New Heal Formula

[Russt]

We've seen the Heal formula before. (Well, some of us.)

MAX damage:
(-0.00000000930070097298*LUK^3 + 0.00000114245440636277*LUK^2 - 0.00000678550546220552*LUK + 0.0144845947915278) * MAGIC * INT
Meh.

From a game developer's point of view, such a formula is impractical and would never be implemented. (Yeah, I'm no game developer, but it's fairly easy to step into one's shoes and realize this.) So about a week ago, I set out to find another one.

This is what I have, and it's 100% accurate so far on single target:
MAX = (INT * 4.8 + LUK * 4) * Magic / 1000 * Heal % * Target Multiplier
MIN = (INT * 1.2 + LUK * 4) * Magic / 1000 * Heal % * Target Multiplier

Unconfirmed Target Multipliers:
48/48 on 1 target
38/48 on 2 targets
33/48 on 3 targets
30/48 on 4 targets
28/48 on 5 targets
These don't match universally, though.

My data:
http://i33.tinypic.com/153mn8w.png

*NEW PROJECT*
Heal recovery.
Right now I'm just working with some early data points here.
136 INT, 7 LUK, 157 Magic, level 1 Heal heals 34-41 HP.
136 INT, 7 LUK, 136 Magic, level 1 Heal heals 29-36 HP.
136 INT, 7 LUK, 136 Magic, level 1 Heal heals two for 18-21 HP.
It seems roughly proportional to Magic, just like Heal damage is. However, my calculated Heal damage with these stats is 3-10, so it's not quite the same equation.

[Kevvl]

So M-Att has less of a base for heal damage than Int? Odd...

[Russt]

Where'd you get that from?

(If you meant LUK, that's just an illusion. Yes, LUK has a higher average multiplier than INT, but INT adds to magic as well, which multiplies the whole thing. So INT is unquestionably the stronger of the two.)

[JoeTang]

You're ambitious. I commend you. I may take a look some time with my own Cleric, but I rarely play anymore.

[Kevvl]

If I had 400 Int and 4 Luck, with a 100 M-Att weapon (500 Magic Total)
308~968
Now if I had 100 Int, 4 Luck, and a 400 M-Att Weapon (500 Magic Total)
48~198

Int > Magic for Heal according to your Formula

Assuming 100% heal.

[Russt]

Kev, if you doubt the Magic, go find me a 400 MA staff. Then I'll be able to test whether it's true or not :)
(But yes, INT > Magic. I thought that was common knowledge. And btw, Heal is 300% at max. Go make a cleric before nitpicking on my formula!)

JoeTang, this is coming from the one who found the Venom equation?

[Kevvl]

I honestly never knew Int was better than Magic for heal. Makes my Luckless so much better :)

[Chompy]

I'll be helping testing heal formula's when she comes!
I'll be helping testing heal formula's when she comes!
I'll be healing around the dungeon
Healing around the dungeon
Healing around the dungeon when I Come!
:f6:

[Technolink]

I honestly never knew Int was better than Magic for heal. Makes my Luckless so much better :)

Dex>w atk
Str>w atk
Luk>w atk
Int> m atk

wouldn't that just make sense?

[Sinnuendo]

Dex>w atk
Str>w atk
Luk>w atk
Int> m atk

wouldn't that just make sense?

W. ATK > DEX, STR, and LUK. >_>

Hence why it take 5 (more or less) of one of those stats to make 1 W. ATK.

However, 1 INT = 1 M. ATK, 1 M. DEF, and .1 Magic accuracy (I think).

[GW2000]

Yeah, the other always seemed like the damage was pretty low. How did you figure this out by the way?

Oh yeah, and I'm willing to test for you.

[Russt]

Observations, assumptions, a lot of borrowed data from Sleepy, and some algebra/statistics.

Nothing too intimidating (though if I showed you the Excel sheet that I worked this out on, you'd probably beg to differ).

[GW2000]

Observations, assumptions, a lot of borrowed data from Sleepy, and some algebra/statistics.

Nothing too intimidating (though if I showed you the Excel sheet that I worked this out on, you'd probably beg to differ).

I see, I see. It is a lot cleaner than nekonecat's version.

[Russt]

Yeah. I don't want to bother you with the details, but if you really want to know you can PM me. As for the cleanliness, that's what I was shooting for :)

Edit: I think I'll post my data. It'll probably be more credible with actual numbers up there than just the formula.

[Hazzy]

Dex>w atk
Str>w atk
Luk>w atk
Int> m atk

wouldn't that just make sense?

Weapon attack is a Mele Class's main damage factor, while a Magician's is the Spell Attack.

Magic Attack is to Mage damage, as Str is to Warrior damage. :f3:
(Thus why 100 Magic Attk from an Onyx Apple does nothing)

[Russt]

Yes. But for Heal damage, the main damage is Magic Attack, but it's divided by 10 (or 9.99). So an Apple is equivalent of +10 Attack, which still isn't that impressive.

[GW2000]

Cool, you posted the data, I was kinda curious. :f2: I'm at Victoria again, so I'll gather some data for you.

EDIT: Alright, I was at Zombie Mushie for a while and gathered the following data.

INT: 331
LUK: 77
M. Atk: 429

Predicted Damage: 909 ~ 2444
Observed Damage: 901 ~ 2411

I'm sure the M. Def of Zombie Mushroom lowered the damage, and the formula is very accurate, better than Nekonecat's, which predicted 585 ~ 2341. If I have time, I'll test out Healing 2 monsters.

[Technolink]

Cool, you posted the data, I was kinda curious. :f2: I'm at Victoria again, so I'll gather some data for you.

EDIT: Alright, I was at Zombie Mushie for a while and gathered the following data.

INT: 331
LUK: 77
M. Atk: 429

Predicted Damage: 909 ~ 2444
Observed Damage: 901 ~ 2411

I'm sure the M. Def of Zombie Mushroom lowered the damage, and the formula is very accurate, better than Nekonecat's, which predicted 585 ~ 2341. If I have time, I'll test out Healing 2 monsters.

Z mushies have 30 mdef, asuming your a higher lvl then them (lol), that should be 15 poitns off your max and 18 off your min.

Thus Predicted Damage: 891~2429
Observed Damage-----: 901~2411

A very nice fit if I do say so myself. I think you've done it Sap. Now just to figure out the multipliers for the other monsters =D

[Russt]

Nice.

The 2-5 are a bit of a mess, though. I'm 99% sure that it's a multiplier over the whole thing, but other than that, the approximations in the thread are all I have for now.

[LazyBui]

Data get.

LVL: 50
INT: 262
LUK: 6
MATK: 350

Fighting Coolies (level 57, 180 mdef) for around an hour.

Projected: 355-1347
Observed: 254-1250

[Secks]

Wow thanks! :f2:

[Russt]

Data get.

LVL: 50
INT: 262
LUK: 6
MATK: 350

Fighting Coolies (level 57, 180 mdef) for around an hour.

Projected: 355-1347
Observed: 254-1250
Is that without defense?
With defense, it'd be 247~1257.
That's without adjusting for the level difference (which I don't know how to do). Maybe magic defense doesn't have a level component at all.

Thanks for the data. Keep it coming! -needs that unmaxed Heal-
I'm thinking of remaking my cleric though, so I could get that.

[LazyBui]

That was projected without defense, I figured that that would be most helpful to figuring out exactly how level is a factor (or if the defense reduction is correct, for that matter).

[Russt]

Well.
Using the weapon defense formula on it gives 229~1191, which is quite a bit off.

[Technolink]

lol. Maybe heal does ignore.

I'll do ya a favor Sap. My cleric should be lvling tomorrow after I get 40 coins, I'll go to something like skeles (maybe not that high), but you get the point, and see if level makes a diff.

Also, I'd think there would be a full multiplier, like every monster after the first takes the same amount of reduced damage. Its hard to test that with heal, you'd need a HELL of a lot of screenshots, then you have to tell which monsters are in what order. That doesn't account of the lag when you pressed the button to when the damage appared to how much they moved.

[Russt]

...You're going to miss, Techno. I hope you realize that. Go to V/H or something.

Also, with area mobbers, all the monsters get hit at the same time. There is no first monster. Every one takes the same amount of reduced damage depending on how many were hit in total.

[LazyBui]

Okay, so I've been doing a little bit of messing around (and I do stress little - Scania is impossible with KSing), and I bring you 2 Coolie hits!

I originally also had a question as to whether or not misses count for the damage decrease, but it appears that it's applied equally to all monsters as opposed to something like Iron Arrow. Hopping into a mob of 5 yields much more stable damage than attacking a single target. It doesn't decrease per target, or so it would seem. This does need some more testing, but perhaps my results as I increase the number of targets I hit will tell us.

Anyway:

Level: 50
INT: 262
LUK: 6
MATK: 350

Enemy level: 57
Enemy MDEF: 180

2 targets, observed damage: 167-967

Those should be pretty close. I thought I saw a couple on the low end that could've been lower, but I wasn't certain due to two numbers overlapping or whatever, so I didn't count them. Should keep that in mind as far as calculations go.

[Tikey]

Is that without defense?
With defense, it'd be 247~1257.
That's without adjusting for the level difference (which I don't know how to do). Maybe magic defense doesn't have a level component at all.

Thanks for the data. Keep it coming! -needs that unmaxed Heal-
I'm thinking of remaking my cleric though, so I could get that.

Magic defense doesn't have a level component. I basically do the same damage on a Viking as I do on a Snail. >_>

[Russt]

Level component = you're below the monster's level and the game nerfs your damage because of it.
If you're level 146, your damage to a Viking won't get a level reduction regardless.

And Bui, are you sure you hit a 967? I'm getting strange results here.

[LazyBui]

Positive. I made absolutely certain that I witnessed the numbers I submitted.

However, the 96x might've been with a miss on another target, I still miss sometimes. Could be that misses affect things oddly.

EDIT: I think I'll do some more testing since I can't sleep anyway. I'll record min/max results for 2 hits and 1 hit/1 miss. That might help more.

EDIT2: Pretty sure misses are a nonfactor. I'm getting 94x fairly often with both single miss and no miss between 2 targets.

http://i266.photobucket.com/albums/ii247/LazyBui/1t.png
http://i266.photobucket.com/albums/ii247/LazyBui/2t.png

Didn't feel like waiting around for max damage on both when it seems as though they're the same. :[
Oh yeah, and I saw a 970 in there. My earlier data showed 967 as the max observed, so it's only three points, but ya.

EDIT3: ...971? o_O It's almost like it keeps rising even though I spent around an hour on 2 targets earlier.

... 972. I should almost stop looking for LOW damage because it's hard to process that and take a screenshot of high damage if I see it.

ok so. It seems much harder to hit minimum than maximum. Either that or I'm just having the opposite luck of earlier (?).

http://i266.photobucket.com/albums/ii247/LazyBui/1d.png
http://i266.photobucket.com/albums/ii247/LazyBui/2d.png

I think it's pretty safe to say that missing doesn't matter, which is good for my purposes. I'll check out 3 mobs in a bit. I can produce screenshots of any of the data I put forth, so just let me know if something else seems wonky.

Hopefully a 967 works for you - I have observed up to 972 though.

http://i266.photobucket.com/albums/ii247/LazyBui/3.png

Surprisingly tired, I might be able to sleep now. If so, I'll do 3 targets later. If not, you'll know.

[Tikey]

Level component = you're below the monster's level and the game nerfs your damage because of it.
If you're level 146, your damage to a Viking won't get a level reduction regardless.

And Bui, are you sure you hit a 967? I'm getting strange results here.

Lemme rewind time for a moment. xD

http://i25.photobucket.com/albums/c58/Mega_Tikey/Maple%20Story%20Screenshots/Maple0023.jpg

If level played a role like in physical damage, I wouldn't be able to hit that much at that level.

[Russt]

Ah, I see.
So magic accuracy is really the limiting factor, not level defense.

@ Bui - That's odd, then. According to your data, the 2 monster multiplier must be >0.788403, but it also must be <0.773176. Contradiction.

And yes, I'm sure I didn't mix the two up.

[Technolink]

I'll go to DTs or something to bring in the final results, but that pic up there is pretty difinitive.

BTW Sap, is that magic formula (the quadratic) the real one, or an assumed?

[Russt]

It's copied off SW.

[GW2000]

Got some more data:

INT: 331
LUK: 77
M. Atk: 429

Predicted Damage: 909 ~ 2444
Predicted Damage on 4 targets: 576 ~ 1549
Observed Damage on 4 targets: 455 ~ 1408

This was done on Voodoos, which have 210 magic defense.

[Russt]

So with defense applied in full, that's -126~-105
Or, on your 4 target range, 450~1444
A pretty nice min damage fit there, though I can't say the same for the max.

[LazyBui]

Any specific things you'd like me to test before I level? I'm starting to get up there on % and I'd think if this is anomalous, it's good for data. Planning on messing around with 3 targets after an APQ.

[Dusk]

While this formula is much cleaner, I still think it's somewhat inaccurate because of the /999. That just feels like it's wrong. A number should probably be adjusted here or there. Nice work though.

[JoeTang]

Divide by 1000 instead?

[Russt]

I had 1000 at first, but one of my data samples only fits if I make it 999.
That particular sample is only off by 1 damage though, so it could easily be a rounding error.

Bui: Yes, more targets would certainly be helpful.

[Afrobean]

Hi guys, I thought I'd pop in and share a few data points from my HP cleric. Only level 35, and only has level 14 heal (ie 140%), but I think the data points are worthwhile given the abnormal nature of the source.

Basically, I pumped pure HP from 1~30. At 30, I had it confirmed for myself that HP meant NOTHING, but I kept going with the project with a plan to leach experience using snail throwing. Well, long story short, that dream was killed when they made snail shell throwing require some sort of accuracy.

Using my Maple Staff, I had:

max hit: 42
min hit: 2
magic: 123
int: 66+2
luk: 4

Using a 0 magic weapon:

max hit: 19
min hit: 1
magic: 73
int: 66+2
luk: 4

Also notice: I still miss quite a bit due to my low magic accuracy (see: low int stat), even though I tested on Zombie Mushrooms and that's the lowest undead thing. This may account for an outlier min hit, such as the min of 2 when I was using my full magic gear, because if I recall, along with missing, sometimes hits will come off as UNBEARABLY weak.

So, guys, does that break this formula too? A quick test for me tells me that my max/min with Maple Staff should be 16~59, and it should be 9~35 with my second set of stats posted. Am I wrong?

EDIT: By the way, don't be heartbroken if this proves your formula isn't 100% accurate. None of the formulae are. Being very accurate for normal builds is good enough, really.

[Nikkey]

http://i151.photobucket.com/albums/s139/WhiteKnightt/MapleWindia/Maple0227.jpg
http://i151.photobucket.com/albums/s139/WhiteKnightt/MapleWindia/Maple0228.jpg

Only the max dmg was observed, because I'm like that, a powergirl.

(changed ign to LagIess, if anyone wonders)

MAX = (INT * 4.8 + LUK * 4) * Magic / 999 * Heal %
Max = (412 * 4.8 + 4*4) * 543 / 999 * 3 = 3250

Removing damage from mdef: 3145.

Doesn't make correct damage. A more correct way would be to actually include the fact that there's a mastery percent (30%, which may be multiplied with 0.9 or 0.8 from all I know) affecting the minimum damage, like all other damage formulas:


MAX = [(INT * K + LUK ) * Magic /1000 * Heal % - mdef*0.5]*heal %
MIN = [(INT * K *0.3 * 0.9 + LUK ) * Magic /1000 * Heal % - mdef*0.5]*heal %

That would make more sense, since all other formulas use that way of calculating.

[Russt]

Not all others. L7, Venom, Phoenix/Frostprey, to name a few from my other thread.
And 1.2/4.8 is the best fit I've found so far, given all the data points.

I don't usually consider not reaching the supposed max damage enough evidence to disprove a formula, unless it's by a wide margin like over 10% of the range (300 damage off, in your case). However, if my equation predicted, say, 3081 for your max damage, that would be valid counterevidence right there. Since a 3083 would be a physically impossible number if the formula was true.

In this case, 3083 is definitely possible, even if it's somewhat unlikely that you didn't hit anything higher. 4.8 is already a pretty tight fit for some of the other data points.

[LazyBui]

Okay, I think something is strange.

Level: 50
INT: 262
LUK: 6
Magic: 350

Enemy level: 57
Enemy MDEF: 180

3 targets, observed damage: 138-840

I'm relatively certain the low end is close to actual minimum damage - but I'm not so sure on the high end.

It seems like I'm hitting way fewer numbers outside a normal distribution (most of my hits end up 250-600 or so) than I would with 1 or 2 targets. Perhaps 1 out of every 20-25 hits exceeded 800. It could just be my luck for today, but I find that to be a little strange.

[Russt]

Hi guys, I thought I'd pop in and share a few data points from my HP cleric. Only level 35, and only has level 14 heal (ie 140%), but I think the data points are worthwhile given the abnormal nature of the source.

Basically, I pumped pure HP from 1~30. At 30, I had it confirmed for myself that HP meant NOTHING, but I kept going with the project with a plan to leach experience using snail throwing. Well, long story short, that dream was killed when they made snail shell throwing require some sort of accuracy.

Using my Maple Staff, I had:

max hit: 42
min hit: 2
magic: 123
int: 66+2
luk: 4

Using a 0 magic weapon:

max hit: 19
min hit: 1
magic: 73
int: 66+2
luk: 4

Also notice: I still miss quite a bit due to my low magic accuracy (see: low int stat), even though I tested on Zombie Mushrooms and that's the lowest undead thing. This may account for an outlier min hit, such as the min of 2 when I was using my full magic gear, because if I recall, along with missing, sometimes hits will come off as UNBEARABLY weak.

So, guys, does that break this formula too? A quick test for me tells me that my max/min with Maple Staff should be 16~59, and it should be 9~35 with my second set of stats posted. Am I wrong?

EDIT: By the way, don't be heartbroken if this proves your formula isn't 100% accurate. None of the formulae are. Being very accurate for normal builds is good enough, really.
Hahaha~ just inputted your data. When you account for the Zombie Mushrooms' defense, the formula actually fits quite well.
Observed | Projected
1-19 | 1-20
2-42 | 1-44

On the contrary, rather than proving it inaccurate, this is very interesting data. It helps confirm that Heal % is multiplied over everything. And it's also helpful as far as order of operations go.

Lemme explain. You didn't see many 1's, right?
And you probably saw a lot more misses than you would've seen with magic claw, right?

Maple does something I call "1-correction" to most damage after defense is applied and whatnot. Basically, it checks whether the damage is within the range of 1-99999, and adjusts it if not. So if a high amount of defense makes your damage go into the negatives, 1-correction turns it into a 1. Hence why most attacks do 1 damage when they can't penetrate defense.

With Heal, however, I believe there either is no 1-correction or it happens before subtracting defense. So after defense, your damage is occasionally negative. This makes no sense to the game, so it turns it into a miss.

It happens with a couple other skills, notably at low levels; I'm not entirely sure whether it's the same case or not.

And Bui, I don't find that strange :P assuming the damage is a uniform distribution, you should only see 800+ damage 1 in 17 times anyway. But I haven't really looked at it yet, so we'll see.


Anyway, replaced the data with an image. Cleaner.

[Afrobean]

Well isn't that interesting.

I'd say this is pretty much it then. How did you get this again?

[Technolink]

Sap, think of Iron arrow and how it misses on the second bonefish when it had wdef up.

Heal is the same logic, a skill with a multiplyer that brings it lower.

[Stereo]

I'm curious about the multi-target numbers.

When I apply the formula like this they seem to fit neatly:

M = (4.8*int+4*luk)*matk/999
Max = (M*t - 0.4*mdef)*%heal
t = multiplier for number of targets,
1->1
2->0.8
3->0.7
4->0.66
5->0.6

There's not really enough data to compare this straight across on anything except the 1 character with 201 int and I don't have an excel spreadsheet set up with the formula to quickly compare this to your other multi-target monsters. Was wondering how well this works out for the other values.

[Russt]

0.4? That's a new figure. I've so far been assuming M*t*%heal - 0.5*mdef to project the maximum damage, and 0.6*mdef for the minimum.

I'll have to look into it later; I'm having my wisdom teeth out tomorrow, and I have to sleep early.

[Stereo]

I got that from the one time I saw actual numbers posted as I couldn't figure out how you were doing it, it could be lower but that's how it is for most skills (applied before %heal, and times around 0.4-0.5)

Also as indicated it works out ok for the 1 character that's got all 5 target amounts max damage noted, as the numbers in previous post result in within 3 damage on every amount.

[Harrisonized]

This is what I have, and it's 100% accurate so far:
MAX = (INT * 4.8 + LUK * 4) * Magic / 999 * Heal %
MIN = (INT * 1.2 + LUK * 4) * Magic / 999 * Heal %
So INT carries more weight than LUK? Interesting to know that...
Hmm... do you think that DEX is a factor in this as well? Because the 'hands' stat is a combination of DEX, INT, and LUK, which suggests that all three are related in some way. It may account for the slight discrepancies in your data and predictions.

[Afrobean]

So INT carries more weight than LUK? Interesting to know that...
Hmm... do you think that DEX is a factor in this as well? Because the 'hands' stat is a combination of DEX, INT, and LUK, which suggests that all three are related in some way. It may account for the slight discrepancies in your data and predictions.
Unlikely, since all holy magicians will have ~10 or less dex, usually 4.

Hands likely does nothing more than whatever it does with the Maker skill. It's even been confirmed that it has nothing to do with magic accuracy, which was a popular theory for a short while.

[Harrisonized]

Unlikely, since all holy magicians will have ~10 or less dex, usually 4.
Many people don't start perfect and until the MTS came out, can't afford to reset that stat to four. Even with MTS out, some people refuse to reset it, thinking that it takes too long to merchant.
Then some have zhelms and some don't. The extra 13~17 DEX from that zhelm might add damage. The horntail pendant, which adds yet another 21~23 DEX may make it worthwhile investigating.
It's like Dits and Shadowers getting more Atk from a zhelm because of the STR on the helmet.

[Russt]

I got that from the one time I saw actual numbers posted as I couldn't figure out how you were doing it, it could be lower but that's how it is for most skills (applied before %heal, and times around 0.4-0.5)

Also as indicated it works out ok for the 1 character that's got all 5 target amounts max damage noted, as the numbers in previous post result in within 3 damage on every amount.
I've investigated weapon defense before. It's pretty much confirmed to be 0.6 off the max and 0.5 off the min before skill percentages, when level is not a factor.

I haven't tested out magic defense much, though my limited samples seem to support the 0.6/0.5. Then again, that was more assumption than actual conclusion, since I was working with a mere 10 defense.

[Technolink]

Sap, is that magic calc on H-S correct?

If so I'll test out the formulur for you on some crazy stuff.

[Russt]

I'm not sure. Go to my thread; the 'fraction version' seems to be the most accurate.

[Afrobean]

Many people don't start perfect and until the MTS came out, can't afford to reset that stat to four. Even with MTS out, some people refuse to reset it, thinking that it takes too long to merchant.
Then some have zhelms and some don't. The extra 13~17 DEX from that zhelm might add damage. The horntail pendant, which adds yet another 21~23 DEX may make it worthwhile investigating.
It's like Dits and Shadowers getting more Atk from a zhelm because of the STR on the helmet.
Nothing you said matters. The point still stands that there is very little difference in dex between any Magicians, and it is illogical to think dex might do something like that.

[Russt]

Next Tespia, if one of my data slaves gets in, we'll test with 4/999/4/4 and 4/4/4/999 to make sure.

[JoeTang]

Are those multipliers agreed on? If so, I'll slap this thing in for v1.00, which you should expect around early August. Possibly later because I have to redraw things. (because someone nags about colours not looking well together. I forget who.)

[Russt]

I'm curious about the multi-target numbers.

When I apply the formula like this they seem to fit neatly:

M = (4.8*int+4*luk)*matk/999
Max = (M*t - 0.4*mdef)*%heal
t = multiplier for number of targets,
1->1
2->0.8
3->0.7
4->0.66
5->0.6

There's not really enough data to compare this straight across on anything except the 1 character with 201 int and I don't have an excel spreadsheet set up with the formula to quickly compare this to your other multi-target monsters. Was wondering how well this works out for the other values.
I tried your way of calculating it.
It's very close for many of the samples, but it just doesn't fit that evenly. No matter what I put for the defense multiplier, there are always some discrepancies if I subtract it before multiplying Heal's %. Whereas they all fit pretty evenly, if not 100% accurately, if I subtract afterward.

That one HP cleric's sample makes this clear.

@ Joe, the multipliers are still a bit of a mystery at this point. I'll play around some more to see what I can get, but we don't have definite answers yet. Other than the approximations in the main thread.


Oh and Bui, if you haven't leveled yet, I've found the problem.
The problem wasn't with the 967. It was with the 167. I see you screened a 176, but is the 167 for sure?
I can't put any sort of multiplier for 2 targets without infringing on that 167.

Anyway, ignoring the 167 (though I hope I don't have to ignore it), I've been able to place bounds on the target multipliers:
2: 0.7885 - 0.8012
3: 0.6905 - 0.6944
4: 0.6210 - 0.6406
5: 0.5699 - 0.5890
Need more data. With enough samples, we'll be able to pin them within two or three decimal places, and then it'll be pretty apparent what they are.
So far, though, it's quite an enigma. It's definitely not an exponential of any sort, nor is it a reciprocal of something.