Football Elo Ranking – How are Elo points calculated?

The Elo ranking is one of the best-known ways of evaluating the relative strength of players or teams. The system was originally developed for chess, but over time it found application in other sports as well. In football, Elo rankings are used primarily by statisticians, analysts, and enthusiasts of sports results modeling.

At Euroranking, we maintain our own proprietary Elo ranking of football clubs. It is updated daily and is one of the most important elements of our analytical system. We use it, among other things, to calculate the probability of advancing in European cup competitions and to create predicted tables.

What is an Elo ranking?

An Elo ranking is a numerical system used to determine the relative strength of participants in a competition. Each team receives a certain number of Elo points — the higher the score, the greater the estimated strength of the team. The most important feature of the Elo system is that the ranking is not based solely on results themselves. The strength of the opponent matters too.

Beating a very strong team should be worth more than beating a clearly weaker one. Conversely, losing to a much stronger opponent shouldn't cause as big a drop as an unexpected loss to a team with a significantly lower ranking. After each match, the system compares the actual result with the expected result — if something happened that the model didn't anticipate, the ranking change is larger.

Where did the Elo ranking come from?

The system was developed by Arpad Elo, an American physicist and chess player of Hungarian descent. Elo worked on a way to more objectively evaluate the strength of chess players. In the classic system, a player receives points depending on the result of a game and the ranking difference between them and their opponent. The system proved practical enough that it was widely adopted in chess.

Over time, the idea of the Elo ranking began to be used outside of chess as well. Its basic principle, however, remains the same: the ranking should respond primarily to whether the result matched the expectations arising from the participants' existing strength.

Why use Elo in football?

Football is a particularly interesting application of the Elo system, because teams regularly face opponents of very different levels. We can, for example, compare a club from Spain that plays most of its matches in La Liga with a club from England, Germany, or Norway. A simple win/loss record doesn't answer the basic question in that case: how strong is this team compared to other clubs in Europe? Elo tries to answer exactly that question.

If a team regularly beats strong opponents, its ranking rises. If it loses matches in which it was the clear favorite, its ranking drops much more sharply. This makes it possible to create a single ranking covering clubs from many different leagues.

Does UEFA use the Elo ranking?

No. The Elo ranking is not UEFA's official club ranking. UEFA uses its own system of club and association coefficients, which is used, among other things, to determine seeding and the position of clubs and leagues in European competitions.

Elo, on the other hand, is a popular tool among statisticians, sports analysts, and people involved in modeling the probability of results. This doesn't mean the Elo ranking is any less interesting — its purpose is simply different. The UEFA coefficient primarily answers questions related to results in European competitions and UEFA's rules. The Elo ranking, on the other hand, is designed to estimate the current relative strength of teams as dynamically as possible.

Euroranking's own Elo ranking

At Euroranking, we maintain our own proprietary Elo ranking. It is not a copy of a ranking from another site. Our system was designed above all with the goal of comparing clubs from across Europe and using the ranking in further calculations.

The ranking covers results from European associations, including not just the most popular leagues. We also include many second-tier competitions, domestic cups, and European cup competitions. This matters because a club isn't confined to a single league — it may play dozens of matches in domestic competitions in one season and then face opponents from other countries in European cups. It's precisely these matches that allow the system to compare the level of different leagues with one another.

What do we use the Elo ranking for?

The Elo ranking on Euroranking isn't just a table of numbers. We use it as one element of our statistical models.

Probability of advancing in European cups. The strength of both teams as derived from the Elo ranking is used to calculate the probability of winning a single match as well as the probability of advancing through an entire round. This is particularly important in European cup qualifying rounds, where teams from different countries and leagues — which are hard to compare directly — often meet.

Predicted tables. Elo is also one of the foundations of our predicted tables. Based on teams' current strength, we can simulate the results of remaining matches and see what the final table might look like across a large number of random scenarios. This means the Elo ranking isn't an end in itself — it's primarily a tool for further football analysis.

What are the advantages of the Euroranking Elo ranking?

One of the most important advantages of our system is its broad scope of data. The ranking covers:

• all European leagues
• many second-tier leagues
• domestic cups
• the Champions League
• the Europa League
• the Conference League

This lets us compare teams not only within a single league, but also across different countries.

A second advantage is daily updates. The ranking therefore responds to the latest results and doesn't stay unchanged for long periods. The way the data is presented is also important — Euroranking was designed so the ranking can not only be read, but also analyzed. Interactive charts let you see how a particular club's strength has changed over time. Our goal is to combine a sophisticated statistical model with as simple and user-friendly an interface as possible.

Does Euroranking have the best historical data?

Our historical database is certainly not the best in the world. There are services specializing in historical football data that already have an established position in the market and possess more complete archives for many leagues or competitions — but when it comes to the Elo ranking, this isn't always the most important factor.

Elo is a self-calibrating system. If the initial values are reasonably chosen, the ranking adjusts to teams' actual strength as more matches are played. In practice, a few seasons of regularly updated results can be enough for the system to adapt very well to the differences between leagues and clubs. That's why what matters more than the sheer number of historical matches is how consciously they were used and how the whole model was constructed.

How does the Elo ranking work?

The basis of the system is a comparison of the expected result with the actual result. For two teams, we can determine the expected probability of victory based on the difference in their rankings. In simplified form, the formula looks like this:

E = 1 / (1 + 10^((R₂ - R₁) / 400))

where:

• E – the expected result for the first team,
• R₁ – the ranking of the first team,
• R₂ – the ranking of the second team.

The ranking is then updated according to the formula:

R' = R + K × (S - E)

where:

• R' – the new ranking,
• R – the previous ranking,
• K – a coefficient determining how strongly the ranking reacts to the result,
• S – the actual match result,
• E – the expected result.

In the case of a win, S is 1; for a draw, 0.5; and for a loss, 0. In our model we also apply additional parameters, including a home-field bonus and different K values for different types of matches.

Example: Reds vs. Blues

Let's say the Reds and the Blues each have 1500 Elo points, and the match is played at the Reds' stadium. The home-field advantage is 60 Elo points, the K coefficient is 20, and the divisor is 400.

For the purposes of the calculation, the Reds effectively have 1560 points against the Blues' 1500 points. This means the Reds are a slight favorite — their expected result is about 58.5%, and the Blues' about 41.5%.

The Reds win. The Reds achieved a result consistent with expectations, though it wasn't entirely certain. Their ranking will rise by about 8.3 points, from 1500 to 1508.3, and the Blues will lose the same amount.

The match ends in a draw. A draw is a somewhat worse-than-expected result for the Reds, since they were the favorite — so they'll lose about 1.7 points, and the Blues will gain the same amount. This is an important feature of Elo: a draw isn't always a neutral result. For a clear favorite it can mean losing points, while for the weaker team it can mean gaining them.

The Blues win. This is a much less expected result. The Reds will lose about 11.7 points, and the Blues will gain the same number of points. So an unexpected win by the weaker team causes a bigger ranking change than a win by the favorite.

Why does the K coefficient matter?

The K coefficient determines how quickly the ranking reacts to results. With a low K, a single match has little effect on the ranking — the system changes slowly and is more stable. With a high K, the ranking reacts much faster, so a team's current form can have a stronger effect on its current position.

At Euroranking we use different K values depending on the type of competition. European cup matches carry more weight than standard league matches. This doesn't mean a result in a European cup match is automatically a "better" result — it's that matches between teams from different leagues provide especially valuable information about the relationship between the levels of those leagues.

How does Elo mix across leagues?

This is one of the most important elements of our system. Imagine a Spanish team that plays only Spanish clubs all season. Based on those matches, we can determine its strength fairly well relative to other clubs in Spain. But we don't automatically know how that strength translates to the level of clubs from England, Italy, or Norway.

This is where European cups come in. If a Spanish club regularly faces clubs from other countries, the results of those matches create a link between the different leagues, and the higher K used in European competitions means that this information has a correspondingly large impact on the ranking.

As a result, the system doesn't create separate "islands" for each league, but gradually builds a shared scale for the whole of Europe. This lets us compare clubs that, in everyday life, practically never play each other.

Why do initial Elo values matter?

An Elo ranking has to start from somewhere. The simplest solution would be to give every club exactly 1500 points. But such a starting point would have a major drawback: the system would have to spend a long time discovering the differences between leagues based solely on subsequent results.

At Euroranking, we took a different approach. Initial values were made dependent on the level of the league. Clubs from different leagues received starting values within a wide range, roughly 1000–1700 points, instead of a single shared value of 1500, depending on the position of the league in UEFA's national ranking at the time points began being calculated for clubs from that league.

This lets the ranking converge much faster on the real differences in level between leagues. This matters especially where historical data is less available. For the biggest leagues we can draw on very long archives spanning more than 10 years, but for some less accessible competitions that isn't always possible.

That doesn't automatically mean the ranking for those teams is unreliable, though. If the initial values are properly calibrated, and the system then receives several seasons of real results, Elo can adapt relatively quickly to new information.

Problems and limitations of the Elo ranking

Elo is not a perfect model of football. Like any statistical model, it has its limitations, and these should be kept in mind when interpreting the results.

Elo doesn't know everything about a team. The ranking itself has no way of knowing that a club changed manager, sold its best player, has a run of injuries, or fielded a reserve lineup. The system only learns about such changes through the results of subsequent matches. That's why it's best to treat Elo as a statistical estimate of strength, not an absolute truth about a team.

Draws are specific to football. The classic Elo system was created for chess, where a draw has a different meaning than in football. In football, a 0-0 result and a 4-4 result are formally the same outcome, even though the course of the match may have been completely different. Basic Elo doesn't analyze the quality of chances or the flow of the match — which is why, in our system, the Elo ranking is only one part of a broader model.

A club's strength can change faster than its ranking. A team can change very quickly. A young squad can make huge progress within a few months, while a club that loses several key players can weaken significantly. Elo needs subsequent results to reflect these changes — a trade-off between stability and speed of reaction.

The drift problem. One of the more interesting issues is so-called ranking drift. Imagine a league whose clubs go a long time without playing any matches against teams from outside their league. Internal Elo changes can still occur — some teams gain points, others lose them — but the whole group can gradually shift up or down relative to the rest of the system.

A good example is the Russian league, whose clubs currently don't take part in European cup competitions. The lack of regular matches against clubs from other European leagues means there's no fresh, direct link between Russian clubs and the rest of the system. In such a situation, Elo may preserve the relative standing among Russian clubs for a while, but it becomes much harder to tell whether the whole league's level has shifted up or down relative to Europe.

This is one of the reasons why an Elo ranking should be interpreted in the context of how it was built, rather than treating each number as an objective, unchanging value.

Elo is a model, not an oracle

The most important thing to remember is that the Elo ranking doesn't say: "this team is definitely better." It says, rather: "Based on results so far and the assumptions adopted, the model rates this team as stronger than that one." That may seem like a small difference, but it matters enormously.

Every sports ranking is a model of reality. Different services can use the same results and end up with different rankings, because they apply different starting values, K coefficients, home-field advantages, ways of weighting competitions, or update methods. There's no single magic Elo value that represents a club's "true strength." That's why what matters isn't just how good the data is, but also how consciously it was used.

Why did we create our own Elo ranking?

Euroranking's goal isn't to produce yet another list of clubs just so it can be sorted from first to a thousandth place. For us, the Elo ranking is above all the foundation of a larger analytical system.

We want to use it to:

• compare clubs from different European leagues,
• track how their strength changes over time,
• calculate the probability of results,
• analyze European cup competitions,
• simulate possible competition outcomes,
• create predicted tables,
• and present this data in a way that's understandable to people who aren't professional statisticians.

That's why Euroranking combines the classic idea of the Elo ranking with its own approach to data, calibration, the relative importance of different competitions, and how the ranking is ultimately used.

The Elo ranking is a tool for analyzing football — not just another ranking table.