Probability of getting the item you want from an M+ run is 5% with a loot table of 8 items. This is assuming you only need one item from the dungeon, which is a milestone you can reach very quickly.
Now this averages to 20 runs per item. This is a lot, but it is okay; so you get like 1 item per week after you do 20 runs (on average) which is acceptable.
But here is the thing: this is the average. You can get lucky which wouldl be great. But if you’re unlucky, you might end up spending 50-100 runs without getting any of the items you want from M+ dungeons.
Here are the numbers:
~13% of the players will not get any of their targeted loot even after running 40 dungeons.
~4.6% of the players will need more than 60 runs before getting any of the items they want from M+ runs.
~1.7% of the players will need more than 80 freaking M+ runs to get ANY targeted item from the dungeons.
~0.6% of the players will run 100+ M+ runs and not get any single drop from the ones they want.
These calculations assume you are targeting one item from each dungeon. It is also assuming you’re timing all your keys. If you’re not, the number or runs will be way more since you will get less loot from untimed runs.
I believe there should be some form of bad luck protection beyond the weekly great vault because according to math, there will be hundreds of thousands of players having miserable time and tens of thousands who will probably get completely demoralized and possibly quit running dungeons because of these numbers.
easiest way would probably have been to make a token system for M+, where after you gotten lets say 10 tokens to make i easy, you can buy an item, that is arround ilvl 200 or so, this would help people and give people an initative to run M+more also.
for example.
missing the time limit, gives 1 token
getting a +1 gives 2 tokens
getting a +2 gives 3 tokens.
getting a +3 gives 4 token plus a loot box that can give an item plus the normal loot that drops.
doing that people would feel that their effort would be rewarded, even if you need 100 tokens to buy 1 item, you eventualy do get the item you want, even if this item would not be at the highest ivl possible. And still you would not get to much of items to fast.
Things are very bad idd when ending with a +1 outcome on a M+ run. It might be me and my characters but i got an extremely unlucky streak with items and its just keeps going!
par I dont run a lot of M+ my self, but if I recall I have not gotten an item from anything higher than +2 key myself, ran some 4s but cant rember any gear that I have started to use atleast.
after 20 runs you can an item which is mostly 23 ilvl below the max ilvl.
the chance to get the item you need in the vault is below 1% i bet without even calculation and it is on a weekly lockout
i like the vault way more then loot system befor. when i was rushing dungeon keys back in bfa i got all kind of loot , problem was it was the wrong one and had not the stats i needet. so it just might be grey loot just for selling.
now i can choose every week for an decent bis peace or an upgrade. also they said befor lunch that they try to make raiding more rewarding in gearing up then just mythic key farms.
Its a bad system. Yesterday i got lucky and got one item from 3 raid boss and then got another one from M+. And it got spoiled by the feeling that my 4 other friends got nothing and I couldn’t even give the lesser upgrades to them because of the stupid ilvl system.
So yeah i hate this if you don’t get anything you are annoyed if you get something while others don’t you get “that” feeling again… Like eating alone in a group while everyone is hungry.
And that’s m+ alone. Loot acquisition and the pacing of loot has been nerfed a lot, making RNG more important than it ever was before. Having done M+ a lot, the only item I managed to get out of 40 M+ runs was an ilvl197 haste vers 2hander that is nowhere near my BiS.
In PvP currently, you feel very bottlenecked to do raids, as it’s a huge ilvl boost, and that you can get multiple pieces of PvE gear per week, whereas at best, if you get lucky with your pvp box, you’ll get two pieces, assuming you have enough conquest points.
I get no loot from M+ at all I’m also unlucky. It’s better to spend your time somewhere else. I do only few runs and wait for reset getting a guaranteed loot from the Great Vault. Farming Honor or Conquests is much more meaningful right now. And tbh, more fun as well.
I’m one of the luckier ones in this regard (except for weapons, i just gave up and did some arena for the first time since tbc just to get a 200 ilvl one), but one of my guildmates got 1 loot out of 15-20 runs that wasn’t even an upgrade for him. It’s ridiculous that this amount of bad luck is even possible in this game. They should just add a currency that lets people gear up even if their luck is this bad.
It’s pretty bad overall. I cleared 10 bosses NM last week, 3 Bosses LFR, 1 World Boss, and 12 M+ runs. I got 1 item of loot, which I couldn’t even use because what I had was higher. 3 of my friends have cancelled their subs because they say the game is just unrewarding after running the 12th M+10 run with no drops.
I’m also unlucky. It’s better to spend your time somewhere else. I do only few runs and wait for reset getting a guaranteed loot from the Great Vault. Farming Honor or Conquests is much more meaningful right now. 
And tbh, more fun as well.