# Gambling
related articles

### Modelling Results of AFL Games

### 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**

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