[Pre-BB] MapleStory Formula Compilation

I used Lucky Seven. I find it easier to keep track of 2 numbers, especially considering that I'm looking for 4 different values (Min, max for both regular and critical). The fewer hits that I have to process, the better.

Sounds like a confirmation to me. You were using TT no?

*Tries something*
Damage Range 30~50, probability to 2 hit a monster with 80 HP

Let me try to do this via the way you do it with dice.

21^2 = 441 possibilities.

Chances to do 80 damage+ added together:
30/50
31/50
32/50
...
50/50
=21

31/49
32/49
...
50/49
=20

etc etc

49/31
50/31
=2

50/30
=1

=(21*22)/2
= 231 chances, 231/441 = 52.4% chance to 2 hit.
Fix'd.

If your average damage is 40, you should always have a greater chance to 2 hit than 50%. This is because you count 40 as part of the 2-hit range instead of a divider.

I was bored without internet:


Iron Arrow:
Per-monster Multiplier: 0.9 ^ (monster# - 1)
Cumulative Multiplier: 10 * (1 - * 0.9 ^ monsters)

Piercing Arrow:
Per-monster Multiplier: 1.2 ^ (monster# - 1) * (0.5 + 0.5 * (time charged / 3 sec))
Cumulative Multiplier: (5 - 5 * 0.8 ^ monsters) * (0.5 + 0.5 * (time charged/ 3 sec))
Marked in big am I unsure of is correct or not.

I'm aware that the per-monster multiplier is already stated in, but cumulative may be funky to find out if piercing arrow is comparable with other skills. From what I know as well, time charged is rounded to lowest integer, correct?

 Spoiler

Sounds like a confirmation to me. You were using TT no?

*Tries something*
Damage Range 30~50, probability to 2 hit a monster with 80 HP

Let me try to do this via the way you do it with dice.

21^2 = 441 possibilities.

Chances to do 80 damage+ added together:
30/50
31/50
32/50
...
50/50
=20

31/49
32/49
...
50/49
=19

etc etc

49/31
50/31
=2

50/30
=1
= 210 chances, 210/441 = 47.6% chance to 2 hit.
Rawr, that can't be right.

Mm, I'd do a different approach. Instead of that, give the fact that the estimated damage will be 80 damage. Therefore, we know already that you have 0.5 - [exact 80 dmg chance]/2 for doing over 80 damage, and less than 80 damage. Thus, the damage is 0.5 - [exact 80 dmg chance]/2 + [exact 80 dmg chance] = 0.5 + [exact 80 dmg chance]/2.

The chance for having exact 80 dmg is this:

1st	2nd
30	50
31	49
32	48
...	...
48	32
49	31
50	30

That is, 21 different possibilities of getting 80 dmg.
We have in total 21 * 21 different possibilities. 21/((21*21) * 2) equals 1/42, therefore the chance of 2-hkoing is 1/2 + 1/21 = 22/42 chance of 2hkoing.

(Oh, did I ever tell you I love working with fractions?)

Edit: the above written is only exact if the damage range really IS from 30 to 50, and not 30.2 to 50.7 or something.

It should be around 0.15 + 0.85 * (time charged / 3)
And it's not rounded to the lowest integer, as far as I know.

Oh, yes. Yeah, I should remove that. That was an early assumption and needs to be retested with a STR marksman next Tespia.

Spell Damage:
Japanese version: (most accurate)
MAX = (Magic *3.3 + Magic*Magic *0.003365 + INT*0.5 ) * Spell / 100
MIN = (Magic *3.3*Mastery *0.9 + Magic*Magic *0.003365 + INT*0.5 ) * Spell / 100

Has there been any work with this one lately? The 0.003365 is a weird, but I've found several different ways to get there, with approximation. Though, the most exact one doesn't really make sense... 0.15^3?

Also, I think magicians need to contribute more to max and minimum damage they do. =[ I'll try to get on and check max and min damage to monsters on my cleric, but I doubt this will help out a lot, lol.

Yes, I've been looking into it the past couple of days. So far my results have led to the 'Experimental version' under your quote.

I can't say it's significantly more accurate than the Japanese version (it's actually less accurate on their samples, but that's a side effect of using regression), but it gets rid of the messy decimals, and never deviates from the Japanese by more than 0.5% on the samples I have.

My main concern with both of them is that they shear off some of the damage ranges. What I mean is, for example, mine predicts 1495~2154 for one sample, but 1492~2144 was observed. If it was correct, the person should never have been able to hit that 1492.

How much tolerance is there on that 0.003365? Eg. would 0.0033 be close enough to satisfy the damage ranges...


Or something like magic*1.1*(3[*mastery*0.9]+magic*0.003(06))

The 0.00336 is too excely for my tastes. I should help with this................
Tomorrow.

Here, I'll show you a comparison.

[spoiler=Copypasta'd for reference]Japanese version: (most accurate)
MAX = (Magic *3.3 + Magic*Magic *0.003365 + INT*0.5 ) * Spell / 100
MIN = (Magic *3.3*Mastery *0.9 + Magic*Magic *0.003365 + INT*0.5 ) * Spell / 100

Russt's version:
MAX = ((Magic²/1000 + Magic)/30 + INT/200) * Spell Attack
MIN = ((Magic²/1000 + Magic * Mastery * 0.9)/30 + INT/200) * Spell Attack
[Note this could also be rewritten as: (compare to Japanese version)
MAX = (Magic *3.3333 + Magic*Magic *0.003333 + INT*0.5 ) * Spell / 100
MIN = (Magic *3.3333*Mastery *0.9 + Magic*Magic *0.003333 + INT*0.5 ) * Spell / 100]

Kyran's version:
MAX = ((.005979 x Magic)² + (.0359 x Magic)) * Spell Attack
MIN = ((.005979 x Magic)² + (.0359 x Magic x Spell Mastery)) * Spell Attack[/spoiler]

and Stereo's revised formula:
(Magic*K[*0.9]*(3[*Mastery] + Magic*0.003)+INT/2)*Spell/100

Observed	Russt's	Kyran's	Japanese	Stereo's (K=1)	K=1.111...
4 - 15	4 - 15	2 - 15	4 - 15	4 - 15	4 - 15
7 - 31	7 - 31	6 - 33	7 - 31	6 - 31	6 - 31
35 - 62	37 - 63	41 - 67	37 - 63	36 - 63	37 - 63
10 - 47	10 - 48	10 - 52	10 - 47	10 - 47	10 - 48
13 - 50	13 - 51	10 - 52	13 - 50	13 - 50	13 - 51
15 - 52	15 - 52	10 - 52	15 - 52	14 - 52	14 - 52
56 - 95	56 - 96	65 - 104	56 - 95	55 - 95	55 - 96
62 - 101	62 - 102	65 - 104	62 - 101	61 - 101	62 - 102
65 - 104	65 - 105	65 - 104	65 - 104	64 - 104	64 - 105
160 - 251	161 - 253	168 - 259	160 - 251	156 - 250	158 - 253
1483 - 2135	1486 - 2145	1526 - 2177	1483 - 2135	1422 - 2125	1435 - 2145
1492 - 2144	1495 - 2154	1526 - 2177	1492 - 2144	1431 - 2134	1444 - 2154
??? - 1031	399 - 1057	361 - 1084	401 - 1053	368 - 1036	437 - 1112
??? - 1539	590 - 1579	533 - 1617	593 - 1572	543 - 1546	656 - 1669
??? - 1270	888 - 1292	932 - 1323	887 - 1287	843 - 1271	902 - 1334
??? - 2149	1514 - 2182	1587 - 2239	1512 - 2173	1439 - 2153	1503 - 2224
??? - 1321	912 - 1321	948 - 1344	911 - 1316	866 - 1300	923 - 1363
??? - 2215	1540 - 2215	1614 - 2274	1538 - 2207	1463 - 2186	1528 - 2258
8817 - 12111	8812 - 12132	9305 - 12531	8816 - 12104	8284 - 11959	8711 - 12422
7014 - 9361	7002 - 9383	7378 - 9733	7008 - 9366	6583 - 9296	6643 - 9383
7176 - 9465	7163 - 9489	7536 - 9836	7172 - 9474	6720 - 9400	6782 - 9489
73197 - 92481	77530 - 92808	83847 - 98864	77899 - 93026	71064 - 91811	72301 - 93258

So far I haven't been able to come up with anything that can satisfy all of the damage ranges without shearing off a single point, especially Cyanne's gigajuice (the last one). It's pretty difficult to make the range turn out like that given the observations that LUK does nothing, INT has a static multiplier, etc etc.

I could incorporate something like magic^1.1 in there to make it fit a bit better, but that would just be drifting further from the truth, since there's no way the formula has fractional exponents. Way too messy.

I've tried to make the japanese one more "understandable":

max: (magic * 3.3 + (magic * 0.9 * 0.1)^2 + int/2)*spell/100
min: (magic * 3.3 * mastery * 0.9 + (magic * 0.9 * 0.1 * mastery)^2 + int/2)*spell/100

I'll check it out later on, not enough time now. v,v

Not pleased with the format, but I'd revise mine to something like that to take into account the giga juice one:

(Magic*1.1*(3[*Mastery] + Magic*0.00306[*K])+INT/2)*Spell/100

Likely K being around 0.8-0.9 (all items in [] are minimum damage again)

The format of what? The chart?
Fiel said something about using the noparse tag with tables, but it's displaying fine on my browser... Iunno.

Edit: Well. K=0.9 fits the gigajuice quite well, as well as most of the high ones, but it shears quite a bit off of the 2-3 digit ones. If you put a K on the 3.3 as well, it doesn't shear anything, though it tends to underestimate.

Updating chart with the following:
(Magic*1.1[*K]*(3[*Mastery] + Magic*0.003)+INT/2)*Spell/100

The above formula, I'd presume.

The format of what? The chart?
Fiel said something about using the noparse tag with tables, but it's displaying fine on my browser... Iunno.

Edit: Well. K=0.9 fits the gigajuice quite well, as well as most of the high ones, but it shears quite a bit off of the 2-3 digit ones. If you put a K on the 3.3 as well, it doesn't shear anything, though it tends to underestimate.

How about like that then o.o

(Magic*K[*J]*(3 + Magic*0.00306)+INT/2)*Spell/100

K around 1.1~1.15, J around 0.9.


& originally I had something stupid like [1-(1-mastery)/10] to try to compensate but I decided a constant K was easier. Which is why I'd said I didn't like the format.

I noticed that if I tag a 0.9 on the same part of my equation, it's basically the same as your general one with K=1.11111 repeating, if you round 0.00306 to 0.003.
I really want to assume J=0.9; it already underestimates as it is, so it can't be much lower, and making it tighter creates a messy decimal (0.92xx)

That leaves us with this:
((1[*Mastery] + Magic/1000)*Magic*K[*0.9] + INT/2) * Spell/100.
with our only unknown being K, which is around 3.2~3.4.

Again, this is assuming a lot and may not fit at all.

Edit: Ran more numbers.

The 35-62 is weird, I can't get it to fit with the rest of the samples. But disregarding it (...maybe I'll double check the Japanese site), the above equation loosely predicts everything else if K is between 3.325 and 3.375. Tight fit; my guess of 3.333 repeating fits in there, but I dunno.

The other thing that can be adjusted is the 1 in front, but 1/1000 seems too right for me to touch. You could try moving it up and down a bit, but I don't think it'll make anything special happen.

Edit @ below post: Dividing by 1.1 makes the lower bound on the gigajuice one really really close (73106)
Otherwise, it doesn't make a noticeable difference on most of the other ones.

Update: I really don't know what's up with the 35-62.

レベル３０（ＩＮＴ２０・ＬＵＫ１４２・魔力４３
使用スキルＭＣ２０（魔攻４０・熟練度６０％
ダメ幅３５～６２

Maybe he hit a red snail or something :/

If you want it a bit higher then divide by 1.1 instead of multiplying by 0.9 >_> 1/1.1 = 0.9090...

The noparse tags are only required if you want to have every cell [noparse][align=center]'d[/noparse].

I'll see what I can do about getting a debugger on my localhost PServer to get the exact calculation for MATK. After having PServers for so long and with Maple being several years old, there should be no reason why there is not a correct formula.

Really, those with private servers should be helping us out, whether by testing a 999 luk mage or a 999 matk one, it can go a long way.

That's how the PKB formula was finalized, a STR bowman, but we had to do it the hard way >_>. Least this is using PSs for a good cause ^^

If private servers can find formulas, can they help find droprates of things by tweaking and testing them? I'm not too informed on this private server stuff, so don't laugh if it's obviously impossible D: