But after a couple months I find myself even more frustrated than last expansion. I have two analyses of why that might be true, one statistical and one psychological.
(If anybody finds any mistakes, please correct. Edited since original post to reflect corrections, and to explain more clearly.)
I used the following assumptions:
Number of items per RF boss: 13.7
(I averaged size of RF loot table for all HoF and ToES bosses)
Number of useful items per class: 3
(I did NOT average this across all classes/bosses. I was lazy and just grabbed the number that seems to show up in Dungeon Journal)
Number of classes with which you share gear: 2.125
(This one is complicated and I welcome a more sophisticated analysis. I made a matrix of the four armor types against the three roles, healing, tank and dps, then averaged all the entries in the matrix and applied it against a 25 person raid. This ignores spec/role; e.g. it assumes that a feral druid will roll on spirit leather. Also note this is just an average: an agility trinket sees more competition than healing plate.)
Average number of items you can use per boss killed, old system: 0.87
(3 / 13.7 * 4. I.e. odds of an item being usable by you, times 4 items per boss)
Then I computed the likelihood of you actually getting an item per boss killed, based on how many of the possible items you already owned. For the new system it's a straight 15%. For the old system it's the likelihood of an item dropping that you can use, then the likelihood of you winning the roll against the statistical average competition, so 0.87 * (1 / number of people rolling).
Average loot per 100 bosses, old system: 15.9
Average loot per 100 bosses, new system: 15
*EDIT: I had this mislabeled before as a percentage "chance of getting loot per boss". Because under the old system bosses could drop multiple useful items, the actual point % for any given boss was a bit lower, but since you could win multiple items the average comes back up.
So this shows a slightly higher rate of loot acquisition under the old system, but pretty close. (And, again, my assumption about the amount of competition you have is probably off.)
But what this analysis DOES not factor in is people passing or trading gear. Although the old system was famous for people rolling Need for off-spec, to trade, or just to be a jerk, the fact is that lots of people DID pass on loot they didn't need, and as the season progressed and people got bettered geared, there were more people like that. That factor dramatically affected loot rates for everybody.
Again, I welcome corrections to this analysis. Post in this thread if you have better numbers and I will update the model.
The other thing I've been thinking about is how the new system feels.
I got mad at a blue poster (GC?) a month or so ago because somebody posted that he wants to see who wins what because he misses the "drama" of loot. GC interpreted this as "loot drama" and thus the change was good, but I believe the poster meant the more positive definition of drama, i.e. "dramatic". And I have to agree....there's an exciting denouement when the loot drops and everybody rolls and you hold your breath and you think "Oh drek! I JUST MISSED winning that item."
In the new system you don't even see your roll. You just suddenly get a message on the screen telling you what you won. So you spend less time being excited/wondering, and you have no information with which to tell yourself you "just missed it".
Elder Coins make it even worse. I've noticed that I feel significantly more cheated when my coin fails than when I get a bag of gold for normal loot. This is totally illogical, because the coin does in fact give me an increased chance of winning loot (as opposed to not have a coin, that is.)
But coins are supposed to feel like a bonus chance, so it feels like a bigger letdown when they fail.
1) Show the loot everybody wins, and show people their own rolls. Both pieces of information will make it "feel" like a closer thing.
2) Give every player a hidden variable of their chance of getting loot, and for each failed roll increase that variable by a small amount. Say, 2%. If you go an entire week of full LFR with no loot, your next roll would get a +32% roll.
Some additional suggestions that have shown up in this thread:
3) Increase drop rates for faster kills.
4) Allow people to "pass" on their loot, giving another (random, eligible) player the chance to take it or pass, and so on. This needs some incentive to pass instead of vendoring, such as "karma" points that increase your chances on the next boss or bosses.
5) Show players their own number rolled.
6) Don't make the roll instantaneous; give the player the sense (even if illusory) that they are "doing something" when making their roll.
7) Give better consolation prizes than just gold. Chance for pets or mounts, valor points, reputation points, gems, flasks, etc.