Elo rating system in sports betting

Principle and calculation in betting strategy

The Elo rating system is a mathematical system for evaluating the skill level of competitors.
This ranking system is actually a real mathematical model that evaluates the strength, or level, of each player compared to other ranked players.
The very particularity of the Elo rating system is that the difference between the ranks of two opponents directly reflects the probability of each of winning against the other: in other words, the Elo rating system is the ultimate tool for bettors!
Once you know the Elo ranking of the opponents, you are only one step away from calculating the probabilities, objectively, and therefore determining whether the situation involves a value bet and also calculating exactly the optimal bet thanks to the Kelly criterion.

On ranking systems

A ranking system is a set of rules that allows opponents to be classified in a given discipline.
In general, for a ranking system, for each victory a competitor earns points. The more points a competitor has, the better their ranking. That's easy.
But, on the other hand, what scale of points should be attributed to one victory or another, according to the respective rankings of the opponents?
And above all, how can we use this ranking to predict future victories or defeats? and more precisely deduce the calculations of their mathematical probabilities?

The Elo math system offers all of this at once. Somehow, the Elo rating system is the ultimate mathematical ranking system for bettors!

Where to find Elo rankings

Chess

Elo system has originally been designed for chess competition, and the world chess federation FIDE maintains the official list of rankings at FIDE.com.

Football Elo ratings

Eloratings.net has an Elo Rating system for international football that ranks countries. This Elo rating system takes into account the kind of match, the home team advantage, and the goal difference in the final match result.
In 2018, FIFA also decided to adopt an Elo based ranking system.

Tennis

tennisabstract.com gives, weekly updated, an Elo ratings list of tennis players.

Others ?

In this article we will discuss how the Elo rating system works, i.e. also how to calculate new rankings after a match. Thus, it is simple for everyone to use this formula (or, even simpler, the calculator) to construct a ranking according to their own preferences.
For exemple, a specific Elo ranking for tennis players based on to their results only clay court, or only on grass court (ratings which can be quite different).

Elo ranking and probability calculations

In the mathematical Elo rating system, only the difference between rankings really matters.
More precisely, for two opponents A, with Elo ranking Elo(A), and B with Elo ranking Elo(B), the ranking difference between the two is d = Elo(A) − Elo(B).
The Elo ranking is constructed and calculated in such a way that the probability of victory of A over B is given by the calculation formula:

P(A/B) = 1/1 + 10^{−d / 400}

For example, a player ranked 1800 who meets a player ranked 1600, therefore with a ranking difference d = 1800 − 1600 = 200, has the probability

P(A/B) = 1/1 + 10^{−200 / 400}≃ 06 = 76%

With a difference of 200 points, the highest ranked wins with a probability of around 76%, or around 3 chances out of 4.
Conversely, with a difference of 200 Elo points, the lowest ranked wins with (only) around 1 chance out of 4 (approximately 24%)
The following calculator automatically calculates the win probabilities for each opponent according to Elo rankings using the previous mathematical formula.

Estimating the probability of victory of a player or team is the central and fundamental question in sports betting.
Using an Elo ranking system therefore directly answers this question.

Calculator: Elo rating converter ⇔ probability/odds

The following calculator automatically calculates, from the Elo rankings of the opponents, the probability of victory of each as well as the corresponding odds for betting. A useful calculation tool for mathematically detecting a value bet situation.

Updating Elo rankings after victory or defeat

A player's probability of victory is also used to update the rankings after a match: the less likely the result was, the more the rankings will change!
More precisely, when a player A with the Elo(A) ranking meets an opponent B with an Elo(B) ranking, his new Elo'(A) ranking is calculated by the formula

Elo'(A) = Elo(A) + K(W − P(A/B))

with

W is the match result: W = 1 if A wins, W = 0 if he loses, and W = 0,5 in case of draw.
K is a ranking stability parameter. The smaller the value of K, the more stable the rankings are and therefore vary little after a match; a lot of matches are necessary to change significantly the ranking. These small values are in general (and in particular in chess) used for strong players, with already a good ranking (professional players, international chess masters, etc.).
A larger value for this parameter K implies on the contrary that each result has a more significant influence on the ranking.
As an example for Elo ranking in chess, the choice is:
- K = 40 until the player's 30th game
- K = 20 for an Elo ranking below 2,400 Elo
- K = 10 for an Elo rating above 2,400.

Elo ranking calculator

The following calculator allows you to automatically calculate the new ELo ranking of two opponents, according to their rankings during the meeting, of course the result of the meeting, and finally the parameter K.

Using this calculator, you can set up your own Elo ranking of players or teams, for example using more or less recent statistics.