for MIN#002 or MIN#017; they'll also need favourable results throughout the final series to finish ahead.

Who Left the Dogs Out?

Freo's selectorial shenanigans of last weekend appear to have spooked the TAB Sportsbet bookie, so much so that he's not yet posted any of the line markets.

I expect he'll address this oversight sometime in the next 24 hours, in which case I'll post the week's wagering and tipping details tomorrow night.

In the meantime, here's a follow up blog on simulating the finals.

MAFL 2010 : Team Dashboard for Round 21

The MAFL Team Dashboard for Round 21 follows:

Final Ladder Positions and Team's Flag Prospects After Round 21

The teams that will comprise the final 8 are now determined - barring Lazarian performances - but their final order is not.

MAFL 2010 : Round 21 Results

Teams, I suppose, finish last for a reason.

And so it was with the Eagles on Sunday afternoon, who appeared to be oblivious to the importance that most MAFL Investors were placing on the outcome of their clash with the Roos. Going into that game, Investors with the Recommended Portfolio were up by about 1.3% on the round and only needed a win by the Eagles - or, worst case, a loss by 6 points or fewer - to finish the weekend in the black.

Why Sydney Won't Finish Fourth

As the ladder now stands, Sydney trail the Dogs by 4 competition points but they have a significantly inferior percentage. The Dogs have scored 2,067 points and conceded 1,656, giving them a percentage of 124.8, while Sydney have scored 1,911 points and conceded 1,795, giving them a percentage of 106.5, some 18.3 percentage points lower.

MAFL 2010 : Round 21

The AFL contend that the Cats are taking on the Blues at home this Friday night. I contend that it's the Blues that are taking on the Cats at home.

When I made the decision to deem this game a Blues home game over 6 months ago, I had no idea quite how important it might prove to be for MAFL Investors. As a direct consequence of that decision, all but the New Heritage Fund were permitted only to wager on the Blues, and forbidden to wager on the Cats. Four of the Funds have taken this opportunity, which means that many Investors now own a large, egg-laden basket named "Carlton".

MAFL 2010 : Team Dashboard for Round 20

The MAFL Team Dashboard for Round 20 follows:

Julia +10.5 Seats

Julia Gillard's in an unusual position this weekend. She can take either side of a wager and probably be happy whether it wins or it loses.

Letting the Computer Do (Most of) the Work

Around this time of year it's traditional to work through the remaining matches for each team and attempt to codify what each needs to do in order to secure a particular finish - minor premiership, top 4, top 8 or Spoon.

Final Ladder Positions: Simulations After Round 20

As I type this late on Sunday evening all ladder-related markets are suspended on TAB Sportsbet, so I'll necessarily be excluding any discussion of value bets in these markets. I'll post subsequently on this once the markets are up.

In the meantime, here's what my simulations now make of each team's chances.

MAFL 2010 : Round 20 Results

Meh.

It's weekends like this one that make me remember a conversation that took place between two of my then team-members outside my office one morning some years ago when things were busy and nerves were generally a little frayed.

MAFL 2010 : Round 20

How nice it is to be at this late stage of the season and still have six of the eight games with some effect on the composition of the final 8.

The Port v West Coast and Brisbane v Adelaide matchups are the two exceptions - though mathematically even Port and Adelaide still have the faintest glimmer of a sliver of hope (if you believe the results of my simulations in an earlier blog, which estimated them both as about 1,000/1 chances to snatch 8th).

Sometimes the Hare Wins

Leading early has never been as predictive of the final outcome as it has been this season.

Consider the statistics. In the 150 games that have produced a clear winner, that winner has led 75% of the time at the 1st change, 76% of the time at the main break, and a startling 89% of the time at the final change. Put another way, only 16 teams have trailed at the final change - by any amount - and gone on to win.

MAFL 2010 : Team Dashboard for Round 19

The MAFL Team Dashboard for Round 19 follows:

Playing the Percentages

It seems very likely that this season, some ladder positions will be decided on percentage, so I thought it might be helpful to give you an heuristic for estimating the effect of a game result on a team's percentage.

Final Ladder Positions: Simulations After Round 19

Two of the markets for final ladder positions are no longer being offered by TAB Sportsbet. Collingwood's victory over the Cats has, it seems, all but determined the destination of the minor premiership, and the Lions' last-gasp win over the Eagles has done something similar for the Spoon.

MAFL 2010 : Round 19 Results

The only conclusion that a reasonable person could reach is that the Recommended Portfolio, concerned about causing undue alarm, has determined the best way to prepare the TAB Sportsbet bookie for its eventual profitability is to do so very, very slowly.

MAFL 2010 : Round 19

It's a strange round indeed - and a pivotal one - that footy fans can look forward to this weekend.

Strange because of the number of games where the outcome appears to be a near coin-toss - a point that we'll come back to a little later in this blog - but not at all strange in terms of the activity level of the MAFL Funds.

Thank the Crows and Blame the Saints

Which teams do you think have generated the most profit for each Fund, and which have inflicted the greatest losses?

When I've looked at this question in the past I've tended to take the most obvious approach to the analysis whereby I've calculated for each team the Return on Net Funds that has resulted from wagers on that. In short, what I've done is to determine how many cents each team has added to or subtracted from the value of a particular Fund as a result of the wagering returns it has directly provided.

Final Ladder Positions: Simulations After Round 18

The weekend results for St Kilda, Fremantle, Melbourne, Richmond and West Coast were the ones that most reshaped the various ladder position markets.

MAFL 2010 : Team Dashboard for Round 18

The MAFL Team Dashboard for Round 18 is below.

Here are a few statistical highlights for each team chosen because the statistic illuminates sustained performance is at the extremes or anomalous performance relative to a team's ladder position:

Collingwood

• Kicked 2nd most goals (278)
• Kicked most behinds (263)
• Have the 2nd best percentage (142.0)
• Ranked 12th on opponent conversion rate (53.5%)
• Ranked 9th on Q4 performances (44% of quarters won, 101 percentage)

Geelong

• Kicked most goals (299) and most total points (2,030)
• Only team to have kicked 2,000 points in the season
• Have the best percentage (146.3)
• Ranked 1st or 2nd for performances in every match quarter

St Kilda

• Kicked fewest goals of any team in the top 8 (222)
• Conceded fewest goals of any team in the competition (191, level with the Dogs) and fewest total points (1,312)
• Ranked 13th on scoring shots per game (22.6) but 1st on opponent scoring shots per game (19.8)
• Ranked 14th on Q2 performances (33% of quarters won, 89 percentage) and 1st on Q4 performances (69% of quarters won, 154 percentage)

Western Bulldogs

• Conceded fewest goals of any team (191, level with the Saints) and 2nd fewest total points (1,328)
• Ranked 1st on conversion rate (56.4%)
• Ranked 1st on 'team most difficult to comment about' metric (aeq with the Roos - 2 comments ... well, now 3)

Fremantle

• Conceded the most goals of any team in the top 8 (237)
• Ranked 3rd on scoring shots per game (28.3)
• Ranked 13th on opponent conversion rate (53.7%)
• Ranked 9th on Q3 performances (47% of quarters won, 104 percentage)

Hawthorn

• Kicked only 3 more goals than behinds (230 vs 227)
• Ranked 15th on conversion rate (50.3%) but 3rd on opponent conversion rate (50.7%)
• Ranking of match quarter performances declines from earlier to later quarters: ranked 3rd for Q1 performances and 15th for Q4 performances

Carlton

• Conceded most behinds of any team in the top 8 (219) and 2nd most goals (235)
• Worst record for 2nd half of season of any team in the top 8 (2-5)
• Have a better than 100 percentage for Q3 and Q4 and a worse than 100 percentage for Q1 and Q2

Sydney

• Worst percentage of any team in the top 8 (101.2)
• Ranked 5th on opponent scoring shots per game (23.5)
• Ranked 12th on Q3 performances (36% of quarters won, 75 percentage) and 4th on Q4 performances (67% of quarters won, 123 percentage)

Kangaroos

• Worst percentage of any team in the top 12 (83.3)
• Ranked 15th on opponent conversion rate (56.6%)
• Ranked 1st on 'team most difficult to comment about' metric (aeq with the Dogs)

Melbourne

• Conceded most behinds of any team in the top 13 (247)
• Better record for 2nd half of season than the three teams above them on the ladder
• Ranked 1st on opponent conversion rate (47.1%) and 4th on own conversion rate (54.5%)
• Ranked 14th on scoring shots per game (22.2)
• Ranked 6th on Q3 performances (56% of quarters won, 145 percentage)

Adelaide

• Better record for 2nd half of season than the four teams above them on the ladder
• Worst conversion rate of any team (49.3%)
• Ranked 13th on Q3 performances
• Have lost more than they've won of every match quarter

Essendon

• Kicked the most goals of any team not in the top 8 (237), the most behinds (225) and the most points (1,647)
• Conceded the most goals of any team (280) and the most points (1,889)
• Ranked 5th on scoring shots per game (25.7)
• Ranked last on opponent conversion rate (57.3%)
• Ranked 5th on Q3 performances (58% of quarters won, 100 percentage)

Port Adelaide

• Kicked the 2nd fewest number of goals of any team (201) and the 2nd fewest total points (1,397)
• Ranked 15th on scoring shots per game (22.2)
• Ranked 15th on Q2 performances (33% of quarters won, 79 percentage)

Richmond

• Kicked the fewest goals of any team (195) and the fewest total points (1,361)
• Have the worst percentage of any team (73.7)
• Better record for 2nd half of season than the nine teams above them on the ladder
• Ranked 4th on opponent conversion rate (50.9%)
• Ranked last on scoring shots per game (21.4) and 2nd last on opponent scoring shots per game (28.9)
• Ranked 16th on Q2 performances (28% of quarters won, 76 percentage) and 15th on Q3 performances (28% of quarters won, 67 percentage)

Brisbane Lions

• Only team not to have recorded a win in the 2nd half of the season
• Ranked 6th on opponent conversion rate (51.4%)
• Have the worst Q1 performance of any team (25% of quarters won, 60 percentage)

West Coast

• Kicked within 5 goals of the 7 teams above them on the ladder excluding Essendon
• Conceded the most goals of any team (283) and the most points (1,947)
• Ranked 8th on conversion rate (51.4%) and 9th on opponent conversion rate (53.2%)
• Ranked 7th on Q2 performances (56% of quarters won, 103 percentage), but last on Q3 performances (25% of quarters won, 72 percentage) and Q4 performances (22% of quarters won, 61 percentage)

MAFL 2010 : Round 18 Results

Every Fund returned a profit on the weekend's wagering, leaving the Recommended Portfolio closer to profitability at the end of the round than it's been since it slipped carelessly into unprofitability in Round 8, and inching the portfolios of MIN#002 and MIN#017 just a little closer to daylight too.

Line Betting : A Codicil

While contemplating the result from an earlier blog, which was that home teams had higher handicap-adjusted margins and won at a rate significantly higher than 50% on line betting - virtually regardless of the start they were giving or receiving - I wondered if the source of this anomaly might be that the bookie gives home teams a slightly better deal in setting line margins.

A Line Betting Enigma

The TAB Sportsbet bookmaker is, as you know, a man to be revered and feared in equal measure. Historically, his head-to-head prices have been so exquisitely well-calibrated that I instinctively compare any model I construct with the forecasts he produces. To show that a model historically outperforms leads me to scuttle off to determine what error I've made in constructing the model, what piece of information I've used that, in truth, was only available with the benefit of hindsight.

MAFL 2010 : Round 18

If the Recommended Portfolio is to make a bid for profitability I've a feeling that this weekend needs to be the start of it.

Final Ladder Positions: Simulations After Round 17

If you're a Pies, Dogs or Carlton supporter - or, I guess, an Eagles supporter with a contrarian nature and a willingness to profit from adversity - you've much to be happy about following last weekend's results and their effect on your team's chances of participating come September.

MAFL 2010 : Team Dashboard for Round 17

Here's the MAFL Team Dashboard for Round 17:

MAFL 2010 : Round 17 Results

Once the Roos had lost narrowly to the Dons on Saturday, Investors with the Recommended Portfolio needed the remaining four results to go their way to finish the weekend in the black. Carlton's second-half rejuvenation a little later on Saturday put paid to any such hopes so that, despite a perfect set of outcomes on Sunday, the Portfolio still dropped in value by a little under 1.4% across the weekend.

Finding Value in the Markets for Final Ladder Positions

In an earlier blog I used a simple method to create one view of the season's final home-and-away ladder.

Those projections had Collingwood finishing third because it lost narrowly to the Cats in Round 19 while the Cats and the Saints were projected to win all their remaining games. Three of the Cats' wins and two of the Saints' were by only a handful of points, however, so it was easy to imagine scenarios in which the ordering at the top was quite different and where, for example, the Pies finish top of the ladder.

MAFL 2010 : Round 17

First, some good news.

Back in Round 14, Investors in the Recommended Portfolio had a line bet on the Saints, who played Melbourne at Dockland. In the Bet Summary for the week I had the Saints giving the Dees 35.5 points start, which meant that their eventual 100-65 victory was a half-point short of covering the spread, a fact that I seem to recall lamenting at some length, certainly in the conversations that I had in the following week, and probably in the blog too (which I'm not of a mind to review at the moment).

Projecting the Final Ladder for 2010 (After Round 16)

It's late July and normally it'd be time for the first whispers of tanking to emerge, but the rejigging of the draft process next year to accommodate the introduction of Gold Coast and GWS has significantly reduced the reward to sustained ineptitude so effectively that, this year, I doubt there'll be much talk of it (or, come to that, much compelling evidence of its existence).

MAFL 2010 : Team Dashboard for Round 16

Here's the MAFL Team Dashboard for Round 16:

MAFL 2010 : Round 16 Results

If ever you wanted evidence to support the aphorism that it's unwise to pre-emptorily enumerate your poultry, Sunday afternoon's Fremantle v Melbourne game is it.

The Importance of a Team's Recent Form: What Bookies (and MARS) Think

When the TAB Sportsbet bookie is framing a market for an upcoming game, clearly one set of data that he uses is the recent results of the participating teams. This raises two questions:

• What proportion of the variability in bookie prices can be explained solely by recent results?
• What relative weighting does the bookie ascribe to each previous game?

Super Smart is Taking Heed of Bookies

Across a series of blogs now we've explored the Super Smart Model (SSM) and investigated its ability to predict victory margins. In this blog we'll look more closely at which variables most influence SSM's forecasts.

Trialling The Super Smart Model

The best way to trial a potential Fund algorithm, I'm beginning to appreciate, is to publish each week the forecasts that it makes. This forces me to work through the mechanics of how it would be used in practice and, importantly, to set down what restrictions should be applied to its wagering - for example should it, like most of the current Funds, only bet on Home Teams, and in which round of the season should it start wagering.

MAFL 2010 : Team Dashboard for Round 15

Here's the MAFL Team Dashboard for Round 15:

MAFL 2010 : Round 16

Faced with six home team favourites Investors could easily have been facing another dose of high risk, low potential return wagering this weekend, but a combination of moderate wagers on the two at-home underdogs and larger wagers on some of the more attractively priced at-home favourites has resulted in a far more balanced portfolio of wagers, at least for those with the Recommended Portfolio.

Simplifying MARS Rating Updates: An Epilogue

In my previous blog I used Eureqa to find a simpler version of the equations for updating MARS Ratings.

There I jumped straight to what I deemed the 'best' solution that Eureqa had found, glossing over a slew of perfectly adequate and much simpler solutions that it also found.

MARS Ratings Revisited: There Must Be a Simpler Way

It's official: Eureqa is an amazing tool.

With all the recent model-building I've been undertaking and writing up here in various blogs, I've become more aware of the predictive power of MARS Ratings.

Predicting Head-to-Head Market Prices

In earlier blogs I've claimed that there's not much additional information in bookie prices that's useful for predicting victory margins than what can be derived from a statistical analysis of recent results and an understanding of game venues.

We saw that the Smart Model - which makes its victory margin predictions using only team MARS Ratings, a team's two most recent results and information about whether or not the relevant game is being played interstate from the point of view of one of the participants -performed about as well as the best model that can be built using bookmaker prices, where performance is measured on any of a number of sensible metrics.

MAFL 2010 : Round 15 Results

For most Investors it was another weekend of nibbling away at the season's deficit.

Carlton's loss on Sunday evening meant that, for those with the Recommended Portfolio, the nibble was only a nip, but a couple of percent is undeniably better than an ocular prod with a dulled wooden implement.

The Relationship Between Head-to-Head Price and Points Start

I've found yet another MAFL-related use for the Eureqa tool, this time to determine the precise relationship between a team's head-to-head price and the start it's giving or receiving on line betting.

Building The Super Smart Model

In a previous blog we investigated the information content of bookie prices in the context of predicting the victory margin of a game.

What Do Bookies Know That We Don't?

Bookies, I think MAFL has comprehensively shown, know a lot about football, but just how much more do they know than what you or I might glean from a careful review of each team's recent results and some other fairly basic knowledge about the venues at which games are played?

MAFL 2010 : Round 15

Investors face a far less breathtaking set of wagers this weekend.

In fact, they can take a complete breather until Saturday since none of the Funds have any interest in Friday night's Port v Collingwood game, despite Port playing at home and being priced at $5.00 head-to-head and +32.5 points on line betting.

MAFL 2010 : Team Dashboard for Round 14

Here's the MAFL Team Dashboard for Round 14:

MAFL 2010 : Round 14 Results

Well that was a good weekend's wagering no matter how you dissect it.

What prevented it from attaining 'fantastic' status was the mercy shown by the teams occupying 1st and 2nd on the table, each of which slacked off in the latter parts of their respective games leading to our losing one line bet (on the Cats) by 4.5 points and the other (on the Saints) by just half a point.

MAFL 2010 : Round 14

If you're an Investor this is probably a blog best read seated.

In six of the weekend's eight games the home team is the favourite, and in five of them it's the short-priced favourite. The reaction from the MAFL Funds to this circumstance - especially from the New Heritage Fund - has been akin to the response you get if you open a packet that sounds even vaguely like a chip packet within earshot of Chi: immediate and overwhelming interest, palpable desire and a fixation on securing a piece of whatever's on offer.

Here's what the result of all that interest looks like.

MAFL 2010 : Team Dashboard for Round 13

Sorry that this is a little late this week. I think I've been mentally recovering from the hiding that MAFL took last weekend.

Anyway, here's the MAFL Team Dashboard:

MAFL 2010 : Round 13 Results (Final)

This'll be brief.

When scanning the week's Ready Reckoner, never do I consider the "Best Possible" or "Worst Possible" results as lying within the feasible set of actual wagering outcomes. How wrong I've been.

Three games, three losses. Waiter, may I have the menu for Round 14 please?

MAFL 2010 : Round 13 - Part II

Even with two attractive-looking matchups in the Cats v Saints and Swans v Pies games, this weekend can't help but seem like the stale bit of the loaf that is Round 13. (Apologies if you're a Melbourne or Adelaide fan, but I'm finding it hard to get enthused about 13th v 15th.)

The weekend's status might be elevated though if the Cats, Swans and Dees all wins, the Cats doing so by 21 points or more, since then the Recommended Portfolio will rise by about 3.9% more than offsetting, if barely, the losses suffered last weekend.

MAFL 2010 : Round 13 Results (Interim)

If I've much more practice in being philosophical after wagering losses I fear I'll wind up smoking a pipe, blogging about the meaning of truth, affecting a permanent, faraway look and calling myself Bruce. (Any Monty Python fans here?).

So far, Round 13 has not been a happy one for any Investor. The Recommended Portfolio has shed 3.7%, MIN#002's Portfolio has dropped 7.5%, and MIN#017's Portfolio has fallen 7.1%, these falls largely due to poor showings by the Blues and the Lions, who went down by 9 and 19 points respectively.

Given the likely prices on offer for the remaining three games, it seems unlikely that a net profit for the round will be the final outcome. Only an upset Sydney win over the Pies might make a difference, but it doesn't look as if any of the Funds is especially keen to invest in that particular result.

MAFL 2010 : Round 13 - Part I

And so we enter the first half - well five-eighths actually - of the split Round 13.

Recommended Portfolio holders have wagers in four of the week's five games, with the Eagles v Dogs clash the only one failing to attract the interest of at least one Fund. New Heritage is the boldest Fund (who'd have guessed?), wagering about 22% of the Fund on three bets including two that are for around 10% of the Fund both of which are on teams that are favourites but by no means raging hot ones in the form of the Hawks and Lions. The third bet is a contrarian, away team wager on Port Adelaide that, when offset by the wagers of Prudence and the Heuristic-Based Funds on the Roos in the same game, makes the outcome at best a small profit for those with the Recommended Portfolio.

MAFL 2010 : Team Dashboard for Round 12

Here's the week's MAFL Team Dashboard.

This week I thought we'd take a look at the correlations between team ladder position and the performance statistics in the Scoring Shot Data and Quarter-By-Quarter Performance sections of the Dashboard.

Here's the summary:

Scoring Shots

• The (rank) correlation between Scoring Shots For (measure A) and Ladder Position is +0.75. It would be much higher but for the effect of St Kilda who are 12th on this measure but 2nd on the ladder.
• The (rank) correlation between Scoring Shots Against (measure B) and Ladder Position is +0.84.
• The (rank) correlation between the Scoring Shot Differential (measure C) and Ladder Position is +0.98.
• Creating and preventing scoring shots seem to be of roughly equal importance in generating success so far this season.

Scoring Shot Conversion

• The (rank) correlation between Own Conversion Rate (measure D) and Ladder Position is +0.72. Collingwood, who are 3rd on the ladder but an astonishing 14th on this measure, drag this correlation down. The Pies could surely have had no better reminder of the importance of converting opportunities than that provided by their 9.22 performance on the weekend, which cost them 2, and almost 4, competition points.
• The (rank) correlation between Opponents' Conversion Rate (measure E) and Ladder Position is +0.08.
• The (rank) correlation between Conversion Rate Differential (measure F) and Ladder Position is +0.41.
• Clearly, this season, success has been far more about converting opportunities than it has been about preventing opponents from doing the same.

Quarter-By-Quarter Performance

• The (rank) correlation between ranking on Q1 performance and Ladder Position is +0.79.
• The (rank) correlation between ranking on Q2 performance and Ladder Position is +0.58, dragged down by St Kilda, who are 2nd on the ladder but 14th on Q2 performances, having won just 4 from 12 second terms.
• The (rank) correlation between ranking on Q3 performance and Ladder Position is +0.69
• The (rank) correlation between ranking on Q4 performance and Ladder Position is +0.65. Two teams have depressed this correlation, Collingwood and Hawthorn, the former being 3rd on the ladder but 11th on Q4 performances, and the latter being 8th on the ladder but 16th on Q4 performances.
• Unusually, it's been Q1 performances that have been most indicative of a game's outcome this season. Winning teams have won first quarters in 71 of the 96 games played so far this season (and they've drawn 2 more), which is higher than any other quarter.
  To put this in some historical context, last season, winning teams won just 68.9% of games (ignoring draws). This season they've won 75.8% (ignoring the draw).

MAFL 2010 : Round 12 Results

As I've probably mentioned before, I dislike draws, not so much for their inconclusive nature, but more for the fact that they make the statistics messy. All the formulae in my spreadsheets that calculate returns need to cater for this once-or-twice-in-a-season phenomenon, and all the tipping statistics now sport an awkward .5 at the end.

MAFL 2010 : Round 12

Is it really the second half of the season already?

Recommended Portfolio holders can look forward to another weekend of cheering for favourites one game and underdogs the next. This week they've one game (Kangaroos v Carlton) in which their interest is solely in the line and not the head-to-head result, and another game in which they've no interest at all (Richmond v West Coast).

In-Running Wagering: What's the Best Strategy?

With services such as Betfair now offering in-running wagering opportunities, the ability to accurately assess a team's chances of victory at any given point in a game is now of considerable commercial value.

Imagine, for example, that your team, who are at home, lead by 18 points at the first change. Would a wager on them at $1.40 be advised?

MAFL 2010 : Team Dashboard for Round 11

Here's the week's MAFL Team Dashboard.

A few things to note in this data:

• Collingwood, despite being placed second on the ladder, have the second-worst opponent conversion rate (56.4%) and a relatively poor record in final terms (which was starkly in evidence on Sunday night)
• Hawthorn are in the eight at least partly because they've prevented their opponents from converting opportunities in front of goal. They're struggling in the second half of games, particularly in final terms where they have a 1-10 record.
• St Kilda, Essendon and Fremantle are all allowing their opponents to convert too many of their opportunities. Essendon's struggles in first and last terms, Fremantle in third terms, and St Kilda in second terms.
• Relative to their respective ladder positions, Melbourne and Richmond are ranked highly on opponent conversion rate.
• Melbourne performs significantly better is third terms.
• Port Adelaide has mastered the art of the whirlwind finish, winning almost two-thirds of the final terms it's played. This hasn't been enough in 6 games out of 11 however.
• The Lions continue to pair lousy first halves with stunning second halves. The round just finished provided an excellent example of this, as the Lions were outscored 10 goals to 5 by the Roos in the first half of their game, before kicking 8 goals to 2 in the second half.
• West Coast performs relatively poorly in second halves.
• The Bulldogs are the best in the league for second terms.

MAFL 2010 : Round 11 Results

Absent an upset victory by either the Tigers or the Eagles - both of which outcomes seemed possible for at least a portion of their respective games - that was just about as good a weekend as Investors with the Recommended Portfolio might have hoped for.

An improbable Dogs victory also tantalised for a few minutes late in the final term on Friday, but that outcome ultimately proved unattainable, leaving the Recommended Portfolio up 2.4c on the weekend and down now just 11.1c on the season.

The portfolio of MIN#017 also finished in the black, though the 8.4c hike has left much still to do to return that Portfolio to parity, languishing as it does still some 37c down on the season. Still, how does one eat an elephant? The conventional answer is: one spoonful at a time.

MIN#002 was the only Investor to suffer losses this week. His portfolio fell 6.3c to 75.2c, a victim of Hope's curiously lacklustre performance so far this season, which has seen it land just 4 of 12 wagers.

In-Running Prediction of the Winner of an AFL Game

I've been planning to create this model for a while.

With it, you can calculate the probability that the home team will eventually prevail given the state of the match at a particular point in the game.

MAFL 2010 : Round 11

Every week I learn a little more about my tolerance for risk.

I feel far more comfortable with an array of wagers that includes the Tigers at $5.50 and West Coast at $6.00 than I did with last week's festival of favourites. Wagering at odds-on prices still feels inordinately Sysyphean to me.

Looking At Team Performance Quarter-By-Quarter

AFL Football - as the cliche goes - is a game of four quarters. The benefit of this arrangement is that AFL scores provide twice as much information about the ebb and flow of each contest as the scores of any other form of football in this country.

With the quarter-by-quarter information alone we can perform some interesting analyses for every team.

MAFL 2010 : Team Dashboard for Round 10

Here's the week's MAFL Team Dashboard.

MAFL 2010 : Round 10 Results

When seven of the weekend's eight contests produce the result that you expected - the right team winning head-to-head, the right team winning on handicap, in some games both - I think you've a reasonable expectation of profit.

No such luck.

Port Adelaide just had too much money riding on them, so the triumphs in the other seven contests nevertheless left those with the Recommended Portfolio down a little over 1 cent for the round. MIN#002 fared no better, his portfolio also dropping by about a cent, while the portfolio of MIN#017 did even worse, dropping over 5 cents.

MAFL 2010 : Round 10

At some point earlier today, for reasons I expect we'll never know, TAB Sportsbet felt comfortable in reopening the Saints v Crows markets, pricing them exactly where they'd been a couple of days previously when the allegations broke and attracting wagers from four of the five head-to-head wagering MAFL Funds. Among them only Hope abstained, as in fact it has on all eight games this round.

The ELO-Based Fund also chose not to bet on this game, deeming the 27.5 points start that the Saints were required to give just 1 point too many.

MAFL 2010 : Round 10 (Coming Soon to a Browser Near You)

Well normally I'd be posting this week's pre-round blog, but, as I type this, the Saints' alleged player sex scandal is still unresolved, at least to the satisfaction of the TAB Sportsbet bookie. As a consequence all St Kilda v Adelaide markets are suspended.

So, we've no ability to back the Saints, which we probably will both on the head-to-head and line markets once we're able. I'll wait 24 hours and see what happens.

Introducing the MAFL Team Dashboard (Round 9)

In the previous blog I promised to provide another dashboard, this one devoted to information about team performance.

Try as I might, I couldn't come up with any charts for this dashboard that seemed to be of any interest, so the final dashboard is, I admit, something of a festival of text and digits with nary a relieving picture in sight. If Gordon Gecko had been a quant jock, I'm sure he'd have proclaimed that "Charts are for wimps" anyway.

MAFL 2010 : Round 9 Results

For the third week in succession, those with the Recommended Portfolio were let down by the Saints' performance in the last game of the round. In Rounds 7 and 8 it was the Saints' ineptitude that caused the disappointment; in Round 9 that ineptitude was nowhere to be seen when Investors most needed it.

Not that the weekend's losses can be entirely attributed to the Saints' victory on Sunday evening. Collingwood, the Roos, Sydney and Carlton all did their bits too, offset only - and not completely - by Essendon, Melbourne and Adelaide victories.

This week I'm trialling a new way of presenting the various pieces of information about wagers, tips, team ratings and margin prediction. I call it the MAFL Dashboard.

Should We Have Been Surprised About the Season So Far?

Surprisals, you might recall, are a way of measuring the likelihood of the result of a chance outcome. They're measured in bits, and one bit of surprisal is the amount of surprise that you should feel in correctly predicting the toss of one unbiased coin.

So, 1 bit of surprisal is equivalent to an even money outcome, 2 bits to a 3/1 outcome, 3 bits to a 7/1 outcome and, more generally, n bits of surprisal is produced by a result with odds of (2^n-1)/1.

MAFL 2010 : Round 9

Just when you get into a routine, someone has to go and change something.

This week the TAB Sportsbet bookie decided to post the line markets a day early, leaving me with the dilemma of deciding whether to follow the time-honoured strategy of placing bets around noon on Wednesday or, instead, to follow the other time-honoured strategy of placing bets just after the line markets go up. In the past, save for those weeks where there's been a Thursday game, these two events have coincided.

Is the Home Ground Advantage Disappearing?

Home teams, as a whole, have not fared particularly well this season, which is one of the reasons that most of the MAFL Funds - all but one of which bet exclusively on home teams - have been testing Investors' patience.

Teams playing at home - truly or notionally - have won only 54.7% of contests so far this season, which puts them on track for the worst aggregate home team performance since 2001 when only 49.4% of home teams were successful. In the 25 seasons preceding this one, home teams have won at a rate lower than 55% on just two occasions: in 2001 as just mentioned, and way back in 1985.

MAFL 2010 : Round 8 Results

Wow. It feels like I'm about to compose a eulogy.

Silly of me really, in hindsight, to hope that the Saints - who, I remind you, should probably be the reigning premiers - could add a mildly cheery note to an otherwise gloomy weekend's wagering. Instead, their failure merely compounded the misery that saw those with the Recommended Portfolio turn a profit in just three of the eight contests, wiping 11.2% off the value of their Investment.

Investors with other portfolios fared no better, MIN#002 dropping 11.8% and MIN#017 dropping 23.2%, leaving them, as those with the Recommended Portfolio, solidly in the red.

Still, it's only Round 8, so there's plenty of time to forgive and forget.

MAFL 2010 : Round 8

Some weeks there's a period where I'm 5 years old again and I hold my breath and close my eyes while I run the Fund scripts and partly fear, partly hope for the worst. This week that apprehension was tied to just how much we'd have riding on the Tigers who were being offered by TAB Sportsbet at $4.50 and taking on the Hawks at the G.

MAFL 2010 : Round 7 Results (Final)

Well at least we weren't left hanging until the end.

There are games that you witness where history's page is rendered inaccurate by the word "loss". When teams play as the Saints did tonight another column is required on the competition ladder, to sit alongside "W" and "L", let's call it "F", for "Failed to Compete" (although other designations also spring to mind).

MAFL 2010 : Round 7 - Results So Far

The round's not yet over as most Investors still have a pecuniary interest in Monday night's Saints v Carlton clash, so this'll just be a short blog to update Investors.

Adelaide's final-term blitz on Sunday evening was welcome relief - apparently there's rarely any other sort if we're to believe TV news anchors - for all Investors, with the profit from the Crows' 50-point victory leaving those with the Recommended Portfolio up 0.64% on the round and 3.24% on the season. MIN#002 and MIN#017 also benefited. MIN#002's portfolio is up 2.25% on the round and now 0.05% on the season, and MIN#017's is down 4.43% on the round and 3.87% on the season.

MIN#002 is the only Investor with no stake in the St Kilda v Carlton game, so he at least can watch the game without the mood-altering effects of a wager. There'll be no such enjoyment though for those with the Recommended Portfolio or for MIN#017 as they all have significant stakes in the outcome.

If St Kilda wins and covers the 15.5 point start they're giving, the Recommended Portfolio will rise by a further 1.63%. If they win but fail to cover the spread then the increase is only 0.68%. And, finally, if the Saints lose, then the Recommended Portfolio will drop by 3.13%, virtually eliminating the season's profit to date. For MIN#017 all that matters is whether the Saints win or lose. A win will trigger a 4.66% increase in portfolio wealth and a loss will inflict a 10.36%-sized hole.

(By the way, I discovered a glitch in the Ready Reckoner calculations over the weekend, so the return for the Recommended Portfolio provided in this blog is slightly higher than what you'd get if you added up the relevant numbers from Friday's table. Errors are always so much more forgivable when they're beneficial, aren't they.)

MAFL 2010 : Round 7

I confess I didn't realise quite how active the six MAFL Funds would be this year once they were simultaneously let loose on the market. This week, their innate tendency to wager has been cunningly exploited by TAB Sportsbet in establishing seven of the home teams as favourites.

So, we have seven wagers from New Heritage (totalling almost 73% of the Fund), six from Prudence (for 25%), five from ELO-Based line (also for 25%), three from Hope (for about 10%), and two each from the currently joined-at-the hip Heuristic-Based and Shadow Funds (for 10% in both cases). In total, Investors with the Recommended Portfolio have about 27.5% of their total funds at risk.

MAFL 2010 : Round 6 Results

Regression to the mean is a bit like unprompted advice from a friend: not always welcome.

But a weekend of regression it ultimately was for Investors with the Recommended Portfolio, as their last-chance Eagles failed to capitalise on their early-game form and eventually went down to the Dockers by over six goals.

With MIN#002 losing also, the only Investor to show a profit on the weekend was MIN#017 who made a 0.55% gain.

MAFL 2010 : Round 6

It's as if someone flicked a switch, which in a fashion someone did.

All six Funds have taken up their option to participate in the weekend's wagering, many of them with an alacrity that can only be exhibited by something inanimate that has no sense of the terror that can be induced by a large wager on a team at $1.01.

Cherishing Inconsistency Where It's Welcome

In an earlier blog we demonstrated the benefits of consistency in football - moderate benefits if the consistency came in the form of generating scoring shots with less variability than teams of otherwise similar ability, and significant benefits if it came in the form of converting more of those opportunities into goals.

Indeed, consistency's a characteristic that sports commentators reserve for their warmest - and often longest - soliloquys, and players and teams, once they've reached an acceptable level of performance, announce as though scripted that they're now "striving for consistency". So, surely, consistency is always a good thing, isn't it?

MAFL 2010 : Round 5 Results

That was a weekend that could easily the unwary into thinking there's something in this statistical modelling stuff.

Six wins from seven bets, with two of the wins coming from seriously unfancied teams, lifted the Heuristic Fund by almost 30% and left it up almost 41% on the season. Investors with the Recommended Portfolio are now, therefore, up over 4% on the season.

Modelling AFL Team Scoring : Part III

This is the third in a series of blogs (here are Part I and Part II) about modelling the scoring of AFL teams and, with the heavy statistical lifting out of the way, in this blog we can look at the practical uses of what we've discovered so far, which is that:

(1) Team scoring can be modelled by the Score Equation

Score = Number of Scoring Shots x Conversion Rate x 6 + Number of Scoring Shots x (1 - Conversion Rate)

(2) A team's number of scoring shots can be modelled by a lognormal distribution with mean determined by the team's strength relative to its opponent and by whether or not the match is a home game for either team, and with a standard deviation of 5.5 scoring shots.

(3) Teams will convert the scoring shots they produce into goals as if drawing from a binomial distribution. The average team will convert 53.64% of its scoring shots into goals.

Modelling AFL Team Scoring : Part II

This is the second in a series of blogs about modelling the scoring of AFL teams.

In the previous blog on this topic I introduced what I called the Score Equation, which represents a way of thinking about a team's score in any game, and is as follows:

Score = Number of Scoring Shots x Conversion Rate x 6 + Number of Scoring Shots x (1 - Conversion Rate)

Then I used empirical data for seasons 2006 to 2009 to show that the bookmakers' starting prices could be used to predict with reasonable accuracy the number of scoring shots that a team will produce in a given game, and that teams, regardless of the number of scoring shots they produce, generally convert about 53.64% of them.

Modelling AFL Team Scoring

Today's blog is the first in a series that will look at statistically modelling the scoring behaviour of teams in the AFL.

If you're profoundly reductionist about it, you can think about a team's footy score as being the product of the number of scoring shots it creates and the proportion of those scoring shots that it converts into goals.

MAFL 2010 : Round 5

Well I did expect the level of wagering activity to ratchet up this weekend compared to last, but I thought Hope would be contributing to at least some of that increase.

That's not the case though. Hope has reviewed the market offerings and decided to return to slumber for at least another week; Shadow has looked at the same market and taken out its metaphorical knife and fork, rediscovering its Round 3-style appetite for the punt.

MAFL 2010 : Round 4 Results

What a pleasant weekend's wagering that was.

On Saturday, Collingwood looked comfortable from the off and eventually annihilated the Hawks by 64 points, and then on Sunday St Kilda teased us long enough to let us feel that we earned our payoff having trailed by a point at quarter time, drawn level by half-time, led by a point at three-quarter time before running out 15-point winners. Two bets, two wins, the Heuristic Fund up another 4.3%, and the Recommended Portfolio now up 1.13% on the season. All of this with the prospect of the Hope Fund commencing trading in the coming round.

MAFL 2010 : Round 4

If last weekend was the SSO in the Opera House this weekend is an acapella duo down the local pub.

We've just two bets and they're both priced at under $1.60. One wager is on the Pies, who face Hawthorn on Saturday, and the other is on the Saints, who take on Fremantle on Sunday.

Goalkicking Accuracy Across The Seasons

Last weekend's goal-kicking was strikingly poor, as I commented in the previous blog, and this led me to wonder about the trends in kicking accuracy across football history.

Just about every sport I can think of has seen significant improvements in the techniques of those playing and this has generally led to improved performance. If that applies to football then we could reasonably expect to see higher levels of accuracy across time.

MAFL 2010 : Round 3 Results

Well that was quite a Sunday.

Investors awoke on Sunday morning with the weekend's profitability hinging on an improbable victory by the Dees against the Crows, which then had to be followed by an almost equally unlikely win by the Dockers against the Cats. In the end, Investors got both results, with a victory by the Dogs providing the proverbial marzipan on the sweet, baked, traditionally tea-accompanying confection.

Coins : The Epilogue

Two previous blogs have been devoted to determining the optimal set of coin denominations that would allow one to produce any amount between 5-cents and 95-cents using, on average, the smallest number of coins. So far, we've solved the 2-coin, 3-coin and 4-coin variants of this problem and I flagged, in the most recent blog on the topic, the difficulty I suspected I'd encounter in trying to find solutions for more coins.

MAFL 2010 : Round 3

This week the Heuristic Fund will again be guided by the selections of the heuristic tipster named Shadow, a situation that will not persist into next week if Shadow's Round 3 tips are responsible for the Fund's third straight weekly loss.

Were Shadow hell-bent on retaining control of the Heuristic Fund - assuming, for the sake of the narrative, that it were sentient at all - it might have chosen to respond to this situation by wagering on a couple of short-priced favourites, hoping to eke out a small profit and in so doing earn the right to manage the Heuristic Fund for at least another 3 weeks.

As it happens, there's only one markedly short-priced favourite this weekend - Sydney at $1.10 facing Richmond - and Shadow has, indeed, thrown bread at the Swans ... but also at six other teams.

MAFL 2010 : Round 2 Results

If you didn't tip the round this weekend you've only yourself to blame. All eight winners were published in the online (and probably the print) version of Melbourne's Herald Sun late on Wednesday night as one of their forecaster's considered selections.

They were Jennifer Hawkins' tips.

It was that kind of round.

Scoring Shots: Not Just Another Statistic

For a while now I've harboured a suspicion that teams that trail at a quarter's end but that have had more scoring shots than their opponent have a better chance of winning than teams that trail by a similar amount but that have had fewer scoring shots than their opponent.

Suspicions that are amenable to trial by data have a Constitutional right to their day in court, so let me take you through the evidence.

We Still Don't Need No 37-cent Piece (And I'm Going Right Off The 10-cent Piece)

A few blogs back we asked and answered the question: if you were to select a set of four coin denominations on the basis that the selected four could combine to make any amount from 5-cents to 95-cents using, on average, the fewest number of them, what would those four denominations be?

There were, it turned out, nine such sets each of which was optimal and required only 2.11 coins, on average, to sum to any amount from 5-cents to 95-cents.

Well since we've solved the problem for 4-coin sets, what about solving it for 2-coin and 3-coin sets?

MAFL 2010 : Round 2

Before I launch into this week's wagering and tipping information, a final reminder: if you want to take part in this year's blog-readers' competition you need to have an entry to me before centre-bounce Thursday night. Details of the competition are in this blog entry.

Entry is free and there are no prizes, which I think has an appealling symmetry to it. Entries can be e-mailed to me at the usual address.

Anyway, onto the footy, which again starts on a Thursday this week but which has no Friday game, it now being traditional for the AFL to avoid games on Good Friday.

Probability Scoring Methods

In Sunday's blog I introduced the three probability scoring methods that I'll be using to evaluate the HELP model's predictive performance this season.

To recap, they were:

The logarithmic score, which assigns a forecaster a score of 2+log(p) where p is the probability that he or she assigned to the winning team.

The quadratic score, which assigns a forecaster a score of 1-(1-p)^2 where p is again the probability that he or she assigned to the winning team.

The spherical score, which assigns a forecaster a score of p/sqrt(p^2 + (1-p)^2), where p is yet again the probability that he or she assigned to the winning team.

Is Luck Alone Enough To Win Your Tipping Competition?

Many of you, I'm sure, have participated in tipping competitions where the leader after a few rounds seems to be unfettered by any knowledge of the game. Frustrating though that can be, some solace can be found by determining how likely it is that their performance can be written off to chance.

Whenever we're making such a determination what we first need to decide is the "level of statistical significance" (or p-value) that we're willing to accept. This level is a probability and reflects our tolerance for rejecting a chance explanation of a result we see when it was in fact due to chance. If, for example, we set our acceptable level of statistical significance to be 5% then we'll rule out chance as the cause of a result if that result would occur less than 5% of the time if someone was actually guessing randomly. The higher we set the p-value the more likely we make it to rule out a chance explanation, and the lower we set it the less willing we are to do the same.

MAFL 2010 : Round 1 Results

It's hard to make money when you're betting solely on favourites.

The Heuristic-Based Fund landed 3 bets from 4 this weekend but the one it lost was the longest-priced and therefore most vital one from a profitability viewpoint, so it finished down 0.6% on the weekend. This leaves those with the Recommended Portfolio down 0.06% for the season - a mere flesh wound at most.

That means strike one for the Shadow Fund. Two more consecutive losses will see it hand over control of the Heuristic-Based Fund to whichever heuristic is best performed at the end of Round 3.

MAFL 2010 : Round 1

We're on.

From a wagering viewpoint, this season has started like most others, with the TAB Sportsbet bookie posting head-to-head odds more than a week before the first game and then leaving them unchanged for over a week. It's as if punters haven't yet realised the season's about to start. Indeed, as I type this, the odds are still what they were Monday a week ago.

MAFL, for its part, has also followed the early season script, wagering lightly, unwilling to risk much until the season's patterns have been established and calibrated. Only one Fund is active and only four bets have been made.

And so the cycle begins again for another season.

Why April's Conceivably Better Than March

It's an unlikely scenario I know, but if the players on the AFL Seniors lists ever got to talking about shared birthdays I'd wager they'd find themselves perplexed.

As chestnuts go, the Birthday problem is about as hoary as they come. It's about the probability that two randomly selected people share a birthday and its longevity is due to the amazement most people express on discovering that you need just 23 randomly selected people to make it more likely than not that two or more of them will share a birthday. I'll venture that few if any of the 634 players on the current Seniors lists know that but, even if any of them did, they'd probably still be startled by what I'll call the AFL Birthday phenomenon.

A Proposition Bet Walks Into a Bar ...

There's time for another quick paradox before the season commences.

Consider the following proposition bet. Each week we'll look at the total points scored in the first game of the round and look at whether the total is even or odd. I win if, across consecutive rounds, the sequence (even,odd,odd) occurs before the sequence (even,odd,even) and you win if the converse occurs. So, for example, if the total scores in the first game of Rounds 1, 2 and 3 were (146, 171, 155) then I'd win. If, instead, they were (132, 175, 162) then you'd win. If no result had been achieved after Round 3 then we'd keep going, starting with the aggregate score for game 1 of Round 4, until one or other of the winning sequences occurred.

The Other AFL Draft

Drafting is a tactic well-known to cyclists and motor-racers and confers an advantage on the drafter by reducing the effort that he or she (or his or her vehicle) needs to expend in order to move.

There's a similar concept in round-robin sports where it's called the carry-over effect, which relates to the effect on a team's performance in a particular game that's due to the team its current opponent played in the previous round. Often, for example, it's considered advantageous to play teams the week after they've faced a difficult opponent, the rationale being that they'll have been 'softened up', demoralised and generally made to feel blah by the previous match.

We Don't Need No 37-cent Piece (But 30- and 45-cent Pieces Might be Nice)

Last night I was reading this Freakonomics blog explaining why a 37-cent piece would make for more efficient US coinage. In the article the question asked was what set of 4 different coin denominations could most efficiently be used to make up any amount between 1c and 99c. Two equally efficient answers were found: a set comprising a 1-cent, 3-cent, 11-cent and 37-cent piece, and one comprising a 1-cent, 3-cent, 11-cent and 38-cent piece. Either combination can be used to produce any total between 1c and 99c using, on average, just 4.1 coins.

Well Australia's different from the US in oh so many ways, and one of those ways is relevant for the present topic: we round all amounts to the nearest 5 cents, having disposed of the 1- and 2-cent pieces in 1991.

So, I wondered, what set of 4 coins would most efficiently meet our needs.

Now Open: This Year's Blog Readers' Competition

Last season a few of you took part in a competition in which participants had to predict the finishing order for all 16 teams and the winner, Dan, was the person whose finishing order was mathematically closest to the actual finishing order at the end of the home and away season. Not only were Dan's selections, overall, closest to the final ladder, but for 3 teams his selections were perfect: he had Geelong finishing 1st, St Kilda 2nd and Melbourne 16th.

A Paradox, Perhaps to Ponder

Today a petite blog on a quirk of the percentages method that's used in AFL to separate teams level on competition points.

Imagine that the first two rounds of the season produced the following results:

Geelong and St Kilda have each won in both rounds and Geelong's percentage is superior to St Kilda's on both occasions (hence the ticks and crosses). So, who will be placed higher on the ladder at the end of the 2nd round?

Using a Ladder to See the Future

The main role of the competition ladder is to provide a summary of the past. In this blog we'll be assessing what they can tell us about the future. Specifically, we'll be looking at what can be inferred about the make up of the finals by reviewing the competition ladder at different points of the season.

Improving Your Tipping

You're out walking on a cold winter's evening, contemplating the weekend's upcoming matches, when you're approached by a behatted, shadowy figure who offers to sell you a couple of statistical models that tip AFL winners. You squint into the gloom and can just discern the outline of a pocket-protector on the man who is now blocking your path, and feel immediately that this is a person whose word you can trust.

Tips for Tipping

You've been forced to enter a tipping competition for a sport you know nothing about and, frankly, have no interest in adding to the list of sports you know something about. The competition is standard in that it rewards you with 1 point for a correct tip and no points for an incorrect tip. Your 15 minutes of research, which represents the entirety of the time you're willing to spend on the endeavour, reveals that the home team consistently wins about 58% of games season after season.

Given that knowledge, which if any of these three strategies is superior:

(a) Match the expected home team/away team mix in your tips, that is, tip the home team 58% of the time

(b) Recognise that you have no basis on which to favour one team over another so tip the home team about 50% of the time

(c) Be lazy and always tip the home team

Make a mental commitment to your answer and try to come up with at least an intuitively appealling logic for it.

Testing the HELP Model

It had been rankling me that I'd not come up with a way to validate any of the LAMP, HAMP or HELP models that I chronicled the development of in earlier blogs.

In retrospect, what I probably should have done is build the models using only the data for seasons 2006 to 2008 and then test the resulting models on 2009 data but you can't unscramble an egg and, statistically speaking, my hen's albumen and vitellus are well and truly curdled.

Then I realised that there is though another way to test the models - well, for now at least, to test the HELP model.

And May All Your Probabilities Be Well-Calibrated

Say I believe that Melbourne are a 20% chance to win a hypothetical game of football - and some years it seems that this is the only type of game they have any chance of winning - yet you claim they're a 40% chance. How, and when, can we determine whose probability is closer to the truth?

In situations like this one where a subjective probability assessment is required people make their probability assessments using any information they have that they believe is relevant, weighting each piece of that knowledge according to the relative importance they place on it. So the difference between your and my estimates for our hypothetical Melbourne game could stem from differences in the information we each hold about the game, from differences in the relative weights we apply to each piece of information, or from both of these things.

You're Reading This Blog: What An Amazing Coincidence!

While idly surfing the web the other day - and, let's be honest, how often do we surf otherwise - I came across a summary of the most recent 450 Monday Lotto draws (note that the numbers from this site to which I refer in this blog might have changed by the time you view them since they're updated with each draw). For those of you unfamiliar with the NSW Monday Lotto format, 8 balls are chosen at random from 45 numbered balls with the first 6 deemed to comprise the "main" draw and the last two designated "supplementary" balls.

Another Day, Another Model

In the previous blog I developed models for predicting victory margins and found that the selection of a 'best' model depended on the criterion used to measure performance.

This blog I'll review the models that we developed and then describe how I created another model, this one designed to predict line betting winners.

There Must Be 50 Ways to Build a Model (Reprise)

Okay, this posting is going to be a lot longer and a little more technical than the average MAFL blog (and it's not as if the standard fare around here could be fairly characterised as short and simple).

Anyway, over the years of MAFL, people have asked me about the process of building a statistical model in sufficient number and with such apparent interest that I felt it was time to write a blog about it.

Predicting Margins Using Market Prices and MARS Ratings

Imagine that you allowed me to ask you for just one piece of data about an upcoming AFL game. Armed with that single piece of data I contend that I will predict the margin of that game and, on average, be within 5 goals of the actual margin. Further, one-half of the time I'll be within 4 goals of the final margin and one-third of the time I'll be within 3 goals. What piece of data do you think I am going to ask you for?

Fund Profiles and Recommended Weightings for 2010

A few blogs ago (and isn't that a distinctly 21st-century measure of time?) I revealed some details about the six Funds that will be operating this season. Three Funds are backing up from last season on the strength of double-digit returns, while three more are embarking on their rookie wagering seasons.

Two Funds from 2009 have been delisted, the Chi-Squared Fund and the Line Redux Fund, both due to performances that, analysis suggests, were more likely due to intrinsic incompetence than to transient misfortune.

The Draw's Unbalanced: So What?

In an earlier blog we looked at how each team had fared in the 2010 draw and assessed the relative difficulty of each team's draw by, somewhat crudely, estimating a (weighted) average MARS of the teams they played.

From the point of view of the competition ladder, however, what matters is not the differences in the average MARS rating of the teams played, but how these differences, on a game-by-game basis, translate into expected competition points.

The 2010 Draw

The AFL's truncated draw will once again this year have a significant bearing on the composition of the final eight and we'll be spending this posting attempting to identify and quantify the implications for each team.

A Place (or Places) To Call Home

It's that time of year again when we need to ruminate over the draw and decide which team, if either, is really the home team for each game.

This year these decisions are even more complex than they usually are since, according to the AFL's official home team designations, 8 teams have two home grounds and 2 more have three home grounds across the season. The nomadic teams include 4 that play only a single game at one of their designated home grounds. I don't think it makes sense to designate a venue as home for a team if that team's players would, unaccompanied by team management, need to ask directions to find it.

Gotta Have Momentum

Momentum, footy commentators will assert at least a few dozen times a season, is vital. When a team has it they string passes together, goals together, quarters together, wins together, maybe even flags together; when they don't, well they don't string much together at all except excuses.

So, I wondered, what might momentum look like, which teams seem to display it and which don't?

To answer these questions I've analysed the win-loss records of the 16 teams over the past 10 seasons and investigated each team's ability to record back-to-back to results. If a team is prone to bouts of momentum then we'd expect it to record back-to-back wins at a rate higher than we could reasonably expect based on its average winning rate.

MAFL 2010 - The Tradition Continues

Welcome to MAFL 2010.

This year MAFL celebrates its 5th season of faithfully frustrating and sporadically enriching Investors. As I trust you've now come to expect, MAFL changes every year and, indeed, this year's MAFL is a little different from last year's.