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.

The Recommended Portfolio has chanced another two-dozen wagers, and it'll be of no surprise to any regular MAFL-Online reader that a large chunk of that activity can be laid at the feet of the New Heritage Fund (assuming, I guess, that a named statistical algorithm has metaphorical limbs). Anyway, the New Heritage Fund has found a wager in seven of the eight contests, which total over one-half of the Fund. Some weeks I wonder if the New Heritage Fund would wager on both teams in every contest were I to allow it that latitude.

Fortunately, the weighted average price of the New Heritage wagers is only $1.62, dragged down by the Fund's largest wager of just over 12% on St Kilda at $1.18, and lifted by 6% wagers on both Sydney and the Roos, each at $2.

The next most active Fund is ELO, which has made five wagers of 5% each and which we hope will be as successful with its wagers this week as it has been over the last 9 rounds. During that period, the ELO-Line Fund has gone 28 and 14 and lifted its price by almost 56c. Two of ELO's wagers this week are on teams receiving start - Essendon and Sydney, each receiving 6.5 points - and the other three are on teams giving start - Geelong, St Kilda and Melbourne.

Our Hope Fund has also made five wagers though they total slightly less than 20% of that Fund. The weighted average price for these wagers of $2.37 is startlingly high and is due mostly to the Fund's largest wager of 5.7% on Adelaide at $3.30, which is also the highest price secured for any of the wagers made this week by any Fund.

Three wagers is all that the Heuristic-Based Fund - courtesy of Short-Term Memory I - could muster, the longest of which is priced at $2 and is for 5% of the Fund on the Dons. The weighted average price of its wagers is $1.72.

Shadow's made only two wagers, totalling 10% of the Fund and with a weighted average price of just $1.34. Its bet on Melbourne at $1.50 is the longer priced of its wagers. Prudence has also made a pair of punts, both small and both on short-priced favourites. Together the bets total 7% of the Fund, the largest for just over 5% of the Fund on the Saints at $1.18, and the other and longer priced is for around 2% of the Fund on Melbourne at an extravagant $1.50.

MIN#002, with the five Hope bets, has the greatest proportion of his bankroll at risk this week that he's had in any single round this season. MIN #017, who by now is surely getting used to it, has over one-half of his initial bankroll in play. It's the sixth time that this has happened this season and the third time it's happened in the last four rounds (and it was 48.8% at risk in the round that's the exception).

Here's the detail:

For the Recommended Portfolio, no game carries a particularly high upside, the Adelaide v Dogs game promising the largest potential upside at 2.6%. The St Kilda v Port game has the largest downside attached to it (5%), and the Melbourne v Richmond game, on which every Fund has made a wager, therefore unsurprisingly carries the greatest potential swing between the best and worst possible outcomes (about 7%).

MIN#002 will also sweat the Dees v Tigers result, as he has most to gain (2.5%) and faces the largest potential swing (7.5%) on the back of this game's result.

MIN#017 would most like the Cats to topple the Pies, since this is worth 6.1% to him, and would least like St Kilda to go down to Port, which would knock over 12c off his Portfolio's price. The Melbourne v Richmond game represents for him, as for all Investors this weekend, the largest potential swing between a good and a bad outcome. For MIN#017 it's a 15% swing.

Here's the Ready Reckoner:

Once again the Recommended Portfolio can afford to lose its first three wagers this week and still return a profit on the weekend.

A cursory glance at the week's head-to-head prices will tell you that it's going to be a very difficult round for tipsters, as five underdogs are priced at $2.15 or less. One way to quantify the tipping difficulty associated with a round is to calculate the average expected surprisals per game.

Surprisals, you might recall, measure the surprise that you can legitimately feel about the outcome of some random event based on your a priori probability assessment of that particular outcome. If, for example, four unbiased coins are tossed and land HHHH, the surprisal associated with this outcome is 4 bits, since the a priori probability of the outcome is 1 in 16 and -log(16, base 2) = 4.

You can perform a similar calculation for the outcome of a footy game using the bookie's head-to-head prices. Consider the Essendon v Carlton game where the market is currently Essendon $2: Carlton $1.75. That implies a probability of victory for Essendon of 1.75/3.75 or about 47% and a probability of victory for Carlton therefore of 53%. So, the surprisal associated with an Essendon win would be -log(47%, base 2) or about 1.09 bits and with a Carlton win would be -log(53%, base 2) or about 0.92 bits. The expected surprisal from the Essendon v Carlton game is therefore 47% x 1.09 + 53% x 0.92 or 0.997 bits, which is very close to the maximum possible expected surprisal for a single contest of 1 bit that occurs when both participants carry 50% probabilities.

If we perform this calculation for all of the week's eight games and then average the results we find that the average expected surprisal figure is 0.94 bits per game, which is the highest average we've seen so far this season (it's a smidge bigger than the figure for Round 9) and surpasses anything we saw in the entire home-and-away season for 2009 and anything we saw in the 2008 home-and-away season too, excepting in the very first round.

The following table provides the average expected surprisals per game for every round since Round 1 of 2006. You'll notice that average expected surprisals per game figure tends to kick up in Rounds 23 to 26, which are the rounds of the Finals and which typically pit teams closely matched in skills against one another.

This table makes it fairly obvious, I think, how atypical this week's average expected surprisal figure is, especially for a round at this point in the season since average surprisals per game has shown a tendency to gently decline across the home-and-away rounds in seasons past.

What the table does perhaps less well is demonstrate how atypical generally the week-to-week pattern of average expected surprisals has been this year, which is a phenomenon more clearly exposed by the following sparklines chart.

Each sparkline in the above depicts the weekly average expected surprisals per game for each round of the season and each uses a scale with the same minimum and maximum (0.7 and 1 bits respectively). Taken as a whole, these sparklines show that seasons prior to this one have had less volatility in the average expected surprisals per game statistic across the rounds. One simple way to exemplify this quantitatively is to note that this season almost one-third of the rounds have had an average expected surprisals per game of more than 0.9 and another one-fifth have had an average expected surprisals per game of less than 0.8.

Across the home-and-away seasons for 2006 to 2009 the proportion of rounds with an average expected surprisals per game of more than 0.9 has been a little under 30% and the proportion with an average expected surprisals per game of less than 0.8 has been about 11%. So, the 2010 figures exceed both the average for low-surprisal rounds and for high-surprisal rounds.

What does this all mean? There are, I think, two possible explanations. One is that the draw has been such that, by chance, it has tended to produce rounds that are one week oversupplied with crackerjack matchups - such as this week - and another week riddled with matches that pit the strong against the weak.

The other explanation is that some or most team's chances have been difficult to estimate from week to week, which has led to the bookies overestimating, and then underestimating, and then overestimating again the gap between the skills of the teams participating in each week's games. BKB's relatively poor showing in the MAFL Tipping this season lends, I think, some weight to this second explanation, though I'd not completely discount the first explanation either.

With my having pointed out the uncertainty associated with this week's fare that's implicit in the head-to-head prices you'll not be surprised to hear that the average number of dissenting MAFL tipsters per game is almost 4.5, that there are no games on which the tipsters are unanimous, and that there are four games in which there are five or more dissenting tipsters.

Here are the details:

• Essendon are 9-6 favourites over Carlton. The Margin Tippers are split 3-2 in favour of the Dons and predict victory margins ranging from Essendon by 1 to Carlton by 6. Three Margin Tippers have this game as one of their Games of the Round: Chi (who tips Essendon by 4), HAMP (which tips Essendon by 1), and LAMP (which tips Essendon by 6). The four best-performed MAFL Tipsters - Easily Impressed I and II, Follow The Streak, and Short-Term Memory I) all tip the Dons.
• Hawthorn are 10-5 favourites over Sydney, with the Margin Tippers again split, this time 3-2 in favour of the Swans. Again the range of victory margins is narrow, spanning Hawthorn by 4 to Sydney by 6. Four Margin Tippers have this as one of their Games of the Round: Chi (Hawthorn by 4), HAMP (Sydney by 1), LAMP (Sydney by 6), and ELO (Sydney by 1). The Top 4 MAFL tipsters are unanimously behind the Hawks.
• Fremantle are 11-4 favourites over the Roos. Once more the MAFL Tipsters are split 3-2, this time in favour of the Roos. Victory margins span a 23 point range from Roos by 12 to Freo by 11. HAMP (Roos by 1) and LAMP (Roos by 6) have this as their 3rd and final Games of the Round. All four Top MAFL tipsters predict a Freo victory.
• Geelong are 8-7 favourites over Collingwood, though for this game the Margin Tippers are unanimous in their support. They're all tipping a Cats win and by margins ranging from about 5 to 12 points, the lower bound of this range depending on the victory margin imputed for BKB, who has this as his Game of the Round and who is giving the Pies 6.5 start but is offering only $1.75 on the line market for the Pies with this start. The Top 4 tipsters are split 2-2 on this game.
• Brisbane are 8-7 favourites over the Eagles, though the five Margin Tippers are all supporting the Eagles and predict victory margins of between 1 and 21 points. ELO tips the Eagles by just 1 point, making this its 2nd and final Game of the Round. All of the Top 4 tipsters side with the Lions.
• St Kilda are 12-3 favourites over Port Adelaide, and the Margin Tippers are split unanimously predicting a Saints victory by margins ranging from 22 to 40 points. The Top 4 tipsters are split 2-2 on this game.
• Melbourne are the nearest we have to a unanimous favourite this week. They're selected by all MAFL Tipsters except Easily Impressed I, who is more impressed by Richmond's 20-point win the Crows in Round 18 than by Melbourne's 10-point win over the Lions. The Margin Tippers are all predicting Dees victories and by margins of between 12.5 and 23 points. The Top 4 tipsters favour the Dees 3-1, with Easily Impressed, as noted, dissenting.
• The Dogs are 13-2 favourites over the Crows. The Margin Tippers favour the Dogs 4-1, Chi being the holdout tipping the Crows by 4 points making this his 3rd and final Game of the Round. Predicted margins range from Adelaide by 4 to the Dogs by 26. The Top 4 tipsters are unanimous in their support of the Dogs.

The Super Smart Model this week obligingly agrees with four of the five ELO wagers, quibbling only about the Geelong v Collingwood game for which it is tipping a Cats win by 2 points, which would be insufficient to cover the 6.5 point spread that the Cats are being asked to give. Here's SSM's view of the round:

You can see that SSM also foresees a round of close contests. Four of its predicted margins are of 3 points or fewer and three more are of 19 points or fewer. Only the Saints v Port game is predicted to be something even approaching a blowout, with the Saints predicted to win by just over 6 goals.

The Bookie Probability Model can find only one set of head-to-head prices that it likes. It recommends a 2.4% wager on Sydney at $2.00 playing Hawthorn. It estimates that a fair price for Sydney is about $1.95, so it doesn't see a great deal of opportunity here - hence, the smallish suggested wager.

Finally then, to HELP, which has clearly been into the catnip again and boldly predicts 8 home team victories on line betting, each with a 67% probability.

I should probably pop the hood on the HELP algorithm but my wagering instinct tells me that there's not much of an edge in that course of action.

Better I think to enjoy a round bountiful in surprisals.