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# Gambling related articles

### Part 1

By Scott McIntosh

(Access AFL calculator from Part 2 of this series)

### Introduction

You think that Collingwood is under-rated and want to have a bet on them. But what is the best bet? Straight up? On the line? A margin bet?

In this article I will introduce a relatively simple but robust model that can be used for determining probabilites and odds of the final score difference for the game of Australian Rules Football. The model uses a normal distribution probability distribution fuction, given a mean and standard deviation. In future articles I will explain how this model can be used to calculate different probabilities and odds associated with the final score difference (eg under/over 39.5 points margin bets).

### Mean

The mean represents the average winning margin. A reasonably accurate mean is given by the bookmakers in the form of the "line" bet. Alternatively, handicappers may determine their own mean, an example of which is the Swinburne computer predictions.

### Standard Deviation

The standard deviation represents how far actual results deviate from the mean. Using historical data of bookmakers lines and actual results the standard deviation of AFL match results is found to be approximately 38. Other good handicapping models of predicting the mean result have the same, or very similar, standard deviation.

### Normality

The graph below illistrates how well actual results correspond to the normal distribution model, where mean equals bookmakers line and standard deviation equals 38. A positive difference between the final result and bookmakers line represents the home beating the line whereas a negitive difference represents the away team beating the line. Statistical tests confirm that the normal distribution assumption is reasonable.

### Graph 1: Difference between final result and bookmakers line (1,056 Home and Away Games : 2000 - 2005) ### Limitations

Whilst this model is quite accurate it assumes the standard deviation is the same for all games. The model does not take into account factors like weather, team playing styles or rule changes, all of which may have an effect on standard deviation. Despite this limitation, for its simplicity the normal distribution model of AFL football results is quite powerful and is probably the best starting point for more complex models.

### Conclusion

Although this article is a bit more technical than I would have liked it provides a good foundation for future articles where I will describe some practical applications of the normal distribution model of AFL football. By using a spreadsheet program such as Excel, a good estimate of probabilities and odds can be calculated for many bet types offered by bookmakers.

Scott McIntosh runs the website Online Poker Room Reviews

Proceed to Part 2 of this series