Avoidance, Mitigation, and Damage Smoothing

The last time we looked at paladin Monte-Carlo simulations, I talked about the possibility of quantifying the damage-smoothing effect.  Before I was able to get around to finishing this post, I revisited the Warrior simulations, and slipped in a sneak preview of how I intended to do that.

The basic idea is that we run the simulation like usual, but we take a moving average of the damage taken per second over the last 5 attacks for the entire encounter.  This 5-attack moving average is our measure of spike damage; the damage that we take in a given 7.5-second period.  The assumption is that “control” stats smooth the damage intake patterns and reduce the representation of high-DTPS values in the moving average, shifting the distribution to lower-DTPS values.  The way we see that is by plotting a histogram of these DTPS values and look at the distribution directly.

To see whether this hypothesis holds water, we’ll try it with four different gear sets.  The first is basically the default gear set I’ve been using in other MATLAB simulations: a moderately balanced, “traditional” tanking set.  The stats are as follows:
STR: 9208
Dodge rating: 4834
Parry rating: 4892
Mastery rating: 6758
Hit rating: 1521
Exp rating: 1777
Haste rating: 0

For the next set, we shift about 4000 rating into hit, expertise, and haste:
Dodge rating: 2834
Parry rating: 2892
Mastery rating: 6758
Hit rating: 2521
Exp rating: 2777
Haste rating: 2000

For the third set, we shift 1000 of that mastery over into haste as well:
Dodge rating: 2834
Parry rating: 2892
Mastery rating: 5758
Hit rating: 2521
Exp rating: 2777
Haste rating: 3000

For the fourth set, we go to the other extreme, and shift all of that haste and 2500 hit and expertise over into dodge and parry:
Dodge rating: 7834
Parry rating: 6892
Mastery rating: 5758
Hit rating: 21
Exp rating: 277
Haste rating: 0

So, without further adieu, let’s put these four gear sets through the sim and see what it spits out.  Here’s the histogram for set #1 (“traditional”):

Gear set #2 (“Mitigation, low-haste”):

Gear set #3 (“Mitigation, high-haste”):

Gear set #4 (“Avoidance”):

You can see just by looking at the distributions that there’s a difference here.  The “avoidance” gear set (#4) looks more symmetric.  The “traditional” gear set is a little lopsided, while the “smoothing” gear sets are both even more lopsided, skewed to the high-damage side.  And correspondingly, they have higher damage intake. But they also look like narrower distributions – more data huddled in the center, and less at the extremes.  To highlight the differences here, let’s consider some statistics.  In particular, the mean and standard deviation of the histograms.

        set #1    set #2    set #3    set #4
mean    0.5261    0.5365    0.5444    0.5138
std     0.1479    0.1341    0.1346    0.1628

OK, so so far our hypothesis seems to hold water.  The “traditional” and “avoidance” gear sets (#1 and #4) take less damage overall than the mastery/haste/hit/exp gear sets (#2 and #3).  However, the standard deviation of the distribution is larger, meaning the damage spikes vary more in size, suggesting that the smoothing gear sets do indeed seem to smooth the damage intake.

However, standard deviation doesn’t tell us enough to feel comfortable with our conclusions.  It says that the distributions are narrower, for sure, but that doesn’t implicitly mean that those distributions are less dangerous.  Maybe we’ve just mopped up the lower end, which is the part we didn’t care about in the first place.

There’s a more telling statistic we could consider that will give us those answers, though.  Let’s for the moment say that we care the most about the damage spikes near the top of the distribution.  That seems sensible – these are going to be the largest damage spikes we take, and the most likely to kill us.  Reducing the number of those events has a disproportionate effect on our survivability, because we’re removing the most dangerous events.  Let’s calculate what percentage of events fall above 80% and 90% of maximum DTPS for each gear set:

       set #1    set #2    set #3    set #4
80%    3.1340    2.2265    2.3817    3.6678
90%    0.7907    0.3500    0.3770    1.2093

Aha.  Here’s the smoking gun.  Only 2.2%-2.4% of all events were higher than 80% of maximum possible DTPS for the smoothing gear sets, compared to 3.1% and 3.7% for the traditional and avoidance sets.  The 90% cutoff is even more distinct: 0.35%-0.37% for the smoothing sets, 0.79% for the traditional set, and 1.21% for the avoidance set.  That means we’re about 3 to 3.5 times less likely to see the most dangerous damage spikes with one of our “smoothing” sets than with the avoidance set.

Thus, it seems that our “smoothness” argument can be quantified, and has a decent bit of merit.  To reduce the number of high-damage events by a factor of ~3 (which is arguably an increase of a much larger factor in survivability), we sacrifice some average mitigation.  We also get a few fringe benefits: our damage intake is more even, which helps our healers, and we do a chunk more DPS because hit, expertise, and haste are also great DPS stats.

This also has some implications for how we gear while leveling, believe it or not.  These results mean that much of the ret gear we accumulate while leveling is actually also really effective protection gear.  And you will be leveling Ret if you’re at all concerned about efficiency (and if not, see Rhidach’s article on how to make your slow, boring grind as protection a little less boring and slow).

With the expansion coming out tonight, I will probably be too busy this week to do much more posting.  So, on this, the last day before we all log in and forge ahead on the new continent of Pandaria, I say to you:  Go forth, kick some ass, and see you at level 90!

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20 Responses to Avoidance, Mitigation, and Damage Smoothing

1. Lakh says:

TY for all the work you’ve done & information you’ve helped make available, it’s been invaluable. I have several guildies who are vocally jealous of the quality & quantity of tankadin theorycrafting out there when compared to their own specs =)

2. Zaephod says:

Echoing Lakh’s response, thank you Theck for your wonderful and thorough work. Hopefully I’ll get some real raiding in this expansion and be able to put this stuff into practice

/salute

3. kalbear says:

This is an absolutely brilliant post that caps so many other great posts. This in particular is really, really excellent in illustrating how tanks don’t care about damage overall, but damage taken in ‘scary’ places – past a certain point of course.

Really nice work. The only thing I think would be an improvement here is to show how at the low end this can be problematic (because the overall level of damage is too high) and at the high end it can be problematic (because statistically not avoiding 3+ hits or damage is essentially statistically unlikely.

4. Knaughty says:

I’m glad to see that the maths backs up the hunch. I was going to recommend gearing for smooth damage intake, so I’m glad to have something to point to as proof.

When you get time (IE: After L90), how about a mitigation value chart that plots “reduction of DTPS events above the 90th % of baseline gear” against hit, expertise, haste, mastery, parry, dodge.

I’m expecting hit, expertise & mastery to be in the top 3 spots and I’m hoping mastery is first.

• anafielle says:

Sorry Knaughty, you got caught in our spam queue somehow! We rarely check it and I just found your comment. Apologies for the delay!

5. Wrathblood says:

Very interesting work. Nice idea charting out the frequency of the upper-bound relative outliers for DTPS. The relationship between the Balanced (#1), Avoidance (#4) and the more Mastery-focused Control gear-set (#2) pretty much turned out as expected (though to be honest the damage saved by the Avoidance gear-set was less than I’d expected. I was working with lower-level gear so hitting the Hit and Exp caps taking more of the budget may have been part of it).

#2 was #3 was a surprise to me, though. Not surprising that Mastery would reduce damage taken by more than Haste, but Mastery being better at *smoothing* damage than Haste was a surprise. Since time when SHoR is up would never be in the 80% or 90% range, I take it to mean that Mastery’s increased blocking ended up kicking in more often than Haste improved ShoR uptime.

On the one hand, improved ShoR uptime is going to be more valuable than blocking more hits. On the other hand, that starts veering into incoming DTPS territory and Mastery would then have to be given credit for increasing ShoR value, which is a contest we know Mastery will win.

I think its fair to say that a blocked melee blow will probably never count as spike damage (other than situations with unblockable physical damage), meaning Mastery > Haste in terms of damage smoothing as well as damage reduction. That’s interesting and not at all what I expected. I need to do some editing.

You don’t have ShoR uptime for the sets, do you?

• Theck says:

Yes, they’re in the title of each plot. S=x% is the SotR uptime percentage.

• Wrathblood says:

Oh, so that’s what that is. Thank you.

6. Nice work. Keep the good work going.

7. Paxen says:

Great work!

Would it be possible to run some similar tests for Brewmaster Monks? The little theorycrafting I’ve seen on that implies that Mastery may be a poor stat, so I’m wary of their conclusions.

Does anybody have any links to solid Brewmaster theorycrafting?

8. Paxen says:

Excellent work. This may be the first time I’ve actually seen numbers that show exactly how the randomness of avoidance is dangerous for a tank.

Is there any chance that you could run a similar simulation for Brewmasters? Their AM is so different that it’s hard to say if it actually does smooth out the damage.

• anafielle says:

Sorry Paxen, you got caught in our spam queue somehow! I’ve just approved your comments today.

9. Wrathblood says:

If I could make request, once you’ve got characters leveled up, professions together, etc would it be possible to run the above exercise, except trading points between Haste and Expertise? Backing into a ballpark number for Hit from Expertise is easy and with the above model, an idea of Haste to Mastery is workable, but I’m curious to see how they trade off against each other.

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