I have yet to get a single key fragment at all. I've been in 2, 3, and four man groups and gotten 3-4 wins in a row with those people and none of us got key fragments. Part of the problem was that some of the games were in ARAM and apparently that was bugged, but even with 10+ wins in Summoner's Rift not a single drop. While I understand it's RNG, I still think the formula for that RNG needs to be tweaked. I am not a casual player, I play up to 8 hrs a day and often more on the weekends. For a casual player that plays maybe 4 games every other day, a system where it's A) hard to get the key fragments while solo, B) requires not 1, but three wins to acquire and C) has a bit too much RNG in it is going to end up with one answer:
Casual players will end up getting more hextech boxes than they will ever be able to open as they will be unable to acquire the key shards necessary. So I propose, either a tweak to the formula, or remove the key shards and instead just make it a single drop. You've already limited the total amount of chests we can receive in a year, which is also based on skill and/or having friends that have a decent degree of skill, why are you also limiting how often we can open these boxes?
Now sure, if you're really having problems you can spend five bucks and get a couple keys and problem solved, but not always. While I can sometimes purchase RP, I live on a fixed income which means things like RP purchases are things I make once every couple of months with it planned in advance and I'd much rather spend that RP picking up things specifically rather than on those keys. In fact I was hoping this system would make it so I wouldn't necessarily need to make those budget choices anymore and I could still pick up some neat skins along the way, but so far I've only been able to open that one free-bee box.
Now, this semi-rant may seem a bit selfish but in the end I'm trying to pitch my opinion for those casual players, those guys that can only play a few hours ever other day and may not be lucky enough to play in big premade groups, this is unfair to them more so it is myself because they are either going to have to be really lucky or never open a hextech chest until next season with how I've seen the drops going so far.