Sports gambling is a form of betting similar to traditional probability games such as roulette, dice, or cards. The result of a sports bet is settled based on the outcome of a sporting event on which none of the betting. Mathematical Models for Sports Betting. Thread starter JamieSignorile; Start date 12/24/13; JamieSignorile. 12/24/13 #1 Hello, I know this isn't directly related to quant finance but it is an interesting topic. Has anybody come across any articles/ books on topics involving creating models for sports betting.

How do you build a sports betting model? What steps are involved? What do you need to consider? Follow these steps to build your own quantitative model, and take your betting to the next level.

What is a betting model?

In it's simplest form a sports betting model is a system that can identify unbiased reference points from where you can determine the probability for all outcomes in a particular game.

The model will ultimately be able to highlight profitable betting opportunities, by judging a team's true ability more accurately than a bookmaker.

However, building a sports betting model can be difficult and time consuming. There are various instructions and orders advised for you to follow when creating a model, which can complicate the process.

With that said, once you have created a successful betting model, it can show you opportunities that the general betting public simply wouldn't consider.

Let's begin.

For this example we use an approach similar to the Actuarial Control Cycle – a quantitative risk assessment employed by insurance companies. There are five main features:

• Defining the problem
• Building the solution
• Monitoring results
• Professionalism
• External forces

Step 1: Specify the aim of your betting model

This appears simple, but many sports bettors miss the point their betting model is trying to accomplish.

Once you have created a successful betting model, it can show you opportunities that the general betting public simply wouldn't consider.

Without an aim you could be overwhelmed with numbers and lose focus of your overall goals.

Although you may argue you can get the data first to see if there are any patterns, this would still need to be tested against a number of hypothesis, each with a different aim.

Therefore starting with a specific, rather than a generic aim, is strongly recommended.

Step 2: Select the metric

The next step is to formalise your investigation into numerical form by selecting a quantifiable metric.

These first two steps relate to defining the problem stage of the Actuarial Control Cycle.

Step 3: Collect, group and modify data

Every model needs data so you can integrate it into your algorithm. There are two ways of collecting data – by yourself, or by using other published data online.

Sports Betting Model

Luckily, there is a plethora of data available on the Internet, some of which is free, while some websites offer a paid service.

Once you have the data, you may realise that there are queries that need to be taken care of.

If we are looking at Premier League teams for instance, should you consider all matches or just their league games? It's possible to make adjustments if the team in question had players missing, or had a mid-week Champions’ League clash.

This is where you can exercise your judgement, determined by what your aim is.

Step 4: Choosing the form of your model

This is where the mathematics comes into play given there are so many models to choose from or invent.

There is a plethora of data available on the Internet, some of which is free, while some websites offer a paid service.

We have proposed a number of models in the past and they can be as complex or as simple as you wish. Our recommendation is not to overcomplicate.

This step can be interchanged with step 3 as the data may lead you to use a particular model, or a particular model may require specific data.

Step 5: Dealing with assumptions

Each model will have a number of assumptions, and you should be aware of their limitations. You may forget to do this, but it's absolutely vital.

For example a significant contributor to the financial crisis in 2007-08 was the misuse of derivatives caused by a misunderstanding of assumptions in contracts such as Collateralised Debt Obligations and Credit Default Swaps.

Previously in this article we highlighted how averages and standard deviations assume events are normally distributed. This for example would need be tested.

Step 6: Build the sports betting model

The next step is to actually build the sports betting model. There are numerous tools to use including online calculators, Excel, MatLab, Java, R programming and VBA.

You don’t have to be a wiz at programming to build a sports betting model, but the more you understand the functionality, the better equipped you will become when testing and analysing the data.

Step 7: Test the model

You don’t have to be a wiz at programming to build a sports betting model, but the more you understand the functionality, the better equipped you will become when testing and analysing the data.

It's paramount that you test the efficiency of any sports betting model to understand how sensitive it is to the results.
In any case the results of the model may lead us to reconsider any of the previous steps.

The key question as always is whether or not the model is making a profit? Therefore you’d need to test that – leading you to running through the cycle again.

Step 8: Monitor results

Assuming that an adequate model has been built and tested, it needs to be maintained as time progresses. This leads us back to the starting point – defining future aims.

Applied knowledge

Understanding the processes involved is paramount when learning how to build a sports betting model.

Quantitative modelling isn’t just about taking a model and applying it, there are a number of processes – not necessarily in the order stated – which should be completed.

Following this process won't guarantee a profit-making model, but it will ensure you are considering the fundamental aspects that are needed to build a new sports betting model.

For an example of how to build a betting model, click here.

Dominic Cortis is a lecturer with the Department of Mathematics at The University of Leicester; and an assistant lecturer at The University of Malta. He is an associate actuary and his research focuses on sports analytics as well as financial and betting derivatives.

David Sumpter, a professor of Applied Mathematics, has shown how soccer can be dissected and broken down into numbers, patterns and shapes in his book Soccermatics. Having already developed a betting model, he has now written a two-part article for Pinnacle, exploring the notion of a magical betting formula and how mathematics can be used to get an edge in betting.

There is an urban legend of mathematical modelling of soccer matches. It is the legend of the mathematical genius, the Einstein of gambling, who has worked out the formula for beating the bookmakers and winning money. If only, the legend goes, you can find the tips that this person can provide, the source of the magic equation, you can become rich beyond your wildest dreams.

After I published the book Soccermatics last year, a few people seemed to believe I might hold the magical equation. I would get messages on Twitter and emails to my work address asking me if I could help them with tips and advice. I was a professor of mathematics who had studied soccer, maybe I knew the secret?

A simple way to find value in the betting market

In one section of the book, I did manage to beat the bookies. But it wasn’t because I found a magical formula that predicts who will win soccer matches.

The basis of my model was far from complicated. It didn’t come from me working out the strength of the teams based on past performance, advanced metrics, expected goals or anything else.

The way I did it was much simpler. I looked at the odds and found a very small but significant bias in how they were set. Bookmakers and bettors hadn’t paid enough attention to predicting the draw in soccer.

Maybe it is because of the popularity of the Over/Under markets. Maybe it is because bettors don’t like betting on a draw. But, whatever the explanation, it turned out that draws in the Premier League were not properly priced.

• Read: How to beat the bookies in the Over/Under market.

Below is a plot of the real frequency of draws in four seasons of the Premier League (2011/12, 2012/13, 2013/14, 2014/15) and the prediction of draws implied by the bookmaker’s odds.

This figure is created by taking the odds provided by four leading bookmakers (including Pinnacle), converting odds to implied probabilities and then looking at the difference between the probability of a home win and an away win.

It turns out that when two well-matched teams meet (i.e. the probability of a home win is only slightly bigger than the probability of away win) then draws are under-priced (circles above red line). When matches are skewed so there is a strong a favourite (i.e. the probability of one team or the other winning is larger than the other) then draws are over-priced (circles below red line).

Want it made simpler? If two teams are about as good as each other then the draw could be a value bet. If one team is much stronger than the other, don’t bet on the draw (betting on the favourite is normally the smartest move in this case).

Testing out the theory of under-priced draws

That was what I found by plotting the odds. I then took that observation and made some money from it. Below are profits for this model for the 2015/16 season.

I tripled my money over the season. Well, actually I didn’t bet throughout the season. But I had doubled my money by Christmas.

Soccermatics came out in May 2016, just as the Premier League was coming to a close. I monitored how it went for my model the season after. Here is the result.

Not so good. There was a small profit to be made in the first few weeks, but then it flatlined for the rest of the season. Not losing money is a small achievement in itself, where the odds are in the bookmaker’s favour, but obviously making money is the objective for most bettors.

Lessons learn from using my model

There are four lessons to be learnt from my model.

Firstly, I didn’t make money by creating a magic formula. Although I did write down a single equation that I then used to decide my bets (it is footnote 17 for chapter 12 in the book if you don’t want to read the rest of it) this equation came from an analysis of the odds.

The basis of my model was far from complicated. It didn’t come from me working out the strength of the teams based on past performance, advanced metrics, expected goals or anything else. It came from a small error in how the odds were being set.

If you want to create your own model of sporting outcomes you need to use the odds as the starting point.

Secondly, I wasn’t just lucky. The original model was consistent with the previous four years of bookmaker’s odds. I downloaded my odds from Oddsportal and then double-checked my model against those on football-data.co.uk. I then made a prediction and applied it to the next year and it continued to work.

There is a lot of randomness in betting and it is possible to win for quite a long period of time with luck alone. But this was a long-term trend that was profitable.

Thirdly, nothing lasts forever. In moments of self-aggrandising I like to think that my book led to a market correction. Maybe the traders at Pinnacle and other bookmakers read my book and thought “we’ve been pricing draws wrong. See those odds for Liverpool at home against Manchester United at the weekend….move the draw odds up by 0.1.” That’s all it takes and my small margin disappears.

This is just one explanation, though. Another is that managers realised that in those big matches between equally good teams they should go for the three points (this is also something I look at in the book). There are other explanations too. The fact is, I will never know for sure, but the odds bias I found has gone.

My fourth and final conclusion is: I am a total idiot. I spent three months developing a betting model. I found a way to win. But instead of placing all my free capital on the model, I published a book with the secret in it, only to see the profits disappear.

Yes, I got paid for writing the book. Yes, I have enjoyed talking about soccer and engaging in the analytics community, but the money would have been nice too.

• How to bet on soccer: The ultimate soccer betting guide.

There is no secret equation for predicting the outcome of soccer matches. Not an equation that ignores the odds, in any case. If you want to create your own model of sporting outcomes you need to use the odds as the starting point.

Football Betting Mathematical Model

Wisdom of the crowd tells us that the betting market can be hard to beat, but sometimes it makes a few small mistakes. It is these you have to look for.

Sports Betting Mathematical Models Definition

In part two of this article I will see if I can find one of those cracks using a combination of an expected goals model and potential biases in recent odds.

Sports Betting Mathematical Models Chart

If you want to learn more about David Sumpter's work you can follow @Soccermatics on Twitter.