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your analysis isnt very good. if u consistently win 51% of your games u will eventually advance to the next skill tier...and at some point u will reach challenger tier. all that is necesary to advance is to improve your mmr, which will happen anytime u win more games than u lose.
the reason you begin to gain less LP when u are close to 100 is because your mmr isnt high enough to advance. i suppose riot decided that it would be better to still let u gain a bunch of lp between 0-80ish so u would still feel like u are progressing even if your mmr has fallen...until u get demoted.