99% of people who bet on sport lose money over a long-term.

Finding an edge to consistently beat the bookmakers is tough.

A privileged few can exploit inside information to know more than the bookmakers about particular events. But that’s not a real long-term solution, as bookmakers will eventually get wise to this ‘insider trading’.

The majority of successful long-term winning sports bettors manage to turn a profit by beating the bookmakers at their own game. They find a way to work out the true probability of events occurring, and bet only when the odds are in their favour. This is commonly known to as ‘value investing’.

Professionals don’t come up with betting decisions off the tops of their head. They don’t use gut instinct, superstition or illogical subjective biases. They use models.

This article is going to have a general look at betting models, and their use in betting on sport.

The Vocabulary Operation

When a new member joins a professional betting syndicate the first thing that happens is that they get sent to a private clinic to have two words removed from their vocabulary.

The words are;


These are words that amateur gamblers use a lot. But luck plays no part in the long-term success of professional gambling operations. And they never make predictions.

The word ‘luck’ is replaced by ‘randomness’.

Instead of ‘prediction’ they use ‘probability’.

Before an ambitious gambler starts thinking about all the technical issues relating to producing a model, the most important steps on the road to success are to embrace the words Randomness and Probability, and to adopt the guiding principles of Value Investing.

With those fundamentals fixed in your mind, you are ready to start thinking about modelling.

The Modelling Mindset

The starting point is to ‘study and understand the demands of the event’. This is before you start collecting any data on past performances.

Be specific, and be realistic.

If you are interested in betting on football, you don’t need to model ‘football’. You just need to model the betting markets you are going to play.

Modelling flat horse racing is very different from jumps racing. If it’s your first effort at producing a betting model, maybe better to concentrate on Men’s Grand Slam and Masters events than all of tennis.

There are so many different markets to bet on these days. Probably better to pick one or two than tackle all of them initially. Specialisation normally means better focus and accuracy.

‘Studying the demands’ specifically means asking yourself ‘what will it take for me to bet profitably in this market?’

The answer may well be something a lot less involved than an all-encompassing model that looks at a whole sport. And the answer is never simply ‘I just need to know what happened in the past’.

Pricing in side markets is generally softer than in the main (most popular/liquid) markets. So modeling Corners or Bookings in football, or ‘who will make more Aces’ in tennis, or ‘make/miss the cut’ in Golf gives you a lower bar to get over into profit.

What are your strengths? Are you a quick thinker, keeping cool well when the bullets are flying over your head? Then betting in-play could be your thing. Got strong database and programming skills? Then focusing on something where there’s a load of data to crunch like Aces, Cuts, Corners or Bookings might make sense.

Tiers of Understanding

Whatever it is that you are setting out to model, a full and proper understanding comes from the ‘Three Tiers of Understanding’;

1. Fundamentals
2. Context
3. Details

Say you are interested in betting on Football Asian Handicaps. The Fundamental is to consider the teams in the leagues and ask the question, ‘how good are the teams?’

Your model could simply start off by taking the average goal difference each team achieved in its previous season. Arrange those teams and numbers from best to worst, and you have a basic Ratings Model of Fundamentals.

Context is Home or Away, playing in sun or in rain, on a good pitch or a ploughed field…. How important is it to both teams, how motivated will they be?

To price a game from our Ratings Model we need to apply Context. Principally we need to make an adjustment for the advantage a team gets from playing at home.

Details are things like Team News, fitness, fatigue, match-ups and tactics. How much stronger/weaker are the teams now than when they played to produce their Ratings? Has a star player departed/arrived? Is a tall centre forward up against a couple of short centre-backs.

So your model should takes its Fundamentals, and then adjust them for Context and Details. The output should be an average expectation. In other words, if this event was to take place an infinite number of times under these conditions, on average how many goals would each team score?

Beware of Pitfalls

Always think ‘probabilities’ not ‘prediction’.

The future is inherently unpredictable. Our universe works by having a few set laws of nature, and then the rest is down to random chance.

So the past is only ever a guide to the future. Do not ever expect something to happen in the future, just because it happened in the past.

It is certainly possible to discern patterns in randomness by looking at the past. Better football teams will have won more games, and are more likely to win an upcoming game than a minnow. But its victory is not certain. There is a % chance that anything that can possibly happen, will happen.

Interrogation of Big Data (analytics) can help you spot the patterns. But it’s still down to you to make the decisions. Data doesn’t ‘tell’ you anything. It’s just a bunch of numbers that you have to make sense of.

The point of amateur betting is to provide enjoyment. Punters pay for the entertainment that betting gives them through the long-term losses they incur to the bookmaker (or commission they pay to an exchange).

The aim of pro betting is to make a profit. It’s got nothing to do with being ‘right’. The process of pro betting can be enjoyable, but enjoyment is not the end in itself.

Imagination > Knowledge

Understanding and applying these principles of modeling and value investing are far more important than any technical skills. If you were rubbish at maths at school, and can’t program a computer don’t worry.

A model using scraps of paper and a pencil but done by someone who understands these basics will be more successful than a fancy program running on a super-computer, if it was programmed by somebody who doesn’t get it. Warren Buffett is the most successful gambler in the world, and he’s never used a computer (for anything other than online bridge) in his life. He models the value of companies and their shares using his brain plus a pen, paper and a calculator.

The tricky, and important part is being able to make sense of the numbers. Sorting the signal from the noise. Picturing how fundamentals, context and details came together in the past to shape the historical results that you can see.

If you can do that then it’s a short step to figuring out how to project the likelihoods of different possible outcomes occurring in the future. Being taught how to do sums by a University statistics professor is probably a hindrance here, not a help.

Committing to the pursuit of finding ‘value’ through calculating probabilities, rather than seeking to win through making predictions is at the heart of all successful investment strategies.

“Imagination is more important than knowledge”. Albert Einstein.

Bayesian Thinking

Thomas Bayes was an 18th century statistician. His theory on probability calculation was to take a reasonable initial estimate, and then to keep refining that estimate as new evidence emerges.

So for example you might model a rating for a football team as their average goal difference from the previous season. As they play games in the new season you update your rating to reflect this new evidence.

You might think Bayesian thinking could also simply be called ‘common sense’. But it is a prevalent human failing for us to get so attached to our beliefs that we hold onto them grimly, even in the face of changing evidence. This is often known as ‘hedgehog thinking’.

Isaiah Berlin used the terms Hedgehogs and Foxes to describe the two broad ways in which people think about modelling an uncertain future. The distinction is in the differing mindsets of people being either willing or unwilling to adapt their thinking to changing evidence.

Hedgehogs adopt a position and stick with it doggedly. They blame mistakes on bad luck, and new evidence is adapted to fit an existing theory.

Foxes are open-minded and adapt to their environment, and to new evidence. They think probabilistically rather than predictively.

ALL good modellers are Foxes.

hedgehog fox

Having ideas and theories is good. But adopting ideas as beliefs, and then clinging to them in spite of mounting evidence that you are wrong – this is very bad. From a sports betting modelling perspective at least.

“When the facts change, I change my mind. What do you do, sir?” John Maynard Keynes.

Poisson Distribution

The Poisson distribution is a statistical tool which can be useful in many modelling tasks.

Poisson describes the probability of an event occurring X times if you know the average rate.

So, you can use it to say how likely a football team is to score 2 goals in a game if you know that the average number of goals they score is say 1.85.

The virtue of the Poisson distribution is that it helps to emphasise to modellers that they should be thinking probabilistically, rather than predictively.

Poisson tells you how likely it is that a team will score 0, 1, 2, 3….. goals based on an ‘expectation’ of 1.85. This is crucially different to predicting that they will actuallyy score 0, 1, 2, 3….goals.

Particularly useful is that Poisson puts a probability number to extreme chances. It is hard for any of us to conceive in our heads how likely it is that a team with a modest 1.85 goal expectation will score 7 goals in a game. Hedgehogs may well say ‘that will never happen’.

But Poisson tells us that in fact a team who scores an average of 1.85 goals will score 7 goals exactly 0.231% of the time, or once in every 432 games. It’s not often, but it’s certainly not ‘never’. This is the sort of relatively rare event that modellers can hope to profit from at the expense of betting hedgehogs who dismiss ‘unlikely’ as ‘impossible’.

For those with enough patience, modellers can also exploit the even more rare events often referred to as ‘Black Swans’.

All probabilistic-thinking fox modellers know that black swans exist, even if they’ve never seen one.

Monte Carlo Simulation

A Monte Carlo simulation is a way of conducting an experiment where you iterate a simulation of an event many times.

It takes some programming skill to set them up (though it can be done in common programs like Excel) but it’s an excellent way to see what happens when you repeat a set of circumstances over and over.

A famous event occurred in August 1913 at the Monte Carlo casino. On a roulette wheel the ball fell into a Black slot 26 times in a row. Gamblers present (hedgehogs) lost a fortune betting on Red during the run, figuring that Red must be ‘due’.

The chance that those 26 spins of the wheel would result in 26 consecutive blacks is over 67 billion to 1. But that it happened was NOT remarkable. It was no more or less likely to occur than any of the other 67 billion different combinations of Red and Black that could have occurred in that 26 spin sample.

So long as roulette wheels keep spinning, eventually a 26 Black run is inevitable. The only remarkable thing would be if you happened to be there to see it.

A Monte Carlo simulation effectively spins a roulette wheel for you lots of times, so you can observe the results. The more likely outcomes will occur most frequently, giving you a distribution of probabilities.

The less likely ones (like Black Swans) will appear in your results, and allow you to say how unlikely these rare events really are.

Knowledge of how frequent the likely, and less likely outcomes are to occur is really useful for model bettors.


The complexity of a model is not directly correlated to its quality. A simple pen and paper model that properly takes account of Fundamentals, Context and Details can be far more effective than a computer simulation programmed by a hedgehog.

Always be wary of confident forecasters. Our world is subject to randomness, and anybody who thinks they can tame it is an idiot or a liar.

Never blame bad luck. Over a long period, luck doesn’t exist. Only randomness does.

Trust in the scientific method. Come up with theories, and test them with experiments and evidence of data. If your theory is wrong, start again. Be a fox, not a hedgehog.

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