Finisher DPS

Well. I've been screwing around with a spreadsheet, attempting to simplify a statistic distribution for Advanced Combo Orb building and Finisher use. It's good and all but I can't seem to find a simple way to implement it into code. Or more so, I'm lazy, so anyways.
Using maxed Advanced Combo, it goes something like this:

Orbs:	1	2	3	4	5	6	7	8	9	10	Finisher
1	0.4000	0.6000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
2	0.0000	0.1600	0.4800	0.3600	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
3	0.0000	0.0000	0.0640	0.2880	0.4320	0.2160	0.0000	0.0000	0.0000	0.0000	0.0000
4	0.0000	0.0000	0.0000	0.0256	0.1536	0.3456	0.3456	0.1296	0.0000	0.0000	0.0000
5	0.0000	0.0000	0.0000	0.0000	0.0102	0.0768	0.2304	0.3456	0.2592	0.0778	0.0000
6	0.0000	0.0000	0.0000	0.0000	0.0000	0.0041	0.0369	0.1382	0.2765	0.4666	0.0778
7	0.0311	0.0467	0.0000	0.0000	0.0000	0.0000	0.0016	0.0172	0.0774	0.3594	0.4666
8	0.1866	0.2924	0.0373	0.0280	0.0000	0.0000	0.0000	0.0007	0.0079	0.0877	0.3594
9	0.1438	0.2903	0.2289	0.1904	0.0336	0.0168	0.0000	0.0000	0.0003	0.0083	0.0877
10	0.0351	0.1101	0.2024	0.2658	0.2135	0.1277	0.0269	0.0101	0.0000	0.0003	0.0083

With this, we will eventually find that the numbers all plateau, giving this:

1	2	3	4	5	6	7	8	9	10	Finisher
0.0535	0.1018	0.0729	0.0903	0.0798	0.0859	0.0820	0.0842	0.0828	0.1333	0.1335

This plateau begins to appear at more or less hit 168, continually evening out to reach those numbers; At around there, your probability of being in the above orb counters or using a Finisher is as above, give or take. With these, we can take a statistical average to find the net average modifier, and Finisher damage;
eg: Probability of having 1 Orb is 5.35%; 0.0535 * 1.5
Add that to the probability of having 2 Orbs
0.1018 * 1.55 + 0.0535 * 1.5
etc.
And you find your average AC modifier is approximately 1.5
Now, you're probably thinking
"wtp. Dumbass, Advanced Combo gives 1.9 at 10 orbs, whywouldyoudothat.jpg"
Factor in Panic damage and you can calculate your DPS:
Modifier * Brandish / Time + Finisher_Rate * Panic * Orb_Modifier * `Modifier / `Time
1.5 * 5.2 / 0.63 + 0.1335 * 3.5 * 2.5 * 1.9 / 0.6

Assuming I did this correctly, we find 1604.47%/s to be our final indefinite DPS.
Brandish alone is only 1568.25%/s.
Knowing that is good, but if it flattens out to 1604.47%, that must mean there is an intermediary point where it's still greater than standard Brandish spam DPS. That's at approximately at hit 79. Considering all the other damage fluctuations that occur in using Panic in this way, you also find that your total damage done is greater at 66 hits.
Thusly, I have proven that using Finishers does in fact improve your DPS.

Is it worthwhile though? Probably not. This model assumes the most ideal situation; That you contact every hit, that you hit every average, and that you do it right. Realistically, you won't be able to make very hit count; if you miss a Finisher, your DPS would significantly drop. In the end, the 36%/s is not worth the extra concentration, and dependence on statistic averages. The difference is even less noticeable with Sharp Eyes, becoming a 29%/s difference. This also does not consider the fact that it may very well be possible to waste damage by breaching the cap.

Anyways. I was extremely bored and wanted to kill time. That sure did the trick.

Cheers.

P.S. Will add mob and Coma numbers later.

Can you do a version for soul masters?

Uh.
What do the table cells mean? I'm not getting it.

Edit: Oh, I see what you're doing.

Uh.
What do the table cells mean? I'm not getting it.

Edit: Oh, I see what you're doing.

Since you're not the only one that was confused at first glance, I'll explain it.

Row = how many attacks used
Column = % chance of having x orbs. When it reaches the Finisher you use it and it resets at 0.
Limit pullout = chance of being at certain point in charging Finisher at a given moment after a large number of attacks. As you can see you can use a finisher about 13% of the time, or once every 7-8 Brandishes.

does it improve any for using panic on orb 5/6? since the multiplier caps at 2.5 w/ orb 5 and it still slightly improves dps at orb 10 i would guess orbs 5/6 to be a bit better.

im certain youll find coma is better dps than pure brandish. panic has always been the worse of the 2.

hooray! i was too lazy to do this.

It's good and all but I can't seem to find a simple way to implement it into code. Or more so, I'm lazy, so anyways.

I dunno about code to use in an application, but I too felt like killing time and wrote this (in Lua cause it's easy. sue me) for outputting your probability tables:

 Spoiler

Code:

[noparse]function makeOrbTable(hitCount, tolerance, orbs)
   if hitCount == 0 then return orbs end
   if orbs == nil then
      local newOrbs = {0.4, 0.6, 0, 0, 0, 0, 0, 0, 0, 0, 0}
      return makeOrbTable(hitCount - 1, tolerance, newOrbs)
   end
  
   local newOrbs = {}
   newOrbs[1] = 0.4*orbs[11]
   newOrbs[2] = 0.4*orbs[1] + 0.6*orbs[11]
   for i = 3, 9 do
      newOrbs[i] = 0.4*orbs[i-1] + 0.6*orbs[i-2]
      end
   newOrbs[10] = orbs[9] + 0.6*orbs[8]
   newOrbs[11] = orbs[10]
  
   if tolerance == nil then tolerance = 0 end
  
   for i = 1, 11 do
      if math.abs(newOrbs[i] - orbs[i]) > tolerance then
         return makeOrbTable(hitCount - 1, tolerance, newOrbs)    -- tolerance not met
      end
   end
  
   return orbs
end

function getOrbTable(mode, limit)
   if mode == 'hit count' then
      return makeOrbTable(limit)
   elseif mode == 'tolerance' then
      return makeOrbTable(-1, limit)
   else
      error('Invalid mode specified')
   end
end

function printTable(mode, limit)
   local orbs = getOrbTable(mode, limit)
  
   for i = 1, 11 do
      orbs[i] = string.format('%.4f', orbs[i])
   end
   io.write('[table] 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Finisher\n')
   io.write(table.concat(orbs, ' | '), '[/table]\n')
end

printTable('hit count', 10)
printTable('tolerance', 0.00001)[/noparse]

Output --

1	2	3	4	5	6	7	8	9	10	Finisher
0.0351	0.1101	0.2024	0.2658	0.2135	0.1277	0.0269	0.0101	0.0000	0.0003	0.0083

1	2	3	4	5	6	7	8	9	10	Finisher
0.0535	0.1016	0.0727	0.0900	0.0796	0.0859	0.0821	0.0844	0.0830	0.1336	0.1336

And then you could

 Spoiler

Code:

function getDPS(mode, limit)
   local orbs = getOrbTable(mode, limit)
  
   local modifier = 0
   for i = 1, 5 do
      modifier = modifier + orbs[i]*(150+5*(i-1))
   end
   for i = 6, 10 do
      modifier = modifier + orbs[i]*(170+5*(i-5))
   end
  
   local DPS = modifier * 5.2 / 0.63 + orbs[11] * 3.5 * 2.5 * 190 / 0.6
  
   io.write(string.format('DPS: %.2f%%\n', DPS))
end

getDPS('tolerance', 0.00001)

DPS: 1616.86%

Except that the 'tolerance' is on the probability values, not the DPS itself. 2lazy2fix.

Feel free to translate into whatever you want, it didn't take long to do. Though I don't see how this would be useful enough to bother.

Edit: Wup.

Code:

modifier = modifier + orbs[i]*(170+[b]4[/b]*(i-5))

And I'm the formula thread guy.

DPS: 1604.45%
As expected. (Bringing the tolerance to 1e-6 gives the 1604.47% answer.)

I have a file with the data I collected from it, with DPS and such. I'll upload it after the 2x now.

does it improve any for using panic on orb 5/6? since the multiplier caps at 2.5 w/ orb 5 and it still slightly improves dps at orb 10 i would guess orbs 5/6 to be a bit better.

im certain youll find coma is better dps than pure brandish. panic has always been the worse of the 2.

hooray! i was too lazy to do this.

The DPS plateaus at 1604.22%/s.


You reach a net damage improvement at 17 hits though, and a positive DPS difference after 38 hits; i.e. after 38 hits, your DPS should always be higher than just Brandish alone.
Again, not significant.

Anyways. Wanted to do Coma to find the value and difference to compare what's what etc.

I can attempt to do values for Soul Masters using estimations for ACA since I don't know if they use the exact same formula. I need a nap first.

---------------
Coma-
On Mobs of 4:
4992.66%/s
5:
5449.72%/s
6:
5906.79%/s

Just to double check, attacking mobs increases orb count faster? Otherwise, Coma DPS is pretty fail at like ~4900%/s on mobs of six.

Went through it quickly, but using numbers based off Hero Advanced Combo (i.e. that -10% on all levels), Soul Masters come out with a 3.9%/s advantage using Panic. Will attempt to calculate using FA and an estimated FA speed.

Okay. I'm not 100% sure about the DPS for this one, but it's for Advanced Combo with FA for a Soul Master;
Here's the probability table, not that it helps much:

	1	2	3	4	5	6	7	8	9	10	Finisher
FA	0.0455	0.0800	0.0822	0.0764	0.0780	0.0785	0.0780	0.0781	0.0782	0.1625	0.1625
FA-Less	0.0789	0.0891	0.0860	0.0869	0.0867	0.0867	0.0867	0.0867	0.0867	0.1127	0.1127

As you can see, FA has a considerably higher amount of probability in being in Finisher state.

I did completely consider how FA builds orbs. i.e.
Chance for one Orb:
0.4 * 0.7
Two orbs:
0.4 * 0.3 + 0.6 * 0.7 * 0.7
etc.

Finally, when applying the damage to the modifiers, had to apply with overall consideration to where your orb count is at; i.e. probability of building an orb from Brandish, and applying the new modifier to FA, etc. Using 0.48 second FA

And I find final DPS to be 1182%/s which is pretty bad compared to pure Brandish. The reason for this should be easily understood;
FA is pomegranate. Does 250% which is ~1.09x stronger than a single Brandish hit (according to some kMS players who state it's max level is 30, 230%), and it is most definitely not 0.92x or less the speed of a single Brandish slash.
i.e.
Brandish DPS: 730.16%/s
FA Standalone DPS (@480ms): 520.8%/s
FA Matching DPS (@330ms): 757.58%/s
Now, if we can time FA to be 330ms (since times seem to be in denominations of 30ms, 360ms is too slow), it would be a DPS improvement on Brandish, unless you have unmaxed Brandish, etc.
The extra damage from AC that's stacked on FA is almost meaningless. Even if Brandish had 1 Orb every time and FA had 10 Orbs every time, it'd still be weaker. Consider it; The largest difference in damage improvement to from Brandish charging orbs is .10; Orbs 1~5;
Let's say you have 1 Orb: Brandish does 1.4x damage; Brandish charges 2 Orbs; FA does 1.5x damage; Not significant.

All this for a 4% increase in Finisher probability; 320% * 1.8 * 2.5 / 0.6 = 2400% Panic; 4% of this is 96%. Definitely not more than the amount of damage you've lost for using FA.

tl;dr: DON'T USE FA WITH MAXED BRANDISH + ADVANCED COMBO

Personally, I don't recommend Finishers at all on a Soul Master though, so meh.

The DPS plateaus at 1604.22%/s.

i think you misunderstood my question.
what i meant was if instead of using panic at 10 orbs, use it at orb 5/6 to take advantage of more panics since the orb multiplier doesnt improve after orb 5.

did the calcs myself, and came up with only a mediocre 1469%. so panic only improves dps on 10 orbs, and perhaps is equivalent if you use finishers at 9/10 orbs (didnt actually check). panicking with any less than 9 orbs is fail for your dps.

coma at 5/6 against 6 mobs is also less dps than brandish at 10 against 3. but only by a meager 50%, so if you want to have 3 mobs stunned it could be worth it to coma anywhere from 5-10 orbs.

i recommend using coma if your hero can 2hko the mobs w/ coma + orbless brandish. you should also be able to 2hko w/ 2 brandishes on orbs 1-3 by then..

1	2	3	4	5	6	Finisher	5 Orb Finisher	6 Orb Finisher
0.0914	0.1736	0.1243	0.1539	0.1361	0.0923	0.2284	0.5958	0.4042

I got this as my result, with which I calculated the 1604.22%/s

What did you get?

Also, for 9/10 Panic

1	2	3	4	5	6	7	8	9	10	Finisher	9 Orb Finisher	10 Orb Finisher
0.0583	0.1108	0.0793	0.0982	0.0868	0.0936	0.0896	0.0920	0.0905	0.0552	0.1457	0.6212	0.3788

Which I got 1602.45%/s

1	2	3	4	5	6	Finisher	5 Orb Finisher	6 Orb Finisher
0.0914	0.1736	0.1243	0.1539	0.1361	0.0923	0.2284	0.5958	0.4042

I got this as my result, with which I calculated the 1604.22%/s

What did you get?

Also, for 9/10 Panic

1	2	3	4	5	6	7	8	9	10	Finisher	9 Orb Finisher	10 Orb Finisher
0.0583	0.1108	0.0793	0.0982	0.0868	0.0936	0.0896	0.0920	0.0905	0.0552	0.1457	0.6212	0.3788

Which I got 1602.45%/s

hum. i got the same numbers for the plateau probabilities, however im guessing i calculated the overall dps differently. since im telling myself the probability of having each orb at any given time, its easy to sum up dps instead of using an average multiplier.

orb	1	2	3	4	5	6	finisher	total
dps	1.131	2.221	1.641	2.096	3.374	2.343	1.886	14.692

each partial dps is 5.2*(plateau probability)*(ac multiplier)/(cast time)
finisher slot = "0 orbs", so its a brandish w/ ac multiplier = 1...

Finisher is 0.2284 * 350% * 2.5 * (1.70 * 0.5958 + 1.74 * 0.4042) / 0.6

It's actually faster than a Brandish, plus it takes an average of AC Multiplier. 10 Orb Finishers do 350% * 2.5 * 1.9; however, since there's a chance that it could either be 5 or 6 orbs, you can distribute them accordingly as I have.

Finisher is 0.2284 * 350% * 2.5 * (1.70 * 0.5958 + 1.74 * 0.4042) / 0.6

It's actually faster than a Brandish, plus it takes an average of AC Multiplier. 10 Orb Finishers do 350% * 2.5 * 1.9; however, since there's a chance that it could either be 5 or 6 orbs, you can distribute them accordingly as I have.

yeah. i just distributed it differently, but it comes out the same since the finisher probability column is orbs 5 + 6.
where is your 0 orb brandish? i think you arent taking it into consideration.

yeah. i just distributed it differently, but it comes out the same since the finisher probability column is orbs 5 + 6.
where is your 0 orb brandish? i think you arent taking it into consideration.

oshi

Hm. Let's see here.

Alright, so you take the probability of Finisher, and multiply it to (Finisher% + Brandish%) divided by the time it takes to do both, calculating it as a single hit should work.

Finishers can't charge orbs right?

With that, we have a pomegranatety 1459.94%/s on my side. I'll have to redo the values earlier, but I'm hoping to have this information useful for the lower levels of Brandish/AC for when it's actually beneficial to use these skills.

oshi

Hm. Let's see here.

Alright, so you take the probability of Finisher, and multiply it to (Finisher% + Brandish%) divided by the time it takes to do both, calculating it as a single hit should work.

Finishers can't charge orbs right?

With that, we have a pomegranatety 1459.94%/s on my side. I'll have to redo the values earlier, but I'm hoping to have this information useful for the lower levels of Brandish/AC for when it's actually beneficial to use these skills.

indeed, finishers do not charge orbs. i still got 10% more than you, but its close. are you calculating dps w/ an average multiplier for ac? the probability of having any given orb isnt a flat 1/(x orbs) type thing, so it isnt valid..

im interested to see the redone conclusions
what i really want to see is a comparison w/ ps/fa + 1 ac + 10 brandish vs 11 brandish

My bad, I was looking at the wrong spreadsheet, but there's still some discrepancy there for some reason.

We're talking about 5/6 Finisher right? I get 1407.96%/s in such a case.
Your average DPS for 5 and 6 orbs is done wrong.


Took an attempt at 1 AC max PS + FA, 660ms PS and 480ms FA, (Faster (3))
Got 723.50%%/s as my result, which is better than PS+FA alone by ~105%, but I'm not 100% sure on this either, because the math was complicated and I may have made a small error somewhere
This is the table I found

	1	2	3	4	5	6	Finisher	PS+FA Total
Prob	0.0656	0.1155	0.1197	0.1109	0.1131	0.2376	0.2376
DPS	0.2584	0.5373	0.6047	0.5186	0.6440	1.1295	3.4927	3.69

6 has significantly higher DPS because you're more prone to be stuck using an extra 6 Orb FA there, thus you have a significantly larger amount of time being stuck at 6 Orbs. Hopefully, I accounted for the first 0-orb PS and the fact that an FA can come off of it with orbs correctly.