Introduction To Elo Rating

September 4, 2019

No matter what your favorite game is, there’s a good chance that you have ever found yourself caught up in a debate about how teams are ranked. And to win such a debate, you need to have a good grasp of the teams and the game itself, although mere sentiments can sometimes be misleading. In the sporting realm, ranking teams takes much more than sentiments, which is why stats, metrics, and other parameters are often used. But still, even when all these factors are compounded, they can sometimes be revealing or misleading.

In light of this, different rating methods are constantly emerging, while others are reincarnating after taking a backseat. Talking about backseat, Elo ranking is one of the longest-running rating systems in the sporting arena.  

In this article, we are going to lift the veil on the Elo rating system and look at its history, relationship with the probability method, and the many areas it is being utilized.

But first…

What is Elo Rating?

The Elo rating system is a method used to calculate the comparative skill levels of players in zero-sum, PvP games. Named after a Hungarian-American physics professor, Arpad Elo, it is mainly associated with chess, although it is also used in many other games including video games, basketball, baseball, American football, board games, and rest-of-the-world football.

Brief Background of Elo’s Rating Scheme

Although subjective ranking in tennis dates back as early as 1881, formal algorithms have been deployed to obtain more objective rankings since the 1920s. During this period, football teams, especially those in the US were attempting to look for the most accurate method to rank college football teams. The Dickinson system used a score-based adjustive system to rate American college football teams between 1926 and 1940, including the crowning of Rissman Trophy champions.

The Dickinson rating system awarded 30 points to a weaker team that triumphed over a strong team. Victory over a weak team, on the other hand, was awarded 20. Defeats counted half as much as victories, with ties considered as half lost and a half won. The final rating was calculated by dividing the total of the two scenarios by the number of games played. Later on, Professor Dickinson incorporated an additional variable, a “sectional rating” to cater for the different points emanating from other teams. The only problem with the Dickinson rating system is that it did not factor in the bowl games, rendering the combination worthless.

The Connection Between The Probability Model and the Elo Rating Method

There is a distinct difference between Elo-type rating algorithms and probability. However, a small heuristic connection between the two models also exists, and it can be demonstrated in an implicit mathematical discussion of Elo ratings as shown below;

Supposing n teams with linear strengths x1, . . . , xn, whose match results are based on a basic probability model with W, as the function of winning probability and (yi) representing the update rule with Υ as the update function.

If team i plays against team j, the new rating i will be;

Υ(yi − yj )W(xi − xj ) − Υ(yj − yi)W(xj − xi).

In this case, considering the functions Υ and W are inversely related by

Υ(u)/Υ(−u) = W(−u)/W(u), −∞ < u < ∞. 

If the rating difference between teams yi − yj is equal to the difference between xi −xj, the expected rating difference equals zero. On the other hand, the rating difference will be unequal because Υ is decreasing, meaning (yi −yj ) − (xi − xj ) expectation is higher after the compared to the first scenario. And in this case, the latter equation then becomes the balance relation. 

Going by the balance relation equation highlighted above, it is simple to see that player i’s rating yi will tend to move towards xi though, which is its strength, although random fluctuations from different matches will occur. As such, a basic W probability model should use a Y function that satisfies the balance relation.

Major Sports Using Elo Rating System

In 1960, the United States Chess Federation (USCF) started using the adjustive Elo system to rank chess players. The same system was adopted by the World Chess Federation 10 years later. Key among the reasons why the adjective Elo system was favored over Dickinson’s is that it was based on a tried and tested statistical theory, which factors in the rating difference between two players when calculating the expected loss probability.  As a result, calculating a player’s new rating becomes easier because their actual performance in a competition is compared against their expected performance. 

Given the firm and well-established accurateness of the Elo statistical theory, other sports also started adopting it. Thanks to the system, tennis became the pioneer in the sports arena to introduce world rankings in 1973, whereby players were awarded ranked in a tournament by summing all the accumulated points over a period of 52 weeks.  Golfing adopted a similar ranking method in 1986, although weighted averages were introduced a year later in 1987. 

In football, Elo-based rankings have been endorsed by FIFA to rank the national teams in women’s football. On top of FIFA’s ranking system helping evaluate the relative strength of all international women football teams, it also comes in handy in profiling the teams within a particular continent based on accumulated points, which helps to curate the list of top teams in continental championships and FIFA World Cup qualifiers. has also adopted an ELO-style team rating system to rank club rugby and international teams on the basis of game venues and the outcomes of the games. According to a research paper published by the International Educational Scientific Research Journal, this Elo-style rating has a predictive ability of 62.6%.

Another game that has leveraged the higher-than-average certainty of Elo ratings in predicting wins or loses is basketball. Here the team’s Elo ranking is influenced by several factors including the games’ final score, venue, the victory margin, probability of winning or losing, and it is based on a zero-sum basis. 

Elo Rating in Video Games

If you are a PlayerUnknown’s Battlegrounds fanatic, you will be surprised to know it is one of the few video games that utilize the very first Elo system. The original Elo rating system works under a very basic concept; winning will increase your rating while losing will decrease it. With that said, the fluctuations in the ratings aren’t overly abrupt, meaning losing a single game doesn’t necessarily spell doom.

Overwatch is also another video game that uses a derivative Elo-like rating system to rank competitive players, although various adjustments are made in between the competitive seasons. 

When it comes to Guild Wars, which is an MMORPG, Elo ratings come in handy when recording the guild ratings gained and lost in the guild versus guild battles. In Counter-Strike: Global Offensive, leagues, and match-makers also use an Elo-style rating system called Glicko-2, with World of Warcraft having previously used it to team up and compare Arena players.

Likewise, League of Legends initially used the classic Elo rating system. After season three, however, the game owners decided to deploy their own customized system. Other notable mentions using modified Elo rating versions include Puzzle Pirates, Roblox, Mechwarrior Online, and Quidditch Manager AirMech.

Other Usage

Assessment plays a critical role in our education system. It not only helps to identify the knowledge proficiency of the learners as well as reinforces their ability to track their progress. Unfortunately, poor assessment practices and methods can significantly hinder the learners’ ability to identify various learning misconceptions or even keep track of their progress.  In return, this may have a significant negative on how they learn and follow instructions. Still, most standardized assessment practices have insufficient performance indicators to gauge students’ competence, simply because teachers and contemporary educational systems rarely accommodate variability and the diversity of learners. With Elo rating, however, the adaptive learning systems can be revolutionized by offering learners content and resources that meet their current needs and skills.

Wrapping Up

As you can see, the Elo rating system is not only used within the gaming realm but also in other sectors like education. The key advantage of this rating system doesn’t lie in its expressive power, but in its simplicity and versatility. And since it does not make fixed assumptions to satisfy a particular scenario or game, it can be modified and applied in a wide range of situations and still provides reasonable accuracy.

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Michael Peters

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Michael Peters is a video game enthusiast who demystifies the complexities of the games in reviews. He is a seasoned writer with over five years of experience in the gaming industry. He writes more about games, boosting, and leveling services. Michael leverages his in-depth gaming knowledge to provide valuable information to video gamers.

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