# 2015 - Round 1 : Taking Monday Off

With the Essendon situation now resolved, at least for the time being, and the TAB consequently willing to field complete Head-to-Head and Line markets, MoS is now locked in for the first week of the season.

Recognising that  MoS' audience has expanded over the break, I'll take more time (characters?) this week than will be typical to explain the various tables and charts that appear here.

(If you are new here and haven't yet read this blog on what MoS is all about, I'd recommend that you do that first. Also, new and seasoned MoS readers might like to review this blog on the main changes from season 2014 before proceeding.)

### WAGERS AND TIPS

This first table provides an overview of the TAB Bookmaker's and MoS' views about each contest.

The first row of the table provides MoS' MARS Team Ratings for the competing teams and shows, for example, that MARS rates Carlton a 996 team and Richmond a 1,002 team, making the Blues a marginally "below average" team, and the Tigers a marginally "above average" team.

Row 2 records the TAB Bookmaker's Head-to-Head Prices as at the time I locked them in for tipping and wagering purposes, which this week was on Sunday at about Noon for every game except the Swans v Dons game. That game was locked in at about 4pm on Tuesday.

Row 3 converts those Head-to-Head Prices into what I call "Implicit Probability Ranges" for the home teams. These ranges span the lowest and highest probabilities that the TAB Bookmaker could logically attach to the home team given the prices shown, assuming that he'd not be willing to offer prices that would imply an expected loss for him.

Consider, for example, the range for the Carlton v Richmond game, which is 33.3% to 38.5%. If the Bookmaker felt that Carlton were less than a 33.3% chance, then a wager on the Tigers at \$1.50 would carry a positive expectation (since (1-33.3%) x \$1.50 is about 1). Conversely, if he felt that the Blues represented greater than 38.5% chances, then a wager on them at \$2.60 would carry a positive expectation (since 38.5% x \$2.60 is about 1). Those two probabilities, then, mark the range of "sensible" victory probabilities for the home team from the Bookmaker's point of view. Note that, for the purposes of these calculations, I ignore the possibility of a drawn game.

The fourth row provides information about the TAB's Line Market. It reveals, for example, that the Blues are receiving 12.5 points start in their game against the Tigers.

Finally, the last two rows record the MoS' wagers for the week, which include, for example, this week a 1.3% head-to-head wager on Carlton at \$2.60 and a 1.3% line wager on Carlton with those 12.5 points start at \$1.90. The percentages shown here refer to the proportion of the relevant Fund at risk. Recall that, this season, the Head-to-Head Fund is 40% of the entire portfolio, and the Line Fund is the remaining 60%, so putting 1% of the Head-to-Head Fund at risk puts 0.4% of the entire Portfolio at risk, while putting 1% of the Line Fund at risk puts 0.6% of the entire Portfolio at risk.

Panning across those last two rows you'll see that MoS Investors have head-to-head or line wagers in every contest except Monday's Hawthorn v Geelong matchup.

In total, those wagers represent about 9% of the Head-to-Head Fund at a weighted average price of \$2.10, and 8.75% of the Line Fund at a weighted average price of \$1.90.

One way of understanding the risks and rewards associated with that portfolio of wagers is via what I call the Ready Reckoner, which appears below and shows the Portfolio gain or loss that will accrue depending on the final game margin for the game in question.

For the Carlton v Richmond game, for example, it reveals that:

• A Carlton loss by 13 points or more, which torpedoes both the head-to-head and line wagers, will knock about 1.3% off the overall Portfolio value
• A Carlton loss by 1 to 12 points, which lands the line wager but not the head-to-head wager, will add about 0.4% to the overall Portfolio value
• A draw, which lands the line wager and has the head-to-head wager pay off at half price, will add about 0.8% to the overall Portfolio value

• A Carlton win, which lands both the line wager and the head-to-head wager, will add about 1.2% to the overall Portfolio value

Returning readers will note the apretzeline nature of these charts relative to those that were the norm last year. That's down entirely to the retirement of the Margin Fund, which I'm already desperately not missing.

That Fund's retirement hasn't, however, meant that only relatively small movements in the overall Portfolio are possible this week. Favourable results in the eight contests in which Investors have a stake would lift the Portfolio by about 8.7%, while unfavourable results would drop the Portfolio by about 8.9%.

The column headed "Disag" on the right provides a measure of how different, in aggregate, are the tips of the Tipster in question relative to all other Tipsters. Formally it reports the probability that a randomly selected tip from the Tipster in question will be different from a randomly selected tip from any other of the Tipsters for the same game. Smaller values indicate less "disagreement" with the consensus view.

Nine Tipsters have very low levels of disagreement (just 6%), while Home Sweet Home has started the season in its accustomed position of Tipster Most Different. A randomly selected peer would be almost as likely to disagree with a Home Sweet Home tip as to agree with it.

Summaries appear at the foot of the table and show, for example, that Carlton is supported by only 9 of the 30 Tipsters (or 30%), while Richmond is supported by the other 21. Across the nine contests there's unanimity of opinion in three of them, as would there be in two more but for Home Sweet Home's contrarian nature. The Lions v Pies games most divides the Tipsters, which come down 19-11 in favour of a Lions victory.

The final percentage at the foot of the Disag column gives an overall indication of the levels of disagreement amongst all the Head-to-Head Tipsters across all the games. This week that figure comes in at 12%, which I'll venture will be around the average level that we'll see this season.

### MARGIN PREDICTORS

The next opinionated mob are MoS' Margin Predictors, of which there are 19 this season. Their opinions are recorded below.

Each row in the top section of this table records the (rounded) margin predictions for the relevant Predictor, expressed in terms of the home team so that a negative figure, shown in red and in brackets, implies an away team victory.

The column headed "MAD", as that headed "Disag" for the Head-to-Head Tipsters, provides a measure of how different a Tipster's predicted margins are from the average predictions of all Predictors. MAD stands for Mean Absolute Deviation and is calculated as the average number of points by which a Predictor's predicted margins differ from the all-Predictor average, ignoring whether the predictions are above or below that average, and averaged across all games.

So, for example, Combo_7's predictions are about 4, 2.5, 0, 3.5, 4, 3, 7, 8 and 5 points different in absolute terms from the respective all-Predictor averages, which results in a MAD for it of 4.2 points per game. Smaller MADs indicate closer agreement with the all-Predictor average, on which basis we can claim that Combo_7 is amongst the lesser divergent Predictors this week. It's also the MoS Preferred Predictor, which is why its predictions sit at the top of the table.

Most divergent of all are Combo_NN2 and Win_7 with MADs of around 8 points per game, and least divergent are Bookie_9, with a MAD of 2 points, and the two new Ensemble Predictors, both with MADs of around 3 points,

Again we find summaries at the foot of this table. For each game these comprise the average predicted home team margin, the combined implied head-to-head predictions (where a positive predicted margin is taken to imply a home team win), a boxplot, which I'll come back to in a moment, then three rows summarising the divergence of predictions for a given game: the high and low predictions, the difference between them, and the MAD for the game averaged across all Predictors. Larger MADs here too imply greater divergence.

The boxplots provide summaries of all the predictions for a single game, the "box" for each spanning the range from about the 5th highest to the 15th highest predicted margin (the Interquartile Range, to give it its proper name), the "whiskers" spanning the entire range of predictions, and the red line denoting the average prediction.

Finally, the grey number in bold at the foot of the MAD column provides a measure of the average level of disagreement across all Predictors and all games. At 5.3 points per game I'd suggest that this is also about what we might expect in a typical round this season.

Margin predictions are most highly variable this week for the Adelaide v Kangaroos and Fremantle v Port Adelaide games where the ranges are both 29 points and the MADs around 8 points per Predictor.

Opinions are least divergent in the Hawks v Cats game where we find that all 19 Predictors have made predictions in about a 14 point range and the MAD is only 3.4 points per Predictor. There are also relatively low levels of divergence in the predictions for the Dees v Suns and Dogs v Eagles matchups. Also, in all three of these contests, there's unanimity about the predicted victors.

### PROBABILITY PREDICTORS

MoS' final class of Predictors are those whose opinions are couched in terms of probabilities.

Firstly, at the top of the table below, are the probability assessments of the Head-to-Head Probability Predictors, these assessments being from the viewpoint of the home team. For these Predictors too I've used the MAD metric to measure divergence, though here the measure is reported in terms of percentage points of probability. So, for example, Bookie - OE, MoS' Preferred Probability Predictor, has Probability Predictions that this week are, on average and in absolute terms, a bit over 7% points different from the all-Predictor average.

On this measure most of the Predictors are of similar levels of divergence, the two Head-to-Head Predictors being least divergent at 6.4% points per game, and WinPred being most divergent at 8.3% points per game. Overall, the average Predictor has probability assessments that are, on average and in absolute terms, about 7% different from the all-Predictor averages.

For these Predictors the summaries at the foot of the table show, for each game, the average probability prediction and then the implied support for the home and away teams (with probabilities greater than 50% being taken to imply a home team victory, and those under 50% an away team victory).

Next come boxplots, which can be interpreted in the same way as those for the Margin Predictor described above, and then game-by-game measures of Predictor divergence, here in terms of the minimum and maximum probability assessments, the difference between the minimum and maximum, and then the MAD across the Predictors.

Probability assessments are least divergent for the Dogs v Eagles game where the entire set of assessments spans only a 10% point range and where the MAD is just 4% per Predictor. Assessments are most divergent in the Dockers v Port game where they span 33% points and show the only double-digit MAD of the round.

The last row provides the Line Fund algorithm's assessment of the probabilities that the home teams will prevail in their respective line markets. In reviewing these, recall that the TAB Bookmaker has set handicaps that he believes renders each contest a 50:50 proposition, so any probability predictions above 50% imply that the algorithm assesses that he's been too kind to the home team, and any below 50% that he's been too kind to the away team.

This week the Line Fund algorithm is keenest about the line market chances of the Lions and the Saints, but it also estimates the Blues', Dees', Crows' and Dockers' chances at 60% or better. Only the Hawks v Cats game has been assessed as anything near to a coin toss on handicap.

### WRAP UP

That's all there is to the weekly tips, predictions and wagers, which, in summary are:

• Rating, price and wagering information