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MM + Coma Macro could outdamage Brandish. (Math inside) - Printable Version

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MM + Coma Macro could outdamage Brandish. (Math inside) - JoeTang - 2011-01-25

StringStrider Wrote:Where do you get that joe?

2 from FA, 2 from MM, nothing else gives orbs?

Plus with ACA1, you don't even unlock the 6th orb.

You were talking about Brandish and Intrepid Slash with maxed Advanced Combo.

MM + Coma Macro could outdamage Brandish. (Math inside) - StringStrider - 2011-01-25

Oh, I really need to start elaborating more lol.

I meant working out 5 and 10 orbs (level 1 and 30) and immediately using the finisher once acquired.

At 5 orbs, I'm seeing 59 combinations (did a probability tree) for 5 orbs (aka level 1 ACA) so I doubt I'll math out 10.

I doubt I'll take the time to work out 10 orbs. It'd take wayyy too long.

MM + Coma Macro could outdamage Brandish. (Math inside) - Stereo - 2011-01-25

That reminds me... could you confirm that you get 6%/orb with level 1-5 Advanced Combo? Data indicates that as a possibility but the skill description says 5%. So it should be 130% with 5 orbs instead of the 125% with just normal Combo.

I tackled the 10-orb charging problem like this:
 Spoiler
On the left is the table of number orbs (down) vs. number attacks (across) - this is strictly counting the number of Intrepid Slash, so it can charge 1-4 orbs depending if FA triggers or not. Plus, attack "0" is the FA from the previous finisher.
Really it should stop after hitting 10 orbs, I did it this way so I could confirm each column adding to probability 1. Row 27 shows how unlikely it is to have less than 10 orbs after the 6th attack (1.3%).


On the right is the damage dealt with each orb - column M is the average damage of the attack starting from each number of orbs. N to S just evaluate the probabilities of charging each number of orbs.
for example,
F25 = E21*$N$21+E22*$N$20+E23*$N$19+E24*$N$18
E21~E24 are the number of orbs on the previous attack, $N$18~$N$21 are the probabilities of charging 4 3 2 1 orbs in the current attack.

M19 = 6.3*(1+MIN(10,A19)*A$29)+1.5*0.4*(0.2*(1+MIN(10,A19+1)*A$29)+0.8*(1+MIN(10,A19+2)*A$29))
This is just ridiculous. Anyway it basically makes sure no more than 10 orbs are ever counted, and takes into account the probabilities of FA going off with +1 or +2 orbs from the IS.


Oh, and as labeled, A29 is the % gained per orb.

MM + Coma Macro could outdamage Brandish. (Math inside) - StringStrider - 2011-01-25

Stereo Wrote:That reminds me... could you confirm that you get 6%/orb with level 1-5 Advanced Combo? Data indicates that as a possibility but the skill description says 5%. So it should be 130% with 5 orbs instead of the 125% with just normal Combo.

If you want I can do some data collection with powerstrike tonight, but my skillbook itself says that I only get 5%. It seems my error may benefit the cause! I accidentally added all 3 points at 121 to ACA, so right now my skill description states that at level 4 I get 5/orb and next level I'lll get 6/orb with an extra orb.

I could totally do a trial over like 100-200 powerstrikes (disregarding crits) and see what my observed max is, if you like.

I do all my math by hand, so if you'd like to work out an estimated %/cycle for ACA 30 and IS 30, I would greatly appreciate it.

I'm basically wondering if when we max ACA and IS if we should keep the tried and true method of only using a finisher when our buff is about to expire.

We really should compile a bunch of data and sticky a guide!

MM + Coma Macro could outdamage Brandish. (Math inside) - JoeTang - 2011-01-25

Stereo Wrote:That reminds me... could you confirm that you get 6%/orb with level 1-5 Advanced Combo? Data indicates that as a possibility but the skill description says 5%. So it should be 130% with 5 orbs instead of the 125% with just normal Combo.

I tackled the 10-orb charging problem like this:
 Spoiler
On the left is the table of number orbs (down) vs. number attacks (across) - this is strictly counting the number of Intrepid Slash, so it can charge 1-4 orbs depending if FA triggers or not. Plus, attack "0" is the FA from the previous finisher.
Really it should stop after hitting 10 orbs, I did it this way so I could confirm each column adding to probability 1. Row 27 shows how unlikely it is to have less than 10 orbs after the 6th attack (1.3%).


On the right is the damage dealt with each orb - column M is the average damage of the attack starting from each number of orbs. N to S just evaluate the probabilities of charging each number of orbs.
for example,
F25 = E21*$N$21+E22*$N$20+E23*$N$19+E24*$N$18
E21~E24 are the number of orbs on the previous attack, $N$18~$N$21 are the probabilities of charging 4 3 2 1 orbs in the current attack.

M19 = 6.3*(1+MIN(10,A19)*A$29)+1.5*0.4*(0.2*(1+MIN(10,A19+1)*A$29)+0.8*(1+MIN(10,A19+2)*A$29))
This is just ridiculous. Anyway it basically makes sure no more than 10 orbs are ever counted, and takes into account the probabilities of FA going off with +1 or +2 orbs from the IS.


Oh, and as labeled, A29 is the % gained per orb.

 My approach

Without factoring the actual damage, I take the approach with the chance of the number of orb existing given an attack, ranging from 0 to 10 and the Finisher. The theory looks appropriate when I go over it, but I'm still not 100% sure, and these are just the probabilities, it doesn't scale in the combinations of which orbs you're attacking with Final Attack and Intrepid Slash (i.e. the probability of going from 1 orb to 3 orbs can be +2 from Intrepid +1 from FA or +1 from Intrepid +2 from FA, which gives slight differences in damage). The damage difference is quite small though, and easily inserted into the table with some care.
The table I have here is the probabilities of attacking with x orbs, or using a Finisher with level 1 Advanced Combo and maxed Final Attack; the probabilities eventually average out to flat rates where your chance to be attacking with 0 orbs is 15.18%, 1 orb is 15%, 2 orbs is 14.95%, 3 orbs is 14.71%, 4 orbs is 14.85%, and Finisher is 25.31%. You never actually attack with 5 Orbs because that's the situation where you're using a Finisher; 14.85% of the time your Intrepid Slash will be at 4 orbs and after that hit you're guaranteed to have 5 orbs at which you will use a Finisher rather than attacking again, after which you have 15.18% chance to end up with no orbs because FA didn't activate, etc etc.

I think these are the numbers with my approach with maxed ACA.

012345678910Finisher
11.88%3.01%12.61%4.54%10.24%5.87%9.60%6.53%8.91%7.03%0.00%19.80%


If there's anything wrong with my approach, please let me know.

I think this Monster Magnet Coma combination is great because, regardless of the DPS comparison, it's super efficient unless you like OHKO with Intrepid Slash, but I don't feel that Intrepid Slash + Panic would ever be useful other than the scenario where Panic can Blind the target, after which I would say spamming Intrepid Slash until the Blind runs out would be best.

MM + Coma Macro could outdamage Brandish. (Math inside) - StringStrider - 2011-01-26

It seems I've stumped myself with my own math. I think I’m over-thinking the simple. I’ve got all my combinations worked out, but the probabilities are confusing me a bit. I think I’m over thinking it. In Brandish/IS spam; there are 4 things that can happen:

B(1) = 1 orbed Brandish (0.78)
B(2) = 2 orbed Brandish (0.22)
F(1) = 1 orbed FA (0.78) (wrt orb charge, not FA activation)
F(2) = 2 orbed FA (0.22)

Now let’s deal with the scenario of 5, 1orbed Brandishes in a row:

B(1)->B(1)->B(1)->B(1)->B(1) = 5 orbs

At first I assumed it was:

(0.78)^5 = 0.2887174368

There’s no way there’s a 28.87% chance to have 5 Brandishes in a row with 1 orb and no FA activations. Then I figured I’d account for the FA’s by multiplying each term by 0.6 for the fact it didn’t activate. Since there should be 5 unsuccessful FA’s

0.2887 * (0.6)^5 = 0.022449312 = 2.24% <- seems a lot more accurate. This problem solved itself.

So say I take a random outcome from my tree:

B(1)->F(2)->B(1)->B (1 orb brandish -> 2 orb FA -> 1 orb brandish -> brandish)

This is where I ran into a bit of trouble, at this point, it wouldn’t matter whether or not FA activates, so I just threw down a B with no subscript while pondering how to deal with this dilemma. I came up with these symbols.

B(0) = Brandish at 4 orbs (you'd get to 5 orbs regardless of the ACA "Proc" or not)
F(0) = FA activates/wouldn’t charge orbs
F(00) = FA doesn’t activate/wouldn’t charge orbs

B(0) accounts for a Brandish at 4 orbs, since you’re going to get to 5 anyway, the amount of orbs charged doesn’t matter. F(0) and F(00) account for an FA activating from the final brandish

Redoing the scenario I get

B(1)->F(2)->B(1)->B(0)->F(0)
And
B(1)->F(2)->B(1)->B(0)->F(00)

Using the former scenario [B(1)->F(2)->B(1)->B(0)->F(0)]

(0.78 * 0.4) -> (0.22 * X) -> (0.78 * 0.6) -> (?) -> (?)

This is the part that’s confusing me, since the first term has already accounted for the FA activation, can I leave out the X? And what do I do for the “?” so I accurately account for those scenarios (The subscript 0’s)? I haven’t taken probability or stats in at least 3-4 years so I’m going off memory here.

MM + Coma Macro could outdamage Brandish. (Math inside) - modular - 2011-01-26

StringStrider Wrote:So say I take a random outcome from my tree:

B(1)->F(2)->B(1)->B (1 orb brandish -> 2 orb FA -> 1 orb brandish -> brandish)

the probability of this occurence is
.78 * .4 * .22 * .78 * .6 * 1 * 1

in words, this is:
p(1orbIS) * p(FA) * p(2orbFA) * p(1orbIS) * p(noFA) * p(1 or 2orbIS) * p(FA or noFA)

each time you brandish, you need to say in your calculation whether or not you get 2 orbs, whether or not FA activates and if it does, how many orbs it gives. when you reach a scenario where you must attack again, but are guaranteed to only be able to charge 1 orb, the probability of you maxing your orbs on that attack is 100% (thats where the 1s come from). so basically, this is the way to show that you have to truncate the number of orbs you can have.

that's one reason to keep track of how many attacks you need for each combination or lump the probabilities together into a table like joe's.

hope this helps..

MM + Coma Macro could outdamage Brandish. (Math inside) - StringStrider - 2011-01-26

modular Wrote:the probability of this occurence is
.78 * .4 * .22 * .78 * .6 * 1 * 1

in words, this is:
p(1orbIS) * p(FA) * p(2orbFA) * p(1orbIS) * p(noFA) * p(1 or 2orbIS) * p(FA or noFA)

each time you brandish, you need to say in your calculation whether or not you get 2 orbs, whether or not FA activates and if it does, how many orbs it gives. when you reach a scenario where you must attack again, but are guaranteed to only be able to charge 1 orb, the probability of you maxing your orbs on that attack is 100% (thats where the 1s come from). so basically, this is the way to show that you have to truncate the number of orbs you can have.

that's one reason to keep track of how many attacks you need for each combination or lump the probabilities together into a table like joe's.

hope this helps..

This helps a LOT! This is what my hunch was. I've just been sooo clustered writing out (by hand) all 59 combinations of orb charging with level 1 ACA that my mind has started to implode.

I really should learn advanced excel stuff... Sum and basic math just wont cut it with the crap I'm doing.


Excel for dummies plz Big Grin