Elo Rating for Football Betting

Statistics, rankings, and predictive probabilities of sports results

A complete guide: from statistics to betting amounts

The Elo rating system is a system made for evaluating the relative strength of players, their performance, and was initially developed for calculating the level and ranking of chess players. This Elo rating method has since been adapted and widely used in many other sports, such as tennis and football.
Thanks to this calculation method, value bets can be mathematically identified, that is interesting bets can be clearly identified, by efficiently calculating the probabilities of the results of the matches.

About Elo rating: the theory

In the Elo rating system, named after its inventor Arpad Elo, a physicist (and chess player) from the University of Chicago, each player's rating is calculated based solely on their results in matches with other players. The particularity of this rating system is that it is directly linked to the probability that a player will beat another player. In short, the Elo rating is the ideal tool for the bettor!

Specialize your data and statistics

First, we have to estalish a ranking of all the teams of interest. For example, we can choise to specialize in national teams; we can find, after all the calculations, a world elo ranking of the teams, or an elo ranking with the history.
We can prefer to specialize our ranking in the championship matches of our country, or limit ourselves to the ranking of teams in particular conditions, for example the results of all the matches played in winter with a temperature of less than 10 degrees.
We then need statistical data: all the possible results of the matches corresponding to our selection criterion. Then, we assign the same initial ranking to all the teams: an arbitrarily high ranking of 1500 Elo points.

Calculate Elo rankings

The next step is to to exploit these categorized statistical data. We calculate an Elo ranking from these past results: all teams start at a ranking of 1500 Elo points, and then for each match a new ranking is calculated.
Using Elo mathematical formulas the new rankings can be computed, or alternatively the following calculator can be used.
Just fill in the ranking of each team, then the result of the match (win, lose, draw), and the new rankings of each team are calculated automatically:

We start again for each result of our statistics, in the chronological order of our database.
We thus finally obtain a complete, specialized Elo ranking of all teams.
We can now move on to exploiting this ranking

Calculate probabilities and odds

With this Elo ranking direct calculations of the probability of victory and therefore of the odds of the match can be made.
This probability only depends on the difference in ranking between the teams: the probability that a team ranked 2000 wins a team ranked 1800 is the same probability that a team ranked 1700 wins a team ranked 1500.
The calculation formula is as follows, for a ranking difference d, the probability of victory is

P = 1/1 + 10^{−d / 400}

which also gives the corresponding odds by calculating its reciprocal.
Following calculator can also be used, calculator which does all these mathematical calculations automatically:

For example, if a team A ranked 1900 meets a team B ranked 1750, the ranking difference is d = 150 and the probability for A to win is

P = 1/1 + 10^{−150 / 400}≃ 70%

that is 1,42 odds.

Value bets: finding interesting bets

We now come to the decisive step: to bet or not to bet!, that is the question …
We therefore compare our previous result with the odds of the bookmakers looking for a value bet : if a bookmaker offers a higher odds, for example 1.5 with the previous example, I bet! Otherwise, I do not, investment in this bet is not valuable.
These calculations and Elo ranking therefore result in an objective, mathematical method of detecting value bets: it is a complete system for making decisions in terms of sports betting on football.

How much to bet? Calculate the optimal stake to bet

In the favorable case, where we choose to bet, we can see that the greater the difference between our estimated odds and those of the bookmaker, the more we have an interest in betting a lot. But how much exactly?
The exact answer to this question is given by the mathematical formula of the Kelly criterion. With the previous example, Elo ranking difference of 150 points, therefore probability of winning calculated at 70% and therefore an odds of 1.4, if a bookmaker offers an odds of 1.5, then using the Kelly calculator I find that I must invest 10% of my bankroll.

The Elo ranking system therefore makes it possible to automatically detect favorable situations and the amount of stakes to bet.

Taking into account specific factors, sports expertise

Sports betting is risky, hazardous, random, ... everyone knows that. But it's not about playing roulette or the lottery either, here math can help you win.
How to use your expertise, your technical knowledge? football knowledge and skills ?
The ELo rating method allows everyone to express their ideas! how? simply by calculating the Elo rankings of teams only from past results selected according to certain criteria. Of course, we will only use and bet on future matches that also meet these criteria.

Elo rating improvements

The Elo rating method can be improved, always with the idea of adding specific technical knowledge to the field to which it is applied. The specialization/selection of statistical data is a source of improvement.
Then, the Elo rating was initially designed for chess players where, during a match, only victory, defeat or draw are possible. In football, the same results exist, of course, but you can also lose or win in different ways: a 1-0 victory is not really the same thing as an 8-0 victory!
This specificity has not been taken into account so far, here is how to take advantage of it. The higher the value of the K parameter , the greater the variation in the rankings will be (for an 8-0 victory for example). On the other hand, if K is small (close to 0), the rankings vary little after a new result (1-0 victory for example, "small victory" judged by an expert).
In addition to the 1/N/2 result of the football match, one can also adjust this parameter, for example in the following way:

K = 10 for 1 goal difference
K = 20 for 2 goal difference
K = 30 for 3 goal difference
K = 40 for more than 4 goals difference

Further improvements can still be made, as the Glicko rating system does , but then also require a greater personal and mathematical investment...

does it work? wager and test without risk

Skeptical?
The Elo rating method allows you to exploit a personalized and specialized statistical database for the detection of value bets, decision-making and up to the exact and optimal stake to invest.
Like any mathematical model, it is important to go through a phase of testing and adjusting the model. Of course, if possible for free and without risk!
How to test the model and the procedure without risk?
Just test it virtually. Prepare the statistical database, then calculate all the corresponding Elo rankings. Then, for example during a month (or more of course, be patient...) evaluate the bets that can be wagered, and note the gains or losses that would have been obtained as well as the new Elo rankings, match after match.
Last step of the free simulation is to calculate global objective indicators such as ROI and ROC and then, without risk, validate (or not) the global method. If so, then you can next bet for real, otherwise try to adjust the model little by little until the method become actually profitable.