Understanding Elo systems.
You will need to understand the concepts for Averages. Mean, median, mode .
In a room of 100 people you can determine averages for many things. For example, the average height, the average weight, the average skill in making a grilled cheese sandwich. As long as you have a system to use for measurement you have the ability to find these values. Regardless of if your using inches or centimeters if you arrange people in the room by height from shortest to highest you have the same order, the measurement value is not relevant, The naturally occurring differences in height remain the same regardless of the value assigned to measure it.
Skill in making a grilled cheese requires more information as well as a method of grading the end result. How ever even if it is not measured the gap between ability will result in an average level of skill existing in any group of people even if you have not measured it yet.
For Elo, the core concept he uses is that In a game of skill, more skilled by definition is expected to beat lower skill. Then he built a measuring system from this concept. To start with an average point, a value then measure via pairwise comparison vs that. The values are then broken down into probability expectations complete with room for deviation, humans are inconsistent after all. End of the day there are mathematical expectations for ratings. The exact values do not matter, the gap between 2 values create its expectation. The expectations are universal, Much in the same way some one 2 inches higher. If that's all you know you simply have a Hight gap and you know how big that is. If you know the shorter person is five four then you can generate the Hight for the taller person. This is what Arpad Elo's system is made to do with its Elo points, the starting value for everybody is the same, then it starts measuring vs that value. Your opponent might be misplaced, but there will be an average level of skill in a population so a majority of games even with RNG distribution will net reliably accurate data over time. Law of large numbers does a fantastic job of sorting out rng + Bayesian inference can assist in reducing the total # required to fit some one into the right bracket of skill.
I have been trying to find a way to make the topic more approachable for less math loving folks. Decided to drop discussing the probability theory, distribution models, How to build a curve, etc. Let me know if this post was helpful and feel free to bug me with any questions.
Not by any means an expert but I did take the time to study the basics unlike a huge number of folks on the boards who are very loud about the topic and very confident in their observations but are filled with ignorance on functionality behind Elo and MMR. Rn=Ro+K(W-We) Being the basic adjustment formula from Elo, which uses 0 subjective data. Yet folks insist there's an issue because they grade from their personal experience.
