Anaxie's Totally Revolutionary SoO Retribution T16 BiS & Theorycraft

[Maegor]

Why do you think that higher difference between mode and mean means more inconsistency?

Let's look at these 2 sets of 10 numbers.
a) 9, 9, 9, 10, 10, 10, 10, 11, 11, 11
b) 6, 7, 8, 9, 10, 10, 11, 12, 13, 14

Both these sets have mean, mode and median equal to 10. Yet a) is a lot more consistent for our purposes.

This isn't what mode means in probability. Histograms produced by simc are similar to a discrete probability distribution, and the definition of mode for that is: "The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled."

This pic shows what I am talking about:

Both graphs are positively skewed (like our simc distributions). Notice that the median is the same, but the mode/median/mean are closer together on the distribution where the std dev is smaller. You are more likely to reproduce the mode of your damage than you are the mean. Therefore, the closer you can make the mode to the mean, the closer you will get to your simdps in all of your pulls.

Granted, and as you have stated, a ton of our damage is from factors related to rng well out of our control (4pc especially). So, eliminating all of the "chance" from our rotation is impossible, but we should try to eliminate as much as possible. Which, btw, from your armory, looks like you are trying to do. Not many people are saying go full retard on mastery to the detriment of crit. But for us, it really doesn't take much crit to make mastery more appealing again, so when you see crit jump ahead, don't go full retard into crit either; even though the differences between dps at the extremes of each are comically small. Seems like at a point, it is hard to fuck up our stats.

PS: I still think something weird happened on your "default" build for your simdps to be at 340k, while your "extreme" builds were all at 354k.

[Weightlifter]

Finally some real mathemathics instead of "shiieeet bros, check our mah new toy, ain't I awesome"


<If you have a problem with the way things are going, the best step is to start to change it yourself. Please, instead of posting like this, which is equally as dribble, contribute mathematics as well if you feel that is what needed. And do not remove Mod warnings.>

[Meiffert]

This isn't what mode means in probability. Histograms produced by simc are similar to a discrete probability distribution, and the definition of mode for that is: "The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled."

Well, how is 10 not the mode in my examples then? It is the most sampled value in both of them (4 times in first, 2 times in second).

PS: I still think something weird happened on your "default" build for your simdps to be at 340k, while your "extreme" builds were all at 354k.

These aren't extreme builds, the default build is what my armory shows, the other builds simply have 3k more of one stat (not reforged, just added extra).


Edit: What do you think of these two distributions?
a) 8, 9, 9, 9, 9, 10, 10, 11, 12, 13
b) 6, 7, 8, 9, 9, 10, 11, 12, 13, 15

Now both of these are positively skewed, both of them have a mode equal to 9, both of them have a mean equal to 10 and yet one of them (a)) is clearly more consistent.

[Maegor]

These aren't extreme builds, the default build is what my armory shows, the other builds simply have 3k more of one stat (not reforged, just added extra).

I'm at a loss as to how you think that furthers any of the discussion.

Edit: What do you think of these two distributions?
a) 8, 9, 9, 9, 9, 10, 10, 11, 12, 13
b) 6, 7, 8, 9, 9, 10, 11, 12, 13, 15

Now both of these are positively skewed, both of them have a mode equal to 9, both of them have a mean equal to 10 and yet one of them (a)) is clearly more consistent.

I see you are fond of making up numbers and using them to argue. You did the same in post #6088 when you tried to say mastery wasn't consistent, when all you really "proved" is that the 4pc is rng, and then said you couldn't do the math for crit, so you really didn't even finish your argument. Never mind that in your "proof" you didn't even acknowledge that your "more mastery" scenario raised your "damage" values ~25%, which when swinging between mastery and crit (which you didn't do), you won't have a swing that much.

As for your sets above, they have no correlation to what we are discussing. With my gear, I have shown and explained that mastery is more consistent. Frankly, there is nothing more I can say to explain this to you. If you want to do what I did, and actually reforge and post your histograms, then we can analyze what it looks like for your gear. Although, tbh, I would like to see it done with a hc or hcwf thok and 575 or higher ilvl.

[Meiffert]

I'm at a loss as to how you think that furthers any of the discussion.

I was trying to see how much more inconsistent my damage becomes when I add mastery and compare it to how much more inconsistent it becomes when I add crit. Do you think that the results will be a lot different if instead of just adding crit I also remove the same amount of mastery to better represent how reforging works?

Edit: Ok, here are the new results, I changed my Thok trinket to hwf version as requested.
Haste > mastery > crit (my current armory setup except with the trinket upgrade).
Dps: 350915
Range: 18330 (5.22 %)


Haste > crit > mastery setup (4119 mastery rating reforged to crit).
Dps: 349865
Range: 18007 (5.15 %)


The damage of both setups is very similar (full mastery being 1050 or 0.3 % higher than full crit).
The mastery setup has slightly higher damage range as calculated by simcraft (ignoring 5 % of worst and best tries).
Mastery also surprisingly has lower weakest result out of 50k pulls by about 6k damage, although we know it has higher absolute worst case scenario (it is just really that infrequent).
Mastery has slightly higher damage on best pull by about 1.5k.
Other than that both histograms look similar to me and please don't tell me that mastery graph is "slimmer" and positioned more to the right and therefore more consistent when we both know the reason it is slimmer and slightly more to the right is because we see a bigger part of the X axis and the whole picture is horizontally compressed by about 10 % compared to crit histogram because of the more extreme worst pull of mastery setup.

I see you are fond of making up numbers and using them to argue.

Yes, I am. That is how disproving a theory with counterexample works.

You said that higher difference between mode and mean equals more inconsistency and showed an example where it is true. I then showed another example where is isn't true.

It's like saying that odd numbers and primes are the same thing and showing examples: 11 and 13 are odd and they are also primes, 8 and 10 are even and they aren't primes. I then show that this hypothesis is wrong because 15 is odd, but it isn't a prime.


You also seem to imply that I try to prove that crit is more consistent than mastery which would mean I somehow win this argument or something.
But that isn't true in the slightest. I don't care at all which one of them is more consistent, I only want to find out.
When I joined this discussion, I actually expected crit rating (below 50 % crit chance) to add more inconsistency than mastery rating.

[Maegor]

Now see, that's good data. When I have more time tomorrow I will try to take a closer look at it.

[Huntingbear_grimbatol]

Try using simc with someone that has gone to the extreme with mastery (take my char in sig if you want) I'm at 20.8k mastery raidbuffed (still 17k haste, 3.5k crit iirc) sim that, then remove say 10-15k mastery and put it into crit. You're not gonna see a huge difference in the loss/gain of 3-4k rating either direction, there are items with haste and crit on them in SoO which we CAN get but we've chosen not to (unless you're human ret pally I suppose, 2h sha sword). Just with reforging and swapping out some gear pieces I got my unbuffed crit to ~20% iirc, that was with mastery/haste items and mostly mastery/exp or pure mastery gems. If you really wanted to you could easily get to 30% crit unbuffed.

For more clear numbers go to the extremes :P
You could also see what would happen if you kept mastery and crit equal. Oh and for fun, put haste, mastery and crit at the same ratings but mastery 1+ rating above and then use Rune of Re-Origination (lei shen agi trinket). I had a bit of fun with that (just messing around) on live doing 5m Holy Light damage per divine storm (10 targets roughly so 500k HoL per)

[xarxz]

mfw raid comp, lag and strat are going to affect your dps far more than any pissing match re: stat weights

[Octa]

mfw raid comp, lag and strat are going to affect your dps far more than any pissing match re: stat weights

Anyone care to go through the 6k posts and see how many times this has been mentioned? I'm willing to guess a few hundred.

The point of the discussion isn't which factors, out of all the factors that exist, affect your DPS the most.

[Deleted]

Looks like I'm the one going to try to go all out crit (including items) just because I'm curious to see what happens. And I got another ret by my side that goes all out mastery, so I'd have a good comparison. We both do just the same so that should be interesting.

[Calimon-ZJ]

Is there any way I can get more mastery out of my gear? Im hovering around 60% but I see a lot of rets at my ilvl with 65%+
Also, do you think a heroic juggernaut belt will be better than my heroic wf one from protectors? Ive been passing on it because of the str loss.

http://us.battle.net/wow/en/characte...limon/advanced

[xarxz]

Changing the belt bracers weapon shoulders and legs to the best in slot items would help.

[Huntingbear_grimbatol]

Is there any way I can get more mastery out of my gear? Im hovering around 60% but I see a lot of rets at my ilvl with 65%+
Also, do you think a heroic juggernaut belt will be better than my heroic wf one from protectors? Ive been passing on it because of the str loss.

http://us.battle.net/wow/en/characte...limon/advanced

You have 5 str gems, that's effectively 800+ thok 9% loss of mastery rating if you're going hard for it. Think I'm at the same ilvl as you with 17548 mastery unbuffed. Depending on your race, professions and what wep (mace is our worst pick imo) + offpieces we your mastery rating can swing by a lot. Other ret in my guild has around 3.5k less mastery than me with 0.2 higher ilvl.

Your biggest waste items is your wep(exp should be avoided on items as much as possible, Thok ring (same reason) and the belt because of the hit. Your bracers are actually my first choice, but I'm Draenei so I can skip 1 hit item in full bis. Any exp you can't reforge away on items is in effect mastery or haste you lost elsewhere.

[Bonkura]

Too much math going on here now. I think you guys killed anaxie.

[Calimon-ZJ]

My only other ring option is from blackfuse which has expertise on it as well (exp/haste). Well there's protectors but hit/crit... no thanks. Since haste can be changed into mastery via gems it shouldn't really matter which one I have. Belt for sure has me about 200 pts over hit cap and I've coined 3 heroic polearms but none of them have been WF so i'm stuck with the mace for the time being.

[Maegor]

Prepare for a wall of text.

Here are the assumptions/notes for the following data:
1. Each build uses the set in the OP to maintain consistency. Of course, if you want to go full crit, the Sha sword is obviously better, and I actually hit over 35% crit (meaning >50% raid buffed/inq) by swapping pieces around and didn't have to throw haste under the bus to get there.
2. I used AMR to build these sets. AMR doesn't have the leg cloak, so before I ran in simc, I changed the back name and ID, so get it in. If anybody knows of an easier way to build 6 builds quickly, let me know.
3. On mastery and crit builds, haste is second priority, and I tried not to allow any haste>other reforges in those builds. I also forced haste to be the same in both builds, since haste is obviously the best stat. This is to not favor the mastery build inherently since it output a greater amount of haste naturally, and would therefore always sim a higher dps. This cost the crit build about 1.4% crit.
4. In the table, the listed stats are in percentages and from the unbuffed column from the results page of simc. I have two haste builds, because AMR AND simc show haste raid buff values over 50% mistakenly (similar to the tooltip), so one is actually amr showing over 50% (with buff) and the other is amr capping at 50% (with the buff).
5. Blacksmithing and Engineering were the professions for the tests.
6. The Equal_Weights_in_Simc was the most equal I could get the weights to output in 10k iterations. Mastery and crit were even with haste a little below. Equal_weights_in_AMR means I set the stat weights equal for mastery/crit, put haste slightly ahead, but put a soft cap on it.
7. My x-axis interval value is (max-min)/5. If this is wrong, somebody please correct me, and I will edit accordingly. Also if somebody from Simc reads this, please know that I wtb y-axis values, so that we can measure how many iterations hit each dps value.
8. Each x-axis interval has 10 bars between it. I am strongly assuming this is the count of iterations that fell around that dps. Bar Differential = (x-axis interval/10)
9. All sims were done with 450s as the fight length and 50k iterations.

A summary of the builds:

Build	Haste	Mastery	Crit	Simdps
Equal AMR	37.21	44.40	22.20	371,919
Equal Simc	42.25	51.93	14.67	373,515
Haste No Cap	47.68	53.52	10.34	372,097
Haste @ 50	46.01	55.00	10.34	373,485
Mastery	34.95	68.21	10.93	370,461
Crit	34.95	38.98	26.73	369,084

Histograms:


Range: 14,254 (3.8%)
X-axis intervals: 14,205.2
Bar differential: 1,420.5
Standard positive skew look, with a sharper rise on the left side, followed by a shallower fall on the right side. Interestingly the average falls on the bar with the most iterations, but I would say it is slightly to the right of the main hump which I would call to be at approximately 369,788.


Range: 14,048 (3.8%)
X-axis intervals: 14962.4
Bar differential: 1,496.2
Similar in look, although with a higher max, and only a slightly higher min, the graph appears less centered and to the left. The average is slightly to the right of the bar with the highest value (# of iterations), and slightly to the right of the hump, which I am going to say is at 371,645.


Range: 13485 (3.6%) Lowest range of the 6
X-axis intervals: 13,432.6
Bar differential: 1,343.3
Graph does look "wider" than the first two, but that is to be expected with a lower range and interval value. Again, positively skewed. The high spike is about a bar and a half behind the average, but I would call the hump of the graph to be at 370,082.


Range: 13,667 (3.7%)
X-axis intervals: 13434.6
Bar differential: 1,343.5
Very similar to above. I would call the hump at 372,142.


Range: 14,665 (4.0%) highest range
X-axis intervals: 14,640.2
Bar differential: 1,464.0
I would call the hump at 368,997. Again positive skew. A lower min, and a slightly higher max, makes the intervals and bar differential higher. This is also a factor in having a higher range.


Range: 14,188 (3.8%)
X-axis intervals: 14,654.8
Bar differential: 1,465.5
Hump around 368,351. Closest average dps to what I see as the hump. A positive skew, like the rest. Lowest min, max and average.

Final Thoughts:
The heavy haste builds had the lowest range, however, the crit build had the closest average to what I saw as the hump. How you think we should measure consistency, would indicate that one of those 3 is the most "consistent". However, the crit build did have the lowest average dps, although we are talking about less than 2% from the highest dps build, which was the build where simc calculated the closest equal stat weights (not surprising at all). I would call the simc balanced and capped haste build the most successful since they had the highest "humps", and didn't have huge ranges (like the mastery build did). As has been talked about over the course of the last 50 pages or so, a higher haste build requires you to be quick (any hesitation inputting commands or even a high latency will cause that haste to be wasted), so choose what build works best for you.

One thing to note, is that as you get close to balancing the stat weights in a sim, very minor changes cause relatively large jumps in weight values. For example, in the sim stat weight balanced build above, m=c=5.45 and haste=5.1, but moving haste down even 150 rating caused it to jump ahead of both the others, and if that 150 rating went to mastery then mastery's weight would fall to around 5.1-5.2 while crit would get closer to 5.5.

Without a better way to pull more data from simc (really would like to be able to see the count of iterations on each bar of the histogram), it is going to be hard to measure such values as std dev and variance.

As I was doing this exercise, I thought of another way to measure consistency. Determine what dps you need to pull in an encounter, draw that vertical line on the histogram, and calculate the number of iterations to the right of the line. Then you divide that number by the total iterations, and the resultant percentage is how often you personally should have a successful dps number that will help your team. Obviously, there are tons of factors that affect your dps on a fight, so you may do lower dps, but since you have to move a shit ton, your dps may be lower. So this is only really a metric that could be measured abstractly, but I think it could be a good measure to see if individual raid members and classes can do the amount of dps required to complete an encounter, or if they need more gear, different build, or if their class is just broke as fuck.

Final Conclusion: balance your stats, and don't let one get way out of whack by totally avoiding it. Running too much crit was shown to actually gimp your dps, and too much mastery had the highest range. 99% of people will probably read that and say, "no shit", but it was interesting to go through the exercise. Hopefully, simc will start providing more data (or if the data I'm asking for is available, somebody can point my derp ass to where it is).

PS - this is going to be hard as fuck to do with the new stats in WoD, and I wish Theck and the devs of simc luck in wrapping their arms around all the possibilities.

Edit PSS - as said in an earlier post, it does seem hard to fuck up our stats as far as simming.

[Meiffert]

Great job doing all of this, Maegor.

Final Thoughts:
The heavy haste builds had the lowest range, however, the crit build had the closest average to what I saw as the hump.

As I understand it though, the hump isn't closer because our often reproduced dps is higher, but rather because our average is lower, which is somewhat unappealing for practial purposes.

How you think we should measure consistency, would indicate that one of those 3 is the most "consistent".

As I was doing this exercise, I thought of another way to measure consistency. Determine what dps you need to pull in an encounter, draw that vertical line on the histogram, and calculate the number of iterations to the right of the line. Then you divide that number by the total iterations, and the resultant percentage is how often you personally should have a successful dps number that will help your team.

I agree, this is actually essentially the same metric I suggested a few posts ago. Exept rather than asking "how often can I hit this dps?" I asked "what highest dps can I hit at least 95 (or 99) percent of the time?"
It would be great if the simcraft authors could add this feature.

Final Conclusion: balance your stats, and don't let one get way out of whack by totally avoiding it. Running too much crit was shown to actually gimp your dps, and too much mastery had the highest range.

Edit PSS - as said in an earlier post, it does seem hard to fuck up our stats as far as simming.

Yeah, I think the most surprising result for many is that mastery produces the widest range.
The best way to make your damage more consistent if you wanted to do it for specific encounters would be to stack haste.

[Maegor]

As I understand it though, the hump isn't closer because our often reproduced dps is higher, but rather because our average is lower, which is somewhat unappealing for practial purposes.

The hump is what I was calling the mode a few posts back. Which that is what is what we are most likely to reproduce, since that is where the density of our sims occur. Obviously, even to hit the humps (aka mode), you have to be playing near perfect. So any amount of high latency or mishits would put you lower, since a sim experiences 0 latency and never mishits. I don't know what more accomplished raiders consider successful, but if a person in my group can hit at least 80% of their sims then I don't view them as holding the group back (even though if I am there, I am upset with myself, but I raid in a casual setting, but am competitive with myself).

I agree, this is actually essentially the same metric I suggested a few posts ago. Exept rather than asking "how often can I hit this dps?" I asked "what highest dps can I hit at least 95 (or 99) percent of the time?"
It would be great if the simcraft authors could add this feature.

Like I wore out in the post, I want more metrics in simc. I want y-axis values so we can measure things like std dev, instead of try to hobble together that value together using range (which I think is possible, but I don't feel like digging through text books in order to back into that value ). You need to be able to measure yourself and your raid members, and see if they are likely, or even possible to hit the values that make an encounter successful dps-wise (healers and tanks can't be measured this way, especially healers. If anybody has a good way to measure healers besides the group staying alive let me know, because hps isn't it).

My idea above really started with the two sets of numbers I gave you shit about (and I'm not saying this is a unique or original idea at all, since I have been measuring my own raid members by this standard for months), where you produced two sets of numbers that had matching modes, medians and means (even though I will still say that in probability this was too simplistic of an example). If, in your example, 9 was the required dps, then set a (the more consistent set) would be successful 90%, while set b would only be successful 70%. It the required dps were 10, then both sets would be successful 50% of the time. If it were 11 or greater, then you either needed better gear, or were gimping your group with a broke class.

Yeah, I think the most surprising result for many is that mastery produces the widest range.
The best way to make your damage more consistent if you wanted to do it for specific encounters would be to stack haste.

I agree, the surprising results were that mastery had a wider range and looked less consistent than crit, and that a heavy crit build had less dps than mastery (I ran some sims that I didn't report with 35%+ base crit that did less dps than the crit build above). In hindsight, with our 4pc this shouldn't have been surprising, since free +50% ds's can offer a ton of HoL damage. Also, a ton of people have been saying that if you want to whore meters, then use DP, which only produces mastery attacks.

I will still contend that in belt situation mastery is a better stat than crit since almost all of your attacks on the belt should be mastery attacks (since even a normal gala trink lines up with AW on 95% of belt time). But, you can only do simc in 100s durations minimum, so you can't really measure mastery vs. crit in a short duration like the belts.

One thing I didn't stress enough above, is that moving stat weights is far easier than I imagined. Most people reading this thread know this, but for those of you that don't, if you sim weights and see crit ahead, it really doesn't take much crit to make mastery and haste jump back in front. So don't go full retard and change all of your gems because crit is 0.1 ahead (AMR will tell you to if you input the weights). If you are trying to get balanced sim weights then haste>mastery>crit is the rule (as has been said since it seems like the dawn of time). I only say this because we still have people ask, and I want them to understand how fluid weights are.

[paoani]

One thing I didn't stress enough above, is that moving stat weights is far easier than I imagined. Most people reading this thread know this, but for those of you that don't, if you sim weights and see crit ahead, it really doesn't take much crit to make mastery and haste jump back in front. So don't go full retard and change all of your gems because crit is 0.1 ahead (AMR will tell you to if you input the weights). If you are trying to get balanced sim weights then haste>mastery>crit is the rule (as has been said since it seems like the dawn of time). I only say this because we still have people ask, and I want them to understand how fluid weights are.

Reforge plots are an absolutely amazing feature built into Simc for doing exactly this. They're already used heavily in the Enhancement shaman community (Relative values of haste and mastery can have an absolutely obscene affect on dps).


In terms of discussion of metrics, I would actually like to see percentile values output by Simc to better see dps in various gear sets. You can get a MUCH better picture of strengths and weaknesses of different builds and specs by looking at the 10th, 30th, and 50th percentiles rather than a simple average. Being able to see various possibilities allows you to better tailor yourself to suit different fights/tiers. In the case that you are dealing with a "breakpoint" dps check like the Siegecrafter belts or (as a longer example) Lei Shen phases, being able to succeed 90%+ of attempts is extremely important. In these cases, your average dps is not the most valuable piece of information to you. Looking at something like a 30th or 10th percentile will give you a clearer picture of how you will be able to meet these checks. If you need to do 300k over x amount of time, it doesn't matter that you average 350k if you only exceed 300k on 50% of attempts.

Something that occurred to me as I write this that may be even more valuable is an option to input values to calculate percentile rankings. If you know you must do 300k+ dps, what percentile is 300k? Will you exceed that dps 90% of the time or 60% of the time? Individual dps checks are something that are comparatively easy to calculate on a per encounter basis, meaning that being able to view percentile rankings for your spec/build can give you a clearer picture of the consistency of success you will have with that spec/build.

I unfortunately don't MS ret anymore so I can't contribute much beyond a theoretical standpoint, but it's an interesting topic to consider. I'm probably going to make a post in either the Raids and Dungeons or General Discussion forums (not actually sure which would be more appropriate).

[Huntingbear_grimbatol]

Mastery has the potential in wild and extreme situations (once in a billion pulls) to have good crit procs (even if we avoided crit), that's the reason why mastery has a higher theoretical number. I don't find that particular strange given the fact that mastery will always increase your HoL damage, if you then get a pull with crits at the correct time ofc that's gonna be a huge factor. Same thing happens with a crit build but then it's the chance of crits you increase and not the crit damage, I am surprised that the crit average over time wasn't higher than mastery though.

- - - Updated - - -

Too much math going on here now. I think you guys killed anaxie.

Somewhere his head has melted :<

- - - Updated - - -

Something that occurred to me as I write this that may be even more valuable is an option to input values to calculate percentile rankings. If you know you must do 300k+ dps, what percentile is 300k? Will you exceed that dps 90% of the time or 60% of the time? Individual dps checks are something that are comparatively easy to calculate on a per encounter basis, meaning that being able to view percentile rankings for your spec/build can give you a clearer picture of the consistency of success you will have with that spec/build.

If whatever spec or class you play can only reach the required dps number 60% of the time then it's broken or you're playing it wrong or with wrong stat priorities, hell if you can't reach a bare minimum 90% of the time then you're bad or doing something wrong. Take siegecrafter belts again, if you can't do them each and every time then you need other people or more people.