# SuperMargin Wagering : What Should We Expect?

Today, the Margin Fund went within a kick of landing 3 of its wagers but in the end went 0 and 5.

Much as I'd like to feel aggrieved about the 3 wagers that were so close to being winners and proclaim that we've been the sufferers of incredible misfortune, unfortunately that's not the case - a fact that we can show in two ways.

Firstly, recognise that the SuperMargin bucket we chose in each of those games was the favoured or second-favoured bucket. For the sake of the calculation here - it doesn't make much difference to the result - let's assume we chose the favoured bucket in each game and that the most likely score, which we'll also assume was the line market handicap for that game, was the mid-point of that bucket.

(To confirm that this is a reasonable assumption, consider the Essendon v Port Adelaide game where the favoured bucket was Essendon by 20-29 points and the handicap was Essendon -25.5 points.)

Now we know from previous analyses that the Handicap Adjusted Margin (HAM) is approximately Normally distributed with mean 0 and standard deviation of about 38 points per game, so the probability of the final score being within the favoured bucket, which is equal to the probability that -5 < HAM < 5, is about 10.5%. (Remember that each bucket, except the 1-9 point bucket, is ten points wide.)

By comparison, the probability that we lose our bet by a kick or less is equal to the sum of the probability that -11 < HAM < -5 plus the probability that 5 < HAM < 11, which is just over 12%. So, whenever we select the most-favoured bucket, we should expect to lose our bet by a single kick about 1 game in eight, and this should happen about 15-20% more often than we win our bet. Based on this calculation, losing 3 out of 3 bets when the final score is within a kick of the favoured bucket no longer seems all that unlikely.

Indeed, we should probably get used to it.

Reviewing the results that the Margin Fund would have produced in 2011 serves to broadly confirm this unfortunate fact. For this table I've measured the amount by which notional bets were lost in terms of 10-point "buckets" rather than in terms of 6-point "kicks". Following the same logic as I used above, the probability of losing a bet by one bucket is the sum of the probability that -15 < HAM < -5 plus the probability that 5 < HAM < 15, which is about 20%.

Each column of this table relates to a different Margin Predictor. The Margin Fund relies on CN2's predictions, so this is the column you should read to understand how that Fund would have fared last season. There you can see that the Fund would have selected the correct bucket in 25 games, which is about 13% of the time, and it would have been in error by 1 bucket in 43 games, which is about 22% of the time. So, had we bet on CN2's margin predictions in the SuperMargin market in every game last season the ratio of wagers lost by 1 bucket to wagers won would have been 43/25 or about 1.7:1, which is roughly in agreement with the ratio of the probabilities we've calculated of 20%/10.5% or 1.9:1.

The column labelled "BA" in the table above provides the results that would have been achieved by wagering on the bucket corresponding to the TAB's line margin for each game. You can see then that CN2 chose the correct bucket about as often as did the TAB Bookmaker and that CN2 was within one bucket of the actual result slightly more often than the TAB Bookmaker. Only B3 was within one bucket of the final result more often, and it selected the correct bucket on fewer occasions than did CN2.

Since the Margin Fund is actually wagering on CN2's predictions only when those predictions are for a Home win or a drawn game, I thought I'd also provide the 2011 results for each Margin Predictor broken down by whether that Predictor selected a Home win, Away win, or drawn game.

Here we can see that, of the 31 times that CN2 predicted a Home team victory and was within one bucket of the actual result, the ratio of losses to wins was 17/14 or about 1.2:1. We can also determine that, if CN2 can again be right 14% of the time with its Home team predictions this season, an average price of just over \$7 will be enough to secure a break even outcome for the Margin Fund.

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