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.

Deadly Strike Works Via Extra Hits

TLDR: see the title?

I've never been 100% certain how Deadly Strike works.  Does Deadly Strike multiply an "existing" autoattack hit, or does it provide an extra hit that is multiplied, the way that Slowdown and Heavy Blow work?

I did a test last year that seemed to indicate the latter (extra blow), and since the other two talents work that way, it makes the most sense to me.  But it's better to have a rigorous test.

Since I have some data with Boss3 tests, I figured to test it next.

To test, I needed a hero with both scatter (to stop the boss proccing) and heavy blow.  Since my Harpy Queen has scatter as her talent, and I have already tested her, she's perfect.

To set the test up, I took off her Berserk 4 crests and replaced them with Deadly Strike 2.  As such, we can expect a slightly longer ramp-up time, so perhaps slightly less damage.  However, the difference should be not more than a second or two of damage at most.  A second's damage in the Boss3 test is ~200000 hitpoints.

Now the actual test.  In the previous test, HQ scored 64953661 damage.

Here's the setup:

Test setup.  Pity you can't see the cresting.

And here's the score:

Boss3 score with Deadly Strike

67936102 damage.  That's 2982441 more damage than the original run without DS crests.  Over 175 seconds (this is approximated time of engagement to account for PD having to amp up), it is 17042 DPS.  In terms of extra hits, it is 0.487 HPS extra.  This is almost exactly the 0.5 extra HPS predicted.

Conclusion: Deadly Strike works via extra hits.

Tested Trixie Treat for Max Speed Hits per Second

I did the "Boss3 test" for Trixie Treat last night.  The "Boss3 test" is ... I think I need to write a post about that.  OK, done.  Read that.

Actually I did my first run at testing TT a few nights ago.  But it failed horribly: I put it down, then looked and PD was dead!  Oops, oh yeah, you can't test summoners using the "standard" boss3 test.  The problem is that whenever a hero summons, the heroes that are summoned are now "last".  And thus the "last-hero-scatter" trick fails.

On that run, I quickly added a few random devoes and did the run.  It did not test anything, but I did at least get the honor badges.

So how to test TT?  Well, at max speed, 2 heroes plus four pumpkies should be adding 450 energy/s to the boss. Then the boss adds another 15 from his own hit. To get rid 465energy/s, we need 93 energy scattered per 200ms. That's challenging. With scatter4 crested on TT, would need 73 from some other hero. I can do that with HQ because mine has scatter8. There's no other way I can do that.

So I decided to run three heroes for the TT tests: PD, HQ, and TT.  Adding a third hero has the downside that the boss will run out of hitpoints. So I'll have to make more assumptions to get a decent number. Challenge accepted.

Testing HQ

First things first, though.  I did a run with just PD and HQ.  This gives me a good baseline to work from.

Boss3 testing HQ.

Here's the result:

Boss3 HQ result.

64953661 damage.  We know that at max speed HQ gets 5.5 HPS (hits per second).  PD gets the minimum 5 HPS.   Somewhat arbitrarily, I am estimating the ramp-up by removing 3 seconds from PD, and 5 seconds from other heroes.

(How long does my PD ramp up take?  He starts out hitting every 600ms; because he is being hit he'll proc after his first or second hit.  I am guessing 2nd.  So, 1200ms to one stack.  Then his speed is 400ms.  Over the next 2 seconds the boss hits him twice, and he hits 5 times.  Then he procs again: 2 stacks.  Now his speed is 200ms.  PD is fully ramped at this point.  Over the next 1.2s, the boss hits him once and he hits 6 times.  Then he procs to 3 stacks.  At this point he has spent 3.4s.  It takes him 4.6s to reach 4 stacks, and 5.8 to reach 5.

Even 3 stacks is enough to get 30000 damage on Boss3 from any reasonably high level hero.  But speedwise, TT and HQ both need 5 stacks to get to 200ms.

All in all, because damage is ramping up exponentially no hero will get very much until almost fully ramped in speed.  So, as an estimate I am going to use 5 seconds as the ramp-up time, and pretend that all heroes get zero damage during ramp-up and full damage (and speed) after it.  PD similarly gets 3 seconds as his ramp-up.)

OK, now we have enough numbers we can compute.  First we compute DPS for PD as follows.  PD and HQ together got 64953661, in 180s.  So, that is 177s of PD damage (at 5HPS), and 175s of HQ damage (at 5.5HPS).  Thus, total hits applied are estimated to be 1847.5.  (Multiply by 35000: this checks out very well with the actual damage applied.)

Testing TT

OK, with HQ's number in hand we proceed to the TT test.  TT gets Scatter 4.  HQ has her talent, scatter 8.   That, along with the pumpkies, should hopefully be just enough.

Boss3 testing HQ+TT.

I did the run and it worked -- no procs.

Here's the thing partway through:

Boss3 HQ+TT test almost done.

The result?  120m damage exactly: killed the boss, just the 3 of them.  (TT does a lot of damage.)  I knew this would happen, and so was carefully watching the time.  There were 53 seconds left when it ended.

53 seconds left out of 180.  So, 127 seconds spent.  But some of that was spent when PD was ramping up, and we need to account for that.  As above, we assume PD ramps in 3 seconds, others 5 seconds.

So now we can compute what TT got.  Over a run of 127s, PD should have gotten 124s of damage, and HQ 122s.  Thus, they should have totaled 21700000 damage and 23485000 damage respectively.  Total: 45185000.  The remaining damage is TT's: that is 74815000 damage.  This was done by TT in 122s (effectively), so her DPS is 613238.  We divide by 35000 to convert this to HPS: 17.5.

Conclusion: at top speed, Trixie Treat (and her pumpkies) average 17.5 HPS.  Trixie herself gets 5.1 HPS.  So the remaining 12.4HPS are coming from pumpkies.