I’ve heard it’s a standardized scoring method for many more competitions than just chess. But what is it and how does it work?
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Every ELO system is slightly different but based on the same principles. You are given a number at the start of your career in that competition. The number is based on your perceived “level.” High ELO means an advanced player, low ELO means a novice.
If you win a match, it raises your ELO, and if you lose a match, it lowers your ELO. But there’s a catch: If you beat someone with a higher ELO, your own ELO score will go up even more. Similarly, if you lose to someone with a lower ELO, your ELO score will go down even more. This works inversely, too; beating low ELO players will not raise yours as much, and losing to high ELO players will not lower yours as much.
Generally, a 1000 is the level of just knowing the ins and outs of the game. Around a 1400-1600 is intermediate. Anything over 2000 is considered to be a very strong expert (a “grandmaster” in chess).
It’s just a simple calculation. Everyone starts with a score, and the score can be increased or decreased depending on the results of a match.
The expected outcome is EA=1/(1+10^((B-A)^)/400 )
Where EA is the expected outcome for A, and B is B’s score and A is A’s score.
EA + EB =1 always where EB is the expected outcome for B
Let S be the outcome of a game. A win counts at 1, a loss counts at 0, and a draw is .5
Let’s calculate A’s new score after the match.
A’ = A + K(S-EA)
K is a linear adjustment and can be tampered with. Usually it’s 16 for masters and 32 for weaker players, but in most games it will be the same for both parties.
So if EA was .75, and A won the game, A’s score will increase
Similarly, B’s will decrease.
If instead, B won the game, A’s score will decrease by a lot, and B’s will increase by a lot thanks to that S-EA term (or S-EB in B’s case) 1-.25 is much bigger than 1-.75 and 0-.25 is a smaller loss than 0-.75
Someone with an Elo score equal to yours should have a 50/50 chance of winning the game (based on skill). This should make sense – you have equal skill, so you should have an equal chance at winning.
When you win, your score goes up. When you lose, your score goes down. How much it goes up or down depends on the relative scores of the players. If you beat someone with a higher elo than you, it probably means that either you were ranked too low, or they were ranked too high, so your score should go up and theirs should come down. If you lose to someone with a lower score, your score should go down and theirs should go up. The greater the difference between you, the more the scores should move. Over the course of many games against many opponents, your score will naturally move towards your actual playing ability and, barring drastic improvement (or the opposite), your score should hover around that point.
You should only be playing against others with a similarish elo score. The goal of the score is to make the game enjoyable for everyone. Playing against someone who is far above your level is frustrating and you probably won’t learn much from the experience. You’ll just get trounced. It shouldn’t be fun for them, either, because there’s no challenge. If it’s too easy, what’s the point in playing? By only putting together people with similar scores, it ensures that everyone will be appropriately challenged by others of a similar level.
There should be *some* variation, though. If you only ever play against someone with the same score, your score can’t really move up or down. So there needs to be a range, where you can play against people of *around* your score, but not necessarily the same.
Exactly how much the scores move and what the range is depends on the specific formula used by the game. Every game uses its own formula, especially in the modern era of online gaming where you may be part of a team. In that case, the game groups teammates based on similar-ish elo scores, and your team has an elo that is the average of everyone on the team. That averaged elo is matched against a team with a similar average elo. Since modern games can track individual performance very well, even if your team wins or loses, your individual score can be affected differently based on what the game is tracking.
Typically, online games don’t want players to know what the formula is. Imagine a team-based shooter like Overwatch or Counterstrike, and the formula gives extra points for headshot kills. Players may think that if they only go for headshot kills, even if the team loses, their score won’t drop too much, or it might even go up despite the loss. Well, then everyone will only care about headshot kills and won’t care at all about accomplishing the actual objective of the match like capturing the point. That would make for a pretty bad player experience. So, the formula is kept hidden, and they may even show you a slightly altered elo instead of showing your real elo, so that you can’t keep track of all the possible metrics and work out the math yourself.
From a practical standpoint, before a game every competitor has a probability of winning, calculated using the competitor’s rating. After the game, the system compares the probability calculated pre-game with the actual result, and modifies the rating depending on the result (adding points if they won, subtracting them if they lost, and generally they’re the same for both competitors), in such a way that a probable result will exchange few points and an unprobable one will exchange a lot. This will give the new rating, that’ll be used for the next game.
There are several Elo-based systems, which differ on how many points to exchange per game, how many points are “one order of magnitude” of probability (i.e. when a competitors has a 10 in 11 probability of winning, and the other a 1 in 11), if there are games with different importance, etc. But the idea is the same: there’s a game, a probability is calculated before the game, and after the game they calculate the exchange of rating points.
The Elo system’s spirit is that there’s a “true rating”, which cannot be known, and which will tell you who will win a game. Now, we only have access to the score of a game. Using those scores as input, Elo tries to get closer and closer to the “true rating”. Of course, this “true rating” is always moving, so you never reach it.
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