@Riot Nerf/Buff Philosophy

We all know that with each patch that comes to the live servers there also comes champion buffs and nerfs, so what I would like to know from the Riot team that works on champion balance is what constitutes a champion for nerfs and also what causes a champion to receive compensation buffs for the nerfs they receive in the same patch. As I see it, I feel that the champions who do receive the compensation buffs have been either 1) Overly nerfed due to playerbase demand or 2) The champion in question just needed power from one part of their kit to be moved into a different aspect of their kit. These are only my guesses as to how Riot does their nerfs/buffs to champions each patch but as I am curious as to what really goes on in the mind of Riot when they nerf or buff champions, I would really like to know the thought process that the balance team goes through when they do select champions for buffs or nerfs. Rito Senpai pls notice me