Unfortunately, that's not possible with the data I have. The export from World of Logs only contains the total damage done by the player and it's not broken down by target in any way. CompareBot can show the damage per target on an individual parse level but that's the best I can do at the moment.
Based on the data provided by raidbots, I compared the relative standard deviation (stddev divided by mean) of varying classes and encounters aka how widespread people deal damage. Done manually, this is quite cumbersome, but this could be something that raidbots could provide on its own. What are your thoughts on it?
Anyway, here is the data: The higher the graph, the more widespread the distribution, i.e., damage varies more.
This is all based on 25man Fireland bosses without Alysrazor (which just fucks up any statistic). For comparison the SimCraft numbers for a Patchwerk were added to see how RNG a spec is under optimal circumstances due to crit, procs etc.
Subtlety, Beast Master, Frost Mage have very low samples overall - do not look too much into that.
Same is true for the 8 Fire Mages that killed Baleroc HC .
95.4% (i.e. two standard deviation left and right from the average) of the people do average +- X% on the given boss.
In other words: As an arms warrior, the damage I and my colleagues deal at Rhyolith is between 45% below and 45% above the
average. If I were an assassination rogue, the damage would only vary between 38% below and 38% above.
Reasons for a big spread include:
Different roles on a fight (Beth'tilac as melee on or below the web)
Different raid buffs and overall raid dps
Different skill (class and encounter-wise)
Reasons for the spread being bigger for class A than B:
Class A can be used in more different situations
Characters from Class A have bigger gear differences between each other than Characters from Class B (unlikely)
Characters from Class A are used in more different guilds (from noob to pro) than class B (unlikely)
People from Class A are played by a bigger variety (skill wise) of people than Class B (unlikely)
Class A is harder to master than Class B
Reasons for the spread being bigger at encouter A than B:
More different roles
Randomness of the encounter
More different people managed to kill the encounter (Baleroc nHC vs HC)
I won't go into much detail about interpreting this data as a lot things have an impact, but two things are likely to be true: all classes are quite close together, with feral cat, arms and balance being somewhat harder to master or, in other words, leaving room for stellar play. Harder encounters which require good execution and good dps have a lower variety but are still surprisingly different.