Boss3 Test: Ronin

I recently rolled a Ronin, lucky that.  So, next up for Boss3 testing: Ronin.  

Here's the setup.

I put Scatter 4 crests on Ronin for the test.  As expected, the boss could not proc.  Good.

Here's the result:

71559684 damage.

Analysis: We want to figure out how many proc hits Ronin does.  PD is assumed to take 3 seconds.  Normally I assume that heroes other than PD (with the Blitz Scroll and Berserk 8) ramp up in 5s.  However, Ronin has a 650ms attack time naturally.  So I am assuming that he will take 4s to ramp up.  

Thus we have PD active for 177s.  He gets 5.0 HPS (all auto hits); 885 hits total.  Ronin gets 176s active, where he will get 880 auto hits.  Total auto hits: 1765.  Each one does 35000 damage, so these should have done 61775000 damage.  This leaves 9784684 damage unaccounted for, which must be Ronin's proc damage. 

We can divide by 35000 to get the total proc hits: ~279.6.  We can divide that by 176 to get the proc's HPS: ~1.59.  This does not match well with the assumptions made by Mr_Perfect in his reddit thread.  (He derives 1.25 HPS.)   My guess is that Ronin gets 6 hits per proc.  This would yield 1.5 HPS, which is reasonably close to our observed amount.

Boss3 Test: Beast Tamer

I ran a Boss3 test for Beast Tamer last night.  Given how much damage he does, and the fact that Grizzly cannot be given Scatter to pull the last-hero-scatter trick, I decided to run three heroes for the test: PD, HQ, and BT.  Adding a third hero has the downside that the boss will run out of hitpoints. 

I have previously tested just PD+HQ; that test can be found here.  So, with that result in hand we proceed to the BT test.  My BT normally crests Slowdown 4, but I removed it. 

I feel naked.

HQ has her talent, scatter 8, and her normal crests (berserk 4).  That should be enough scatter to keep the boss from proccing.   Here's the setup:

Let's kill a boss.

I did the run and it worked smoothly -- no procs.  The result?  As expected, 120m damage exactly: killed the boss before time ran out.  I knew this would happen, and so was carefully watching the time.  There were 18 seconds left when it ended.

18 seconds left out of 180.  So, 162 seconds spent.  But some of that was spent when PD was ramping up.  As in previous boss3 tests, I assume PD ramps in 3 seconds, non-berserk-8 heroes in 5 seconds. 

So now we can compute what BT got.  Over a run of 162s, PD should have gotten 159s of damage, and HQ 156s.  Thus, they should have totaled 27825000 damage and 28350000 damage respectively.  Total: 56175000 damage.  The remaining damage is BT's: that is 63825000 damage.  This was done by BT in 159s (effectively), so his DPS is ~401415.  We divide by 35000 to convert this to HPS: ~11.47.

How does this compare to what we'd expect?  Well, each of BT and Grizzly get 5.0 HPS individually from their autohits.  In addition, Grizzly has Heavy Blow 8, which gets another 1.25 HPS.  Then are their procs: BT's proc has a 12s cooldown, thus .0833 HPS.  Grizzly's proc has a 5s cooldown, thus adding .2 HPS.  [see comments]  Total expected hits is 11.333 HPS.  

The test confirms the prediction.

Boss3 Test: Heavy Blow

Heavy Blow is supposed to work via extra hits, 1 in 10 chance each.  Time to test it!  I am using my Harpy Queen again for this, removing her normal crests (Berserk) for Heavy Blow 4 crests.

Here's the setup...

HQ + HB

And here is the result:

HQ+HB damage.

67921653 damage.

When I tested this same pair of heroes, except using Berserk crests on HQ, I got 64953661 damage.  The difference is 2967992 damage.  Divide by 35000 to find extra hits from HB: ~84.8 hits.

As we have done before, we estimate HQ's ramp-up as if she was full speed for 175s.  So, at 5 auto hits per second, that's 875 hits.  The extra hits are almost exactly 10% of the auto hits.

Thus, the test confirms our model of HB.  Yay.

Boss3 Test: Grimfiend

Next up for Boss3 testing: Grimfiend.  In this case I feel it is known pretty well how he works, but there is still to some extent some question.  In particular, Grim's demon form has a cooldown of 3 seconds, but lasts 12 seconds.  At max speed, how does this shake out?  Does he proc 3 times per demon form (at 3 seconds, 6s, and 9s), or does he proc 4 times (also on 12s)?

Here's the setup.

I'm ugly.

As you can see, my Grim has scatter (it's at 6), so there should be plenty of scatter to stop the boss proccing.  His crests are Bulwark 4, which won't change the test more than trivially.

Here's the result:

PD + GF damage.

63806836 damage.

Analysis: We want to figure out how many proc hits Grim does.  Grimfiend has Berserk 8 in demon form, but he starts human, and he is not berserk in human form.  So I am assuming that he will take the same 5s (estimated) to ramp up as any other normal hero.  PD is assumed to take 3 seconds.

Thus we have PD active for 177s.  He gets 5.0 HPS (all auto hits); 885 hits total.  Grimfiend gets 175s active, where he will get 875 auto hits.  Total auto hits: 1760.  Each one does 35000 damage, so these should have done 61600000 damage.  This leaves 2206836 damage unaccounted for, which must be Grim's proc damage.

We can divide by 35000 to get the total proc hits: 63.05.  We can divide that by 175 to get the proc's HPS: ~0.36.  This matches fairly well with the assumptions made by Mr_Perfect in his reddit thread.  (He derives .32 HPS.)

We can also calculated expected procs.  GF will proc first at around the 4 to 5 second mark.  (Why not 7 seconds?  He does not get energy from being hit, but the PD is ramping up and GF is swinging faster.)  Assume it's 4 seconds.  Then at that point he transitions to demon form every 15 seconds.  Thus he gets exactly 12 transformations to demon form during the course of the run.  In all of those transformations except the final one, he gets either 3 or 4 procs.  (This is what we want to know.)  So we know he should get either 36 proc hits, or 48 proc hits.  Obviously, 48 proc hits is closer to what we observe (63 hits).  So I guess he is getting all four procs as a demon.  But the estimate is still low.  What explains the additional 15 hits?

Should run this again.

OK, next day.  Same lineup.  Result:

More PD + GF damage.

64263405 damage.  This is .7% more than last time, that is, easily within experimental variance.  But it's higher, so it's in no way suggestive that my result last time (with extra 15 proc hits) was a fluke.  Not sure what's going on here.

UPDATE: UraniumSnail pm'ed me to suggest the GF has Berserk 8 in both forms.  The wikia page is unclear on that; I guess I assumed wrong.  That speeds him up by 2 seconds in the ramp-up at the start, thus adding 10 hits.  (Estimated, natch.)  This gets us close.

Immortep Exceeds Expectation

I ran the Boss3 test on Immortep.  Like Vlad, I think Immo can trigger a proc if the only energy reduction on the boss is him with Scatter 4.  So I added my HQ to the lineup to make sure that doesn't happen.

Here's the setup:

Immo not evo.

Immo has on Bulwark crests, but you can't see that.  HQ has Berserk.  Neither of these should chance the test result more than a tiny amount.

And here's the outcome:

Better than Vlad!

106022552 damage. My earlier test of just PD+HQ got 64953661 damage. So we can see the delta from adding Immo is 41068891 damage. Immo has 1000ms attack speed, so as in the previous tests, I model his ramp-up as 5 seconds of nothing followed by full damage. So, 175s. We find the number of hits by dividing by 35000: that's ~1173.4 hits.

In 175s, there should be 875 auto-hits. So, we find ~298.4 hits from procs. According to the wikia article on Immo, he procs every 5 seconds, so we estimate 35 procs during the run. Thus, he's hitting ~8.53 times per proc.

The wikia article says that Immo's proc pulses every 0.2s, for "just under 5 seconds", with a 20% chance per pulse to hit. Taking "just under 5" as 4.8, that works out to 4.8 hits per proc.  Incorrect!  4.8 HPS is clearly ruled out by my test.

My test shows a roughly 35.5% chance to hit each pulse (assuming pulses of 200ms, and 24 pulses).  This is unexpected.  On the other hand, since the wikia is already claiming that Immo's in-game description is wrong for the duration of Sandstorm, it's not too shocking that we might have the percentage wrong too.  (Where did the asserted 20% come from?)

I plan to re-run the test tomorrow.  At the least I can replicate the result, and verify visually that Immo is continually proccing (as the wikia article suggests should happen).

Update: here's another run.  Same setup and double checked for nothing wrong.

Ditto.

105959354 damage.  That is .05% less damage than before, that is, basically indistinguishable from the earlier run.  I did watch it carefully, and I can verify two things asserted at the wiki.  First, the proc really is 5 seconds.  Second, there really is a brief gap where it's not on.  That might be a graphical glitch or it might not, but you can certainly see it.

Anyway, the conclusion stands.  At max speed, Immo hits substantially more than he has gotten credit for.

Tested Vlad for Proc Hits

I have not done a boss3 test for a few days because I ran out of things I was curious about that I could test.  (There are several heroes I'd love to test but I can't since I don't have.)  But as I was cheesing in the recent guild war, I was reminded again of how nasty Vlad is.  It always seems like he gets a lot of hits.  So I wondered if our understanding of how he works is correct.  Hey, I can test it!

Setup for Boss3 test of Vlad

The setup is a bit more complicated than the vanilla Boss3 test, because I was afraid that Vlad's proc would give the boss enough energy to proc.  So I added my HQ to make sure the boss stayed flat.  (My HQ has scatter 8.)  I was not sure if this would cause the test run to end early, so I watched carefully.  It didn't, though: the test went the full three minutes.  Here's the result:

Is this too much? 

99394792 damage.

My earlier test of just PD+HQ got 64953661 damage.  So we can see the delta from adding Vlad is 34441131 damage.  Vlad has 1200ms attack speed, so as in the previous tests, I model his ramp-up as 5 seconds of nothing followed by full damage.  So, 175s.  Assuming all hits are full damage, we find the number of hits by dividing by 35000: that's ~984 hits.

In 175s, there should be 875 auto-hits.  So, we find ~109 hits from procs.  Vlad procs every 6 seconds, so we estimate 29.16 procs during the run.  Thus, he's hitting ~3.74 times per proc.

The wikia article on Vlad says that his proc hits every 0.4s, for 4 seconds, with a 30% chance per pulse to hit.  That would suggest he averages 3 hits per proc, but that is clearly ruled out by my test.

One anomaly about Vlad is his fear infliction.  I don't think it varies when it happens, and I think it happens immediately every time.  So I'd suggest a different model for his proc: in the tick that it procs, it hits all enemies in range and inflicts fear.  For the remaining time, it works as wikia indicates (9 pulses, 30% chance per pulse).  In this model, we expect 1 guaranteed hit plus an average of 2.7 over the rest of the time.  This gives an expected 3.7 hits, which is within experimental error.

Verified Slowdown Hit Operation

I have run out of obvious things I wanted to test with Boss3.  So instead of a new hero I thought I'd experimentally verify something that "everyone knows": how slowdown crests work.  Since I think I know how they work, I am going to work out a damage prediction before I collect data.

At max speedup, we know that HQ gets 5.5 HPS, and PD gets the minimum 5.0 HPS.  They are in the fight for 180 actual seconds, but we estimate that PD ramps up in 3 seconds, HQ in 5 seconds.  So, the total hits we expect are 885 for PD, 962.5 for HQ.  Total is 1847.5.  At 35000 hitpoints of damage per hit, expected damage is 64662500.

The actual number from the earlier run was 64953661 damage.  Now let's add on the effect of slowdown.

Slowdown has a 25% chance to happen on each auto-hit.  When it does happen, it adds one extra hit.  At max speed, all heroes get 5 HPS of auto attacks.  Thus, we expect slowdown to add on average 1.25 HPS.

This raises HQ's expected hits by 218.75, for an expected hit total of 2066.25.  Expected damage is thus 72318750.

Now, we run the test.  I realized last time that showing a snap of the two heroes in the "challenge a boss" team UI is not very useful for the purpose of testing crests, since you cannot see the cresting on that UI.  So, instead I have a snap of HQ crested:

HQ with slowdown crests.

And here's the result of the run:

Boss3 result for HQ with slowdown.

72711760 damage.  My prediction is off by just ~.5%.  We have experimentally confirmed the existing theory of how slowdown works.