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How to recognise the maths of football and football betting mathematics?

Are you using football betting mathematics to choose realistic selections? Or are you confusing the maths of football and predicting match results?



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Updated on 31 October 2018
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The phrase ‘the beautiful game’ captures what many fans find so appealing about football, and professional sport of all kinds.


Soccer is gloriously unpredictable and following a team can often produce a frustrating succession of disappointments separated by a few moments of ecstasy!


With that in mind, it might seem as though football is closer to art than science.


However, maths can be used to explain a large amount of what goes on in a football match, and that means it can be turned toward betting.


This post looks at two distinct things:

1.    The football mathematics

2.    The football betting mathematics

The football mathematics


When most people think about the use of football mathematics, they instinctively turn toward the idea of probability theory and predicting what is going to happen.


We’ll come on to that, but for the time being it is worth reflecting on all the other types of maths that can be used to understand what happens on a football field.


Game theory and rational-decision


To start, have you ever considered why it is three points for a win and one for a draw? The answer, should you wish to look it up, lies in the mathematics of game theory and rational decision-making.


In its truly basic form, would the behaviours of competing teams change if the perceived benefit of a win is much greater than a draw or a loss? For instance, would a team that is currently drawing a game try harder to secure the win as a win has a much more positive outcome than drawing the game.


Game theory and rational-decision making is a much wider subject as it can be deployed against economic behaviours all the way through to player psychology at poker tables.


Barcelona ‘tiki taka’ versus Bayern Munich ‘blitzkrieg’


There is increasing interest in using geometry and algebra to understand passing styles.


Barcelona are the greatest team to demonstrate the ‘tiki taka’ style of short passing, which has brought them huge amounts of success.


Although, it’s unknown whether Barcelona understand the mathematical concepts, they perform a continuous type of triangular geometric shape. The revolving geometry makes it almost impossible for the opposition to close Barcelona down.


The only way to defeat the ‘tiki taka’ approach (assuming it is applied precisely) is the way that Bayern Munich did in the semi-finals of the Champions League a few years ago using extreme pace and strength in a ‘blitzkrieg’ style. All of that can be explained using mathematics.


Soccer coaches using analytics


If one looks at teams that are leading the way in terms of analytics and football mathematics such as Brentford, Brighton, FC Midtjylland and Hoffenheim, they are increasingly using maths to direct their set-plays.


Hoffenheim has a huge – the size of several cinema screens – digital screen on their training pitch with player tracking, so that they can stop and review what they are doing in real-time and replay their matches.


The purpose of this, is so coaches can show players on the screen what will most likely happen in any different type of set-play, and how each player can maximise the probability of a goal-scoring opportunity.  


The coaches will often break down each set piece into minute stages. The free-kick or corner taker will also work with video-tracking professionals to get the correct run-up and contact on the ball to secure the right trajectory into the danger zone.


This is all done using maths.

The football betting mathematics


However, for most people, the allure of football betting formulas is that they can help you predict what is going to happen, and hopefully you can turn that into a winning bet. This refers to the branch of maths called statistics.


The different types of maths, which describe the overall sport may help you decide on a winning bet based on a team’s game play.


What are football statistics and are statistics reliable


However, soccer statistics, simply refers to collection, organisation and presentation of numerical information related to football.


Everybody that has ever watched a football match on TV knows there are a huge range of statistics that are made available to viewers:

•    The amount of possession of each team

•    The number shots placed by each team within 90 minutes

•    How many fouls were committed, number of yellow or red cards received

•    The number of corners and free-kicks

•    and the most important statistic of all; how many goals have been scored!


The important thing to remember is that each of the figures above are simply random. However, when taken in aggregate, the match stats can represent important indicators of the capabilities and the strength of each team, which can all be tracked over time.


This means that each team can be mathematically evaluated. If you know which of these statistics is the most important variable in determining a team’s success. You can then start to compare them and work out how relative teams match up.


Of course, there are literally hundreds if not thousands of variables available to assess, and this means that statistical processes are needed to process them.


Within the broad theory of probability, most of football betting mathematics is within the Bayesian school of statistics.


Without going into too much detail, this refers to the degree of belief that a given event will happen, which is usually inferred from the aggregate data available from the past.


A range of statistical tools are available to help take the data from the past and process it to give a probability of something happening. Each team winning, the number of yellow cards or the margin of victory.


Regression analysis in football


The most important technique used in the maths of football is the regression analysis. While there are many approaches to perform a regression, the fundamental approach is a technique used to test the relationship between an independent (predictor) and a dependent (outcome) variable.


A simple regression might test the relationship between pass completion rates as the independent variable, and goals scored as the dependent variable.


However, a multinomial regression can factor in many variables; so, you might use a multinomial regression to test the relationship between any of the key match independent variables:

•    Shots-on-target

•    pass completions

•    number of fouls

•    number of corners

•    number of throw-ins

...All Against the home goals scored as the dependent variable.


If you know the relative importance of each of these variables, you can take the data for the upcoming match and regress it to find the probability of a specific number of goals being scored.


Much of this is now completed through machine learning techniques; so, a simple neural network can be used to find the relationships between variables and specify the regression algorithm, an increasingly common technique in football betting mathematics.


Poisson distribution in football


A Poisson distribution is also widely used in the football betting mathematics, as it is an extremely accessible tool.


This is a statistical technique that looks to determine the probability of the frequency of a given event occurring – goals for example – in a known time series – a 90-minute match.


This involves calculating how strong or weak a team is at home and away compared to the league average, and then from there to work out the probability of them scoring any specific number of goals compared to their opponent. This is a relatively simple statistical method for determining the probability of an outcome.


The maths of probability in football betting are a slightly different thing than the maths of betting in football; knowing, accurately, the probability of something happening is only half of the requirement in turning that into a successful bet.


To have a successful bet, a different style of maths is required.


How to bet? When to bet? How much to bet?


In any form of gambling, a simple mathematic equation is required to determine whether to bet or not; is the probability of winning greater than the return for winning the bet?


One should never play roulette, because the probability of winning (1/38) is slightly less than the return for winning (37/1); people count cards at blackjack because they can, theoretically, reverse the 1% advantage the house has over them by tracking high-value cards, giving them a fractionally higher chance of winning than the pay-out suggests.


In football betting mathematics, this is slightly more difficult; in blackjack or roulette the exact probability of winning is known, because there are only 52 playing cards in blackjack or 38 squares on a roulette wheel, so every permutation is quantifiable.


A football bet, as the opening paragraph noted, is gloriously unpredictable; it is not possible to know the exact probability of something happening, the best you can hope for is to predict it slightly more accurately than the market at large.


This raises the single biggest challenge in football betting mathematics; how much do you bet on any given selection?

Football betting stake mathematics


Most amateurs risk far too much of their stake, as a percentage of their bankroll, and go broke very quickly, but maths can help make better choices.


The most famous mathematical tool for doing this is the Kelly Criterion; this is a simple equation that compares the ‘edge’ the gambler thinks that they have over the market, the price available in the market or from bookmakers, and then the available bankroll.


If the equation gives you a positive figure, then that represents the percentage of your bankroll to bet; you have an advantage bet. If it is a negative figure, then no bet, you have no advantage.


Remember your ‘edge’ over the market translates to the difference between what you believe the probability of winning the bet is compared to what the market believes.


The problem with the Kelly Criterion is that it was meant to be used in sequences of events that are identical; spins of a roulette wheel, tosses of a coin.


Although in both cases, a negative value would be returned for the reasons discussed above; there is no advantage. Casino games are inherently stacked against you!

However, if you had a loaded coin that came up heads 60% of the time, then the Kelly Criterion can specify bets to make each time for exponential bankroll growth.


The problem for football bettors is that no two matches are the same, so the theory is not perfect.


Nonetheless, using football betting mathematics at every stage of the betting process, from making a selection to making a wager, will make you a much better football bettor over time.


The worst thing that will happen is that you lose less money less quickly, but you might even find yourself betting to a profit if you get the maths right.


Good luck!


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