So after damage being nerfed by 10%, and then with it reverted, I feel like a lot of people are confused about why it makes such a huge difference in match duration and overall feel of arena... Maybe even Blizzard. Some people may expect that 10% less damage means it takes 10% longer to kill an opponent in arena, but this isn't the case.
TLDR: Blizzard doesn't always think enough about what they're doing and sometimes it shows. The 10% damage nerf can increase match duration by a lot, while still not fixing the burst issue of some classes.
Disclaimer: This is napkin math without any real data. It does nothing more than illustrate the kinds of problems umbrella changes in %damage can cause and doesn't prove that the hotfix did cause these sorts of issues (although anecdotal evidence would suggest that it did).
The following is a time to live (TTL) graph and it shows how long it takes a player to die given a specific amount of health, dps and healing. The basic formula is:
TTL = health/(damage per second - healing per second)
The following is a graph with Dps along the x axis and TTL on the y axis in seconds. I've chosen some arbitrary values for health (300k) and hps (10k).
It's clear from the graph that below 10kdps TTL is infinity, which should be obvious because if you do less damage than healing then you aren't killing anything. The major take away from this is when dps is very close to hps, then very small changes in the dps cause a very large change in TTL.
The following graph shows the same TTL curve with the 10% damage nerf (in green):
Lets compare some values from the two curves.
@15kdps
TTL(prenerf) = 60s
TTL(nerf) = 85.7s
% increase in TTL = 42.8%
That's a huge difference in the time it takes to kill someone in arena. Of course the values I've chosen are arbitrary and arena is more dynamic, so lets look at some more examples.
If we consider a simplified situation using the most popular ideal match duration (from a poll in another post) of 4min and calculate how the 10% damage nerf affected this ideal.
Here I'm calculating how much more dps than hps to get a 4minute match.
(dps - hps) = 300000/240
(dps - hps) = 1250
Since we don't arena in a vacuum where healers are afk and people die to auto attacks over 4min we need a value for hps before applying the nerf. I'm going to choose the same an arbitrary hps value as before of 10khps. The amount of healing does affect the result.
dps = 10k + 1250
dps = 11.25kdps
TTL(nerf) = 300k/(11.25k*0.9 - 10k)
TTL(nerf) = 2400s, or 40minutes(!)
% increase in TTL = 1000%
Again, this is a very simplified situation using values I've invented instead of real data, but I think it illustrates the point. When dps is close to the hps then very small increases, or decreases, in dps cause huge changes in the feel of the game. However dampening would also prevent this from happening, but dampening shouldn't be relied upon to make the game playable.
In real arena matches dps isn't constant; it fluctuates. The above shows how much the nerf affected a low constant dps (i.e. without cooldowns or procs). We know some comps are scoring kills in 6s or less (god comp, jungle, combat rogues, etc...) Lets see how much the nerf affected these situations.
TTL(prenerf) = 6s
(dps - hps) = 300000/6
(dps - hps) = 50k
And choosing an arbitrary hps value of 10khps...
TTL(nerf) = 300000/(60k*0.9 - 10k)
TTL(nerf) = 6.82s
% increase in TTL = 13.6%
In this specific invented situation the 10% damage nerf only gave a fraction of a second of extra time to try and survive, which is less than a global.
The takeaway from this is that the nerf greatly affected situations that were already fine (constant damage pressure), and barely affected the situations that were out of control (burst during cooldowns for specific classes).
The safest way to blanket nerf burst is to increase health. Lets look at a 15% health increase (tldr it's going to increase the time for both situations by 15%)
TTL(burst) = 6s
TTL(burst, with extra hp) = (300k * 1.15) / (50k)
TTL(burst, with extra hp) = 6.9s
% increase in TTL = 15%
TTL(constant dps) = 240s
TTL(constant, with extra hp) = (300k * 1.15) / (1250)
TTL(constant, with extra hp) = 276s
% increase in TTL = 15%
However this causes an issue where % based heals are improved.
So what's the solution? Now that the 10% nerf has been reverted the game isn't really better, but a different kind of bad.
I have some suggestions:
1) Reduce the amount of guaranteed healing (instant heals, dps self healing, and abhorrent talents like ysera's gift and spirit bond)
2) Remove or change % health healing (warlock heals, conversion, and aforementioend ysera's gift and spirit bond)
These changes lower the amount of guaranteed healing making adjustments to overall dps less chaotic; giving more room for error when making balance changes. In cases where a class needs self healing as a survival tool then it should be counterable (casts), dispellable, or have a major dps tradeoff.
3) Adjust the burst of problem classes individually by nerfing burst cooldowns instead of making umbrella changes that affect every class and spec. Increase damage elsewhere to make the adjusted classes stay viable in PvE (this actually assures that a class still puts out decent pressure in pvp)
4) Finally some consideration should be given to changing dampening to some other mechanic that prevents matches from lasting too long. Much in the way that %dmg nerfs affect classes and comps different, so do %healing reduction during dampening. Also long drawn out matches that go into deep dampening aren't exciting.
Ok then. I actually find thinking about this stuff fun...