Rn=Ro+K(W-We)
^ this or some variation of this is what you see ran when a game ends. What you get for winning or losing is MMR not LP. LP is a secondary system thats made from your MMR and your Tier and division.
When your MMR Is lower then Tier your being placed with players below your Rank, to get your rank to match your MMR the system slants your Gains to favor the direction MMR is at. When the gap between MMR and Division get dramatic you see the system play catchup. Demoting an entire Teir, Skipping divisions and promo games, for example.
My rule of thumb? Look on OP.GG. Check the match average MMR and compare that match average to your personal Rank. If average is far under, expect higher losses lower gains. About even expect roughly even gains give or take 3-5 points. If above, expect to see higher gains then losses.
There are 2 easy ways to build Titles in a ranked ladder. 1. Population %s. Not a great option for players, it shifts randomly, you lose your spot if you don't constantly play, and it will lock people out of accurate ranges. 2. Set MMR ranges for low uncertainty. MMR does not magically know player skill and has a calibration period where it sees who your beating and who crushes you. After enough data is collected it starts to consider you as less uncertainty for its rating. That's the K variables job. So when an account is at a reasonably low uncertainty, the system expects to have their rating be representative of good expectations for average performances. ITs a range of expectations rather then absolute value, which is why it has a bit of wiggle room.
So you take that concept, and you make arbitrary ranges, say 1200-1250 would be silver 3. When that account is lower uncertainty they should be sitting at s4-s2. The lower the uncertainty the closer they will be to s3 if the raiting of say 1225 would represent proper probability theory expectations.
(MMR uses a probability distribution. The exact #s don't really matter, 1225 has no meaning outside of the system the same way 8 can have different context. 8 out off 10 is high, 8 out of 1000 is low. 8 out of 8 is max. Different systems, different rules. The MMR system says, 1225 wins vs 1225 50% they are equal skill. so 10 games should more or less be 5 to 5. if it was 0 to 10 then odds are 1 of the players has the wrong rating. Both move to reflect that. then its just a matter of building class intervals off %s. so 1500 v 1500 = 50% odds but 1500 vs say 1300 would be 76% to 24% odds. That way you can say 1500 is more skilled then 1300 because it consistently beats those players. When the values on 2 accounts are accurate you see this expectation to win represented. If the system is wrong, and you see different results, it adjusts the accounts raitings. if you ran it over and over with the same players, eventually it would have their rating points reflect the correct win%s between the two players because that's how it moves points when inaccurate.)
