I mined flair data on /r/leagueoflegends for the last three days and got a sample of 1276 valid flairs from users (valid as in the flair is in the format <[summoner name] (region)>). After removing an additional 324 flairs in which the summoner name does not actually exist (or in a region without Riot API) and 146 flairs in which summoner name exists but has no ranked records, I am left with 806 flairs. The ladder distribution of these users are as follows:
In comparison, this is the ladder distribution for the NA server a few weeks ago:
It seems that /r/leagueoflegends users are mostly in Gold or Platinum. Comparably most players on the NA server are in Silver. This is probably not a surprising result since we can reasonably infer that the users on a discussion board for a game are more skilled than the average player population.
However, as with all analyses, it's good to note the limitation of the data at hands. Unlike /r/summonerschool, /r/leagueoflegends do not have a verification process built in place, so theoretically a user can masquerade as someone else with ease. Furthermore, many users choose to not report their summoner name as their flair so there is non-response bias within the data. Overall, there is room for a better study in the future.