I made my own notes and compared them to the rates Plarium publicized. 

With ancient, void and sacred shards, my own calculations do meet with the percentages given by Plarium within a range of 1%. 

My sample size is more than 10.000 shards (several accounts, counting shard pulls from clan mates).

Ive tracked every shard Ive opened for almost 2 years.  My observed results are consistent with expected results.  Somewhat disappointing, but within normal distribution for voids.   Very lucky, but within norm for sacreds.  Pretty much hitting ancients right on the mark.

that said, em yea, only suckers buy shards imo.

Your results simply do not add up. Assuming you're referring to Ancient Shards when you say "crystals" (because if you were talking about anything else, then I cry for your wallet), after 200 pulls without a legendary champ, you enter mercy mode, wherein you gain a bonus chance to get a legendary champ for every shard you pull without getting one - 5% for ancients. This means after 119 ancient shards, you are *guaranteed* to get a legendary on your 220th.

From 1000 ancient shards, the *minimum* you could have received would be four legendary champs.

Agree that it doesn't make sense, and the terminology of crystals makes me feel like you might be talking about a different game

In any event, if your buddy does indeed start to post some things on social media then keen to see it.  Come back here and post links to it to further the knowledge.  I am not convinced that there's an issue until I see it or someone posts something a bit more than this.