TLDR. Your LP gains are in relation to a Gap between MMR and Title. MMR below Title. Slanted Gains on loss. Above. Slanted Gains on Wins. In the right range, more or less equal Gains and losses. Far as I can tell the LP system is entirely reactive to MMR.
Wall of text.
In Elo systems There is a K variable in the Rating adjustment formula. Which is Rn=Ro+K(W-We). With the Context of an Elo MM system this means that Ro is used to build games and RN is your points after a match. W is the result of a game, win loss draw and is what controls the if you have positive or negative gains. We is system expectations and its used to impact uneven games, beating some one lower then you rewards less points, beating some one higher rewards you with more.
K is uncertainty, its the idea that low data = high inaccuracy on a correct skill rating. A player with 2 games vs 200 should be treated differently. K is lowered in 2 ways usually. # of games and Position on ladder curve. K multiplies the result of the (w-we) which makes early games have a more rapid change in your rating. This moves player away from their starting Elo who are outclassed or Outclass the average player. As it slows, its reduces rubber banding.
MMR systems Are a Tweak on Elo systems, designed to track an individual on a team rather then treat the team as a singular value. That way each player has a individualized Stake in a match and consistent trends in play result in a skill rating specific to a single member for RNG "pick up" style games.
Riot has added extra layers to their MMR system, Mostly for Player perception. They do a lot of stuff to keep people queuing up and playing rank, not all of which adds any mathematical quality or positives to a standard MMR system, thou some features do help prevent abuse despite some being abuseable.
Elo is well documented, very easy to study. MMR is a bit harder, but understanding the needs of the system give you a good idea what changes are required and again as its mathematical systems your able to run Simulations and test for accuracy. Microsoft Also publishes a good deal of information on their MMR system called TrueSkill so you can look at the concept, math, and logic behind a MMR system. Its also a pretty widely used MMR system. Riots very proprietary with their systems but studying the foundations gives you a pretty good idea on some of their systems
A Title is a concept that goes all the way back to Elo. You have a Player in a Range of MMR that earns them the Title. Say 2200-2600 = Masters and everything 2601 and above = GM. The idea of a range of Rankings = a Title is not new. What Riots MMR to Titles are is hidden, They also have extra steps as titles are built of LP not MMR. Resulting in many moments where some ones Rank does not accurately reflect their Title. Like I mentioned before Riot has extra features for player perception. Division 4 is stupidly difficult to demote from. The demotion protection on Division4 is higher then any other rank. To keep people from rage quitting if they drop a Tier.
The LP system consistently looks the be playing catchup for your Title to the MMR range. Something I am actively Testing I took advantage of the fact Remakes and Lobby dodges Drop LP. I have Flopped every promo via dodges. Yet I still promoted the account from B1 to S1 despite winning 0 promotional games.
