Major TL;DR:
This page is incredibly long and less a presentation than a big scratch sheet of paper for me when doing my work on these calculations. Not all of you will want to read it, so I want to sum it up as concisely as possible. The long and the short of it is proc sets are OP, just as we suspected all along, and ZOS's fix of removing crit from them made nearly no difference in them. If I were to give rough estimates of the weapon and spell damages equivalents of the proc sets Viper, Selene, and Skoria, it would be at roughly 900, 1900, and 800 unbuffed. Presently, I don't have the applicable ranges figured out yet, but know that these numbers go up when using weaker attacks and go down as you crit higher and more frequently. I am working on an equation to predict the weapon damage equivalence of proc sets in a given scenario. The only things that I am really missing to verify these calculations are parses from in-game and someone to check my work and thought processes. If you still want to read the rest of this, well, enjoy.
Proc sets have been around for a long time, and for a long time we have been saying they were overpowered. Unfortunately, because of how they work, it is difficult to actually measure how strong they are. There are already innumerable interacting variables that affect damage and no one wants to go to the trouble to figure these things out quantitatively. I don't even want to do this, it's a mess and very time consuming and rather imprecise. I also had been acting under the assumption that someone had already gone to the trouble to do this and would soon post the results.
TLDR, this paragraph is somewhat off-topic and you can disregard it:
Well, today I was bored and thought about the last week. Before this week, the only spec I ever played was magicka and the only class I ever really touch is Templar. I got bored with that on Monday and decided to mess around with one of my many toons that I had already leveled to 50, my bosmer stamina dragonknight. I have been buying sets and trying out many combinations trying to get something that fit my playstyle, because of course the end goal is to 1vX (in this case, in Sotha Sil). It was fun, though very weak for many reasons, but I can tell when a set is or isn't performing to my needs. I wanted a very high damage build without crippling my defense nor sustain, like my magplar's. High, even unreasonable bar to set, I know. The best place to start was the meta, and, well... skipping the details I tried many sets that just couldn't meet my standards. The only thing I had not looked at were proc sets, because I absolutely refuse to use proc sets. It is my opinion that they are so overtuned and anyone using them is crutching and not worth serious consideration as a great player. Without real evidence, however, my feelings on that aren't really worth a damn (wont change how I feel though). Tired of waiting for the analysis to be dropped into my hands from someone like Asayre, I got off my lazy arse (figuratively, not literally. I was seated the entire time) and got to work.
My first stop, Sorcerer Arithmagic, led me to the UESP build editor which I trust to be very reliable and accurate, if not incredibly frustrating to navigate (don't hit the backspace button or you may lose everything). Now, earlier today I did a few calculations (and the results will shock you!) but let's take a new example, fudge it a little bit, and hope it still works out. If not, I'll type up my results of previous examples in order to get a point across or something. I have not run these numbers yet, they will be new to me as I type them. Let's consider an Imperial Stamina Dragonknight. This sDK will be a total scrub in PvP and he wants to make a build that can deal the most damage possible while spamming Wrecking Blow. He decides on Clever Alchemist and Fury because of the sheer amount of weapon damage available in them.
Starting from scratch, a bare naked player has 7958 Stamina and Magicka. He puts 64 attributes into Stamina, which add 111 each, so adding 7104 Stamina onto his base for 15062 Stamina points. Somehow, this scrub has got his hands on perfect gold versions of Fury and Clever Alchemist. In fact, he is a developer and hacked the Live game to have the Fury jewelry have robust traits in legendary (gold) quality. These jewels have 870 Stamina each, which adds 2610 Stamina to his base for a running total of 17672 Stamina. Because this player has a modicum of sense, all of his traits are Impenetrable, because he wants to live through the crits he sustains. All 7 pieces of gear have gold stamina enchants on them, adding 868 on the three large pieces and 351 on the four small pieces, which amounts to 4008 Stamina bringing the total to 21680 Stamina. Fury has a single stamina set bonus of 967 at full golded quality, topping his base Stamina off at 22647.
The Scrub-onknight now equips his sharpened gold battle-axe of fury, because as you can imagine he never got high enough in a campaign to get a nirnhoned one, and he wasn't thinking about the benefits of a sword or a mace. O well, his loss. His weapon damage is 1571. That's okay though, because he has used a dev command again to give himself 100% uptime on clever alchemist, and he found a bug with caltrops that let's him take a crit from that every second forever, wherever. He neglected to share or fix this bug. Clever Alchemist contributes 790 weapon damage and Fury adds another 879. He also has 3 golded weapon damage enchants on his jewelry which combine to add 522 weapon damage, bringing his base weapon damage to a total of 3762. Crazy!
Now, this reinforced mantis shrimp is wearing 5 medium armor and has excellent uptime on both forms of brutality because he is a DK, so we multiply 3762 by 1.37 as see him walking around with a whopping 5154 weapon damage. His stamina, because he is wearing 1 piece of heavy, is boosted 14% through being an imperial and using undaunted. This brings it to 25817. It's somewhat low, but that's because his food ran out! He chugs 5 Dubious Camoran Throne, just to be safe, for 3192 Stamina, bringing the final value of it to 29010. Did I round? Slightly. Why? Get over it. If he can cheat, I can round to the ones place.
According to UESP, the tooltip for Uppercut is equal to 0.14935S + 1.56805W + 2.14396, with S being Stamina and W being Weapon Damage. Let plug these numbers in and... we get 12,416. I am doing this with you and, well, I actually expected higher. But remember, this is no CP. OK. Moving on!
So the other devs found and fixed his precious caltrops bug, so the Dumpsterknight decided to switch out Fury for a more reliable set. Maybe one he can gank with. He has been silently reading the forums and noticed how everyone is calling proc sets OP, so he thinks he must have it for himself. He gets a full set of viper, golded, perfect, with jewelry. He looks at it. He sees he is trading his hacked Fury for a legit Viper and the only real difference in damage output is the trade of 879 weapon damage for 6400 poison damage every 4 seconds. So, his weapon damage drops from 5154 to 3950. Quite a lot! Is it worth the viper proc? Even I don't know yet! Let's find out...
Using the equation above, the tooltip comes out to... 10528.
So lets put him into a fight now, shall we? You have found yourself in the unfortunate position of having 0 resistances. This could be a bug, or it could be corrosive armor. Doesn't matter. In four seconds of you derping off in a load screen, he hits you with a WB spam. If he has Fury on, you would have taken 37249 damage in three hits, or 49666 in four hits. If he has Viper on, you would take 6400 damage on the first hit and then 31585 damage from the 3 hits of uppercut, for a total of 37985 damage. In four hits, you'd take 48514 damage.
Wow. I did not honestly expect that. By the fifth hit, viper will be in the lead again. This was also assuming robust fury jewels, which do not exist. I think this speaks for itself.
Note that these numbers have assumed no crits and battle spirit has not affected them yet. This is not to say you must be dead from this damage, or whatever. The key tidbit of information to get out of this is the effective weapon damage that proc sets, in this case specifically viper, have. Perhaps this will convince people (devs) that they are absurdly high? Ah, whatever. As I said above, if my assumptions and calculations are correct, this should speak loudly and clearly. If you notice any errors or improper reasoning, please bring it up. I made a number of them in the first few tries of this earlier today; after all, I'm not Asayre.
Anyway, let's stick to talks of builds, funny stories (like the time I got jumped by 8 AD as I rode across the bridge and they bashed me to death as I fell out of my chair laughing), map strategy, which in game snacks you prefer, and of course... Ice trebs.
Really dissapointed.