The blossoming relationship between Football and Mathematics

Mathematics and may seem like strange bedfellows. While one demands precise calculations to quantify, evaluate and establish the validity of conjectures, the other is notable for being somewhat chaotic, random and unpredictable.

Creating order from chaos

In recent years, the challenge of containing the rather haphazard nature of a football game into the framework of mathematics has turned into big business. For football teams and coaches, finding an extra edge through the use of data can make the difference between winning and losing. It can affect decisions that are made before and during a match and also drive the direction of the recruitment process, with data now utilised customarily to identify transfer targets.
The desire for advanced statistics is not limited to professionals from within the sport. Fans and those with access to media platforms have also become obsessed with the numbers behind the action. After all, tactical analysis is further enhanced when it can be backed up by cold, hard statistics. In fact, stats and data add value to every area that the sport reaches – from the inner sanctum of the clubs themselves to the betting and fantasy sports industries that operate from within the game's orbit. There is no getting away from the fact that mathematics are now an intrinsic part of the modern game.

Improved access

The good news for those in the game is that statistics are now more widely available than ever. So, even teams in the lower and non-leagues can gain access to certain statistical data without prohibitive costs. Devices to measure player metrics can also be purchased for a relatively low outlay and can help teams at all levels to improve their performance and plan their training sessions more efficiently. This type of technology was first approved for live matches in 2015, used by Germany in their successful World Cup campaign back in 2014, and has since been adopted by most professional teams. Of course, gathering as much data as possible is one thing but turning that data into useful information is another, and that is perhaps an area were teams are still hamstrung. Top data analysts do not come cheap and non-league budgets limit the amount that can be invested in this area. It is often left up to the existing coaching staff to extrapolate the data on iPads using stock software.

Many websites and companies that compile football statistics aimed at the betting world are also giving space to non-league football. Having some hard data to work with is great news for those looking to wager at this level. Stats have long been used by punters to gain an edge over bookmakers and with so many sources now available, serious bettors can now gather data and build their own mathematical models.

A model for success

One such model is the Poisson Distribution system, which works on the basis that understanding the frequency at which an event has occurred allows us to better predict the probability of it happening over a fixed period of time. By determining the probability of outcomes of certain football match matches, odds can then be calculated and used to find value in the market. Identifying high-value bets is the holy grail of the sports bettor and formulas to achieve this, such as the Kelly Criterion, which originated in the financial sector, have now been applied to sports. This method takes the punter's bankroll, the odds on offer, and the perceived odds of the event actually happening, to calculate how much should be wagered on each bet. The system lacks precision because it relies on the bettor estimating the probability of the bet winning against the true odds offered by the bookmaker. However, seasoned bettors can learn to do this more accurately over time or use their own models (such as the Poisson Distribution mentioned above) to make more accurate calculations.
Such systems can be applied to many popular markets such as Match Result, Correct Score, Over/Under Goals, Handicaps and Both Teams to Score. Of course, every system has its faults and limitations but modern mathematics has done a good job of reducing the events on a football field into a workable equation.

Summary

Terms such as sports science and moneyball have become commonplace in sport. Maths is used to decide which players are best suited to play in each game, what system to use against which team, when to make substitutions, what trajectory to use on throw-ins, which defensive system to use and what way to dive on a penalty. Even the diagonal system of control used by referees is a result of a simple mathematical calculation. And, of course, at the highest level of the game, recruitment targets, player wages, transfers fees, amortisation values and contract details are all arrived at through mathematical analysis. The same is true on the periphery of the sport where betting, fantasy leagues and the sports media are delving ever deeper into the world of big data and statistics. Never before in the history of the game has so much been decided by the number crunchers.
And in a game dominated by money, it is perhaps somewhat reassuring to know that even those with the biggest bank balances still have to turn to mathematics to stay ahead. It raises the possibility that any team can beat another if they can find that mathematical edge.

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