Rn=Ro+K(W-We) Raiding adjustments in MMR are some deviation of this formula. So ΔR=K(W-We).
In English. Your New rating = your Old rating + K variable multiplied by the Match results after subtracting system expectations. Delta R is change in R, so the exact # of points you gained or lost at the end of the match.
Because averages exist naturally the assumption is that in any finite group of people there will be an average level of skill. Elo simply looks to find who is At, Above, and Below that average. So you use a Curve.
Now, the errors people make. They don't understand what values represent and provide/use bad context. I have about 200+ games and there are 11 different champions I maintain a 100% WR on. Why am I not higher? All of those 11 champions are sub 3 games. They account for a fraction of my total games played this season. 11 champs at 100% looks good until you find out that its only like 15 of my wins this year.
It seems like it is the goal of the game - keep you from climbing UNLESS you are absolutely amazing at the game.
Yes and no. MM does want to keep you from climbing if your not stand out from the average, it also wants to keep you from sinking if your not stand out from average. There's nothing forced about this thou, as averages occur naturally. MM is your results get compared to the average around you then adjust to reflect your results.
Forced MM is unnatural, and it breaks a Elo systems back. You cant use Skill ratings for accurate assumptions about skill when their generation is unnatural. You cant Rig results with inaccurate skill ratings with any accuracy. Forced 50% is a stupid argument you destroy any naturally occurring curve for average skill so you lose the very metric your system generates skill expectations with.
Now Riots class interval expectations might have issues. That would come into play with MM ranges. Using a Probability distribution you make assumptions for what **accurate **ratings look like so that you have an exact measurement of how much better player at 1200 would be compared to say 1000. the value of this scale is irrelevant as the values are arbitrary. The expectation between 2 values is what matters. In chess 200E (Elo points) = 1C (class interval) and it represents a 3 to 1 expectation roughly. So about 75% of games 1200 wins vs 1000. This is used for We generation.
You do that because at some point you just don't expect the skill gap to provide good data. Beating your cousin or best friends little brother in smash brothers 100 out of 100 games does not make you #1 smash player of all time, just that your opponent is not near enough to your level of skill for any kind of competition to happen.
So, when you sink to far in a MMR system, your rating does not match your skill, the We expectations for you do not match your results. Your account will correct back upwards. If you get a fatty streak from some teammates? the opposite holds true, and you sink back down. this happens because your MMR is the Mean range of your performances and its looking to put you on the curve with everybody else who shares a mean range like yours.
At which point its "fair" because who ever has a better game will win and the system assumes you have equal odds for that.
People need to think of the system like a bank balance rather then a win tracker.
I will stop here and give you a moment to ask any questions you have. then if your interested still lets move on to talk about why people get stuck in a class interval and why WR for total account is not an accurate measurement due to K factor changes, and the impact that duoing makes.
I do need to point out that you absolutely have to modify the formula I listed to account for team games, but its still provably functional just takes more data points.
