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> Spell Damage, the calculations, Originally started by - GrobbleWobble
Necromis
post Oct 12 2004, 06:36 PM
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damage calculation, the formula

NOTE: I have edited the original post to remove posts that were not related to the information of this topic. Nothing of value was lost. Thanx D O M

QUOTE ( grobblewobble Posted: Jul 1 2004 @ 11:20 AM )
Alright, I'm not finished yet, but I have a temporary result. If you ignore the effects of guild level (set to nomad 1), I found:

damage = RND1 * (Str^2 * 0.015 + 5) * DamMod * Sizefactor + RND2 * Att / 10

RND1 and RND2 are random numbers between 0 and 1, but RND1 has a minimum value of 0.33

Sizefactor is a factor depending on your size compared to the monster's size: Sizefactor = 1 + 0.15 * (YourSize - MonsterSize).


1: Sizefactor is relative to monster size
2: dependence on Str is non-linear; this formula works well for str < 60


QUOTE ( aardless gs Posted: Jul 1 2004 @ 12:19 PM )
You are absolutely right on the defense thing: I once tried creating a monster with 850 def, and a character with 300 att would hit it every turn. Boosting def to 1000 decreased only slightly the hit chance to around 80-90%.


QUOTE ( Crusher Junior Posted: Jul 1 2004 @ 07:45 PM )
Spell damage formula (from Archi's Dojo):

spell(A/B) at spell lvl SL does damage= 3A + B * SL / 13 - 10

I think A/B is the number that spells have under Damage (like 15/6).
The A would be 15 and the B would be 6. SL stands for Spell Level. This is from Archi's Dojo and is from Demise, so any experts out there, if you feel like correcting me...then yeah, correct me


QUOTE ( scphillips Posted: Jul 1 2004 @ 10:53 PM )
from slimey's guide same a/b format as the listed damage, damage = a + (b*sl)/10. I'm pretty sure the demise one doesn't cross over because 3A would have the lower spells like firebolt or coldblast doing 45 damage at a very early level, which cannot be right.

(to make sure i'm not being very harsh) Thanks for posting that formula though, I hadn't gone looking for demise stuff when I was thinking about spell damage formula, always interesting to see the demise side of things, but if that's definetly the one for demise then that's one thing that doesn't translate over to one well


QUOTE ( grobblewobble Posted: Jul 2 2004 @ 08:32 AM )
Ok, I gathered data about spell damage. We have 2 candidate functions:

From Archi's Dojo

spell(A/B) at spell lvl SL does damage= 3A + B * SL / 13 - 10


From Slimey's page (I'm the one who came up with it, and actually it was for healing; I'm not sure at all healing works the same as damage. Besides, I think I was plain wrong.)

damage = a + (b*sl)/10


However, I am now sure that neither of these formulas are on the right track. It appeared that spell damage increases in a highly non-linear way. Here are some data. I tested two spells: Firebolt(10/1) and Blue Flame(15/11). The tests were on a monster of normal size with no resistances.

I tested 2 more spells: Cold Blast(15/2) and Acidic Spray(30/11)

First off, it appeared that the minimum damage a spell does is 50% of the maximum damage. I only show the obtained maximum damage here.

SL 15: FB 25, BF 53, CB 39, AS 92
SL 65: FB 35, BF 117, CB 59, AS 170
SL 115: FB 38, BF 172, CB 66, AS 230
SL 265: FB 43, BF 313, CB 89, AS 386

Totally non-linear. I'm trying to think of a formula predicting these values..


QUOTE ( aardless gs Posted: Jul 2 2004 @ 12:50 PM )
Comparing Blue flame and Cold blast, it seems that, indeed, an increase of 0/1 in spell power, will inrease damage by 10%*SL.
If that is correct, we can remove that effect and get the following adjusted table, where all spells are equalized to x/1 (e.g. Acidic spray becomes 30/1):

SL=15 FB=25 BF=38 CB=37.5 AS=77
SL=65 FB=35 BF=52 CB=52.5 AS=105
SL=115 FB=38 BF=57 CB=54.5 AS=115
SL=265 FB=43 BF=48 CB=52.5 AS=121

The interesting thing about this table, apart from the suspicious behaviour of BF and CB at level 265, is that AS is almost exactly three times FB, and twice BF and CB. So there is a linear effect of the first component of a spell's power. I can't make sense of the residual values, I suspect a log(SL) , but they increase even slower than that.

A tentative formula might look like:
damage= 2*A*Log(SL)+(b-1)/10*SL
This formula will overevaluate high spell level damage, underevaluate low spell level damage, and be more or less correct for spell levels around 50.

P.S. Grobble: I suspect that SL 265 damage is not as accurate as the other values.



A better estimate of the damage function yields:

Damage= [(3.3-sqrt(Log SL)]*Log(SL)*a+(b-1)*SL/10

3.3 might not be the exact value, it seems it slowly creeps forward from 3.267 at SL=15 to 3.295 at SL=115. It might be better to use 3.28. SL 265 values range too wildly to use them reliably, IMO.


QUOTE ( scphillips Posted: Jul 2 2004 @ 03:44 PM )
interesting stuff

btw, while you're hacking around with your spell levels you might as well try and prove/disprove the statement "SL for damage calculations comes from your current guild INSTEAD of the guild that you learn the spell in"


QUOTE ( A. J. Raffles Posted: Jul 6 2004 @ 03:56 PM )
"Why do you suspect that SL 265 damage is not as accurate as the other values, Aardless?"


QUOTE ( aardless gs Posted: Jul 7 2004 @ 02:38 PM )
Was that a question? *Jumps at the opportunity to spam*

The predicted values of the estimation function, using 3.28 as constant, are:

SL=15 FB=25.8 BF=53.7 CB=40.2 AS=92.5
SL=65 FB=35.1 BF=117.6 CB=59.1 AS=170.2
SL=115 FB=38 BF=172 CB=68.5 AS=229
SL=265 FB=41.8 BF=327.6 CB=89.1 AS=390.3

Consequently, the error matrix looks like:

SL=15 FB:+0.8 BF:+0.7 CB:+1.2 AS:+0.5
SL=65 FB:+0.1 BF:+0.6 CB:+0.1 AS:+0.2
SL=115 FB:+0.0 BF:+0.0 CB:+2.5 AS:-1.0
SL=265 FB:-1.2 BF:+14.6 CB:+0.1 AS:+4.3

As you can see, the largest errors occur at SL 15 for FB, at SL 15 and 115 for CB, and especially at SL 265 for BF. A possible cause for errors could be that my estimation sucks: this is a distinct possibility, though I am confident that if Grobble's data is accurate, then my estimation is rather good, with errors well below 5%.

When I wrote that SL 265 damage data wasn't accurate, I was using 3.3 as constant. The only really bothersome data with 3.28 is, as stated above BF at SL 256. I am now convinced that 3.28 is the correct value of the constant (as opposed to almost certain), since sqrt(Log500) =1.642854 , 500 being the highest possible SL, and that 1.64... x2= 3.2857.


QUOTE
btw, while you're hacking around with your spell levels you might as well try and prove/disprove the statement "SL for damage calculations comes from your current guild INSTEAD of the guild that you learn the spell in"




AJ is correct, I tried turning my healer into a sorcerer, at guild level 9 (i.e. SL 5), he dealt 66 damage with the spell "poison", and healed a little more than 20 with "heal". Both spells are 15/6, so he obviously cast damaging spells at his healer SL, and healing spells at current guild SL.


QUOTE ( scphillips Posted: Jul 7 2004 @ 04:28 PM )
thanks for the heal vs damage related bug comment aardless.

weird being called sc, but still cool with it

to have a third (and meaningful thing) in here: You only really addressed the heal vs damage related bug with one class (ie. you didn't flip back to your healer and throw out numbers), so (and someone kind of said this above), what happens if heal and damage spells have different effectiveness formulas? Want to run your test formula on all the heal spells and see how they come out?


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Necromis
post Oct 13 2004, 10:14 AM
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QUOTE ( aardless gs Posted: Jul 9 2004 @ 02:27 PM )
laugh.gif, your persistence is starting to pay-off: the formula fails in predicting healing spells. Preliminary results on other damaging spells are encouraging. I'll post more info and spout more numbers in the week end, or Monday; I hope to infer the healing formula by then, but for now I'm a bit in the dark...


I. Testing the damage formula

I selected a few spells with different A/B from Grobble's spells. They are: Lightning Bolt (LB, 15/4); Thunder Bolt (TB, 20/7); Cause Heavy Wounds (CHW, 13/4); Cause Fatal Wounds (CFW, 20/9); and Teleport (TEL, 25/8).

For each spell, except teleport, I tried to determine the max damage at SL 51 and 100. For teleport, I only tried it at SL 150, because the casting cost was too high in the other cases to throw it repeatedly. Since I couldn't always determine the max, I decided to post the range of observed values. According to Grobblewobble, the range is from simple to double; although I have seen slightly greater ranges, in a couple of cases (tested on 0% resistance creatures).

SL=51 LB:30-64 TB:50-97 CHW:29-55 CFW:55-107
SL=100 LB:44-87 TB:70-136 CHW:41-79 CFW:79-156
SL=150 TEL:110-205

The predicted max values are:
SL=51 LB:65.8 TB:97.98 CHW:59.1 CFW:108.2
SL=100 LB:85.97 TB:134.6 CHW:78.5 CFW:154.6
SL=150 TEL:203.2

Errors on prediction are:
SL=51 LB:+1.8 TB:+0.98 CHW:+4.1 CFW:+1.2
SL=100 LB:+0.97 TB:-1.4 CHW:-0.5 CFW:-1.4
SL=150 TEL:-1.8

Overall, I am satisfied by the predictions, although there seems to be some fine-tuning value needed, possibly an added constant.

Random notes: if the formula is correct, then it seems the spell damage is dealt separately to each group of monsters, with a reroll for each group.

---------------------------------------------------------------------------------------


II. The healing formula

I tried to come up with good max values for healing spells, so I walked on traps and cast each one 20-30 times. A stroke of luck made me select SL 9, as one of the levels: I don't think I would have inferred the formula otherwise.

SL=9 MH:9 H:31 R:87
SL=46 MH:21 H:61 R:160
SL=100 MH:34 H:94 R:238
SL=150 MH:42 H:121 R:305

MH stands, of course, for Minor Heal, H for Heal and R for Restoration.

The healing formula seems to be:

A*Log(K*SL)+(B-1)/10*SL

where K is:
3 in the case of MH
6 in the case of H
9 in the case of SL (that's where the stroke of luck came in)

Predicted values, rounded to closest decimal, are:
SL=9 MH:9 H:30.5 R:87.1
SL=46 MH:19.9 H:59.6 R:159.9
SL=100 MH:32.4 H:91.7 R:238.2
SL=150 MH:43.3 H:119.3 R:305.2

Errors on prediction:
SL=9 MH:0 H:-0.5 R:+0.1
SL=46 MH:-1.1 H:-1.4 R:-0.1
SL=100 MH:-1.6 H:-2.3 R:+0.2
SL=150 MH:+1.3 H:-1.7 R:+0.2

Errors are a bit high on MH, so the formula may be incorrect in that case. We are all a lot more interested in restoration anyway, aren't we?



Since Braindead, is both unattentive, and has little faith in my formula  , here are the predicted values of the other formulas:

A ) Grobblewobble's: Healing = A + (B * SL) / 10

Predicted values rounded to closest decimal:
SL=9 MH:7.7 H:20.4 R:51.7
SL=46 MH:18.8 H:42.6 R:99.8
SL=100 MH:35 H:75 R:170
SL=150 MH:50 H:105 R:235

Error matrix:
SL=9 MH:-1.3 H:-10.6 R:-35.3
SL=46 MH:-2.2 H:-18.4 R:-60.2
SL=100 MH:+1 H:-19 R:-68
SL=150 MH:+8 H:-16 R:-70

B ) one from Archi's Dojo

spell(A/B) at spell lvl SL does damage= 3A + B * SL / 13 - 10


Predicted values rounded to closest decimal:
SL=9 MH:7.1 H:39.2 R:119
SL=46 MH:15.6 H:56.2 R:156
SL=100 MH:28.1 H:81.2 R:210
SL=150 MH:39.6 H:104.2 R:260

Errors:
SL=9 MH:-1.9 H:+8.2 R:+32
SL=46 MH:-5.4 H:-4.8 R:-4
SL=100 MH:-5.9 H:-12.8 R:-28
SL=150 MH:-2.4 H:-16.8 R:-45


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aardless
post Oct 14 2004, 10:22 AM
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laugh.gif, you may want to edit the top of the first post with the formulae, so that people who don't want to read through all that stuff can get to the interesting part.


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post Oct 18 2004, 12:12 PM
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I'd like to retake back an affirmation: a monster with 850 def would every time been hit by a char with 300 Att. Well: it's because chars have got wisdom and intelligence: stats which raise our hitting chances.

I think that's the reason! ohmy.gifk:


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Straxx
post Apr 3 2005, 02:27 AM
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*Rise from your grave!"

I've been trying to figure out these formulas for a while now. Assuming I wrote them correctly in Excel, these formulas seem to be off. I cast WoD at SL 62 with my healer and dealt 130-196 dmg to the Giant King. According to Excel, I should only deal 138 dmg.

When you write: Damage= [(3.3-sqrt(Log SL)]*Log(SL)*a+(b-1)*SL/10 do you mean: ((3.3-(SQRT(LOG(SL))))*(LOG(SL)*A)+(((B-1)*(SL/10))/10))?

Also, I've never seen anyone discuss the merits of using Cure at higher Spell Levels. It heals 20/15 and removes poison/disease. Compared to 40/13 for Restoration. Since Cure costs more it should heal more as well at some point I think. It does have a higher value for B.

And what use is Magical Skill? Thieving and Fighting are easy to figure out but shouldn't total magical skill enter into things as well?

I've been talking to David Allen about the formulas and unfortunately he no longer has the source for mordor. He says he modified it and it became demise... so no luck there.
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post Apr 3 2005, 03:42 AM
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how can you calculate the damage cone to a monster?? Monsters have resistance to magic and also are resistant to a type of spell....
You may be able to calculate the damage you should be inflicting.. but not for a specific monster.

If i'm wrong, please say so. i'm quite interested in this...



QUOTE
I've been talking to David Allen about the formulas and unfortunately he no longer has the source for mordor. He says he modified it and it became demise... so no luck there.

well that was a bit dumb... crybaby.gif
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fart642000
post Apr 3 2005, 04:00 AM
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QUOTE (unleashed @ Apr 2 2005, 10:42 PM)
well that was a bit dumb...  crybaby.gif


yep

doesn't make much sense to not make some sort of back-up of it (then again maybe something happened to it)

o well


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post Apr 3 2005, 06:19 AM
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QUOTE (Straxx @ Apr 2 2005, 10:27 PM)
I've been trying to figure out these formulas for a while now. Assuming I wrote them correctly in Excel, these formulas seem to be off. I cast WoD at SL 62 with my healer and dealt 130-196 dmg to the Giant King. According to Excel, I should only deal 138 dmg.
*


I've always estimated spell damage using Grobblewobble's formula, and it usually seems to work pretty well: damage = a + (b*sl)/10 .

For WoD @ SL 62, that's 30 + (51*62)/10, or 346.2. The Giant King has 50% Magic Resistance, so that's reduced by 50% to 173.1: exactly in the range of damage you measured.

QUOTE (Straxx @ Apr 2 2005, 10:27 PM)
Also, I've never seen anyone discuss the merits of using Cure at higher Spell Levels. It heals 20/15 and removes poison/disease. Compared to 40/13 for Restoration. Since Cure costs more it should heal more as well at some point I think. It does have a higher value for B.


Well, if Grobblewobble's formula is correct, the two should heal about the same at spell level 100: 40 + 130 vs. 20 + 150. But Restoration costs (minimum) 7 SP and Cure 8 SP, so even at spell level 500 (!), Restoration would remain slightly more efficient in terms of HP healed/SP. My guess is that Cure is worth it if you're poisoned or diseased, but otherwise, Restoration is slightly more efficient.


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post Apr 3 2005, 07:48 AM
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QUOTE (Nudibranch @ Apr 3 2005, 04:19 PM)
Well, if Grobblewobble's formula is correct, the two should heal about the same at spell level 100: 40 + 130 vs. 20 + 150. But Restoration costs (minimum) 7 SP and Cure 8 SP, so even at spell level 500 (!), Restoration would remain slightly more efficient in terms of HP healed/SP. My guess is that Cure is worth it if you're poisoned or diseased, but otherwise, Restoration is slightly more efficient.
*


well if you actually did get both spells at minimum spell cost, even 1 point would make a large difference...
If you think about it...
let's say you had 215 spell points.
215/8 = about 26 casts of cure.
215/7 = about 30 casts of restoration.

Being only about 4 casts more, this could indeed help the character survive in the dungeon about 13.5% longer...

I say every point counts smile.gif
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aardless
post Apr 3 2005, 11:34 AM
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Straxx: correct me if I'm wrong, WoD is a 30/51 spell. If you're at SL 62 then I have a max damage of 414,69. I'm using the formula I posted with the 3,3 constant replaced by 3,2857. Excel might complain about the square brackets, just replace them with normal brackets.

As Nudi pointed out, the Giant King has 50% magic resistance, so that maximum damage you deal should be around 207, and minimum around 103 (that is, assuming my formula is correct).

About Cure, you're right, it's never been discussed, I'm pretty sure it follows the same formula I posted above, with a slightly higher K (maybe 10? dntknw.gif ) than Restoration. However I'm too tired (cuz I've been trying to find out the formula for hand-to-hand combat, and I'm a bit fed up with data collection, ATM) to collect data to find out. It would seem reasonable that at some point it should become more efficient than Restoration. Giving it a K=10, it heals slightly more than Restoration at about SL 350, while still costing more. At SL 500 Restoration heals 746 hp, while Cure would heal 774 hp. So according to the formula, it would seem that Cure never becomes more efficient. Increasing K to 12 has negligible effects. Although hard data may prove me wrong. dry.gif

DA says that to everyone.


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Straxx
post Apr 3 2005, 03:00 PM
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My mistake, I had some trouble inputing the formula in excel, but now it's fine. I've modified Seths spell guide to include damage done and number of enemies hit. I also fixed some rounding errors.
You can get the updated version here

QUOTE
DA says that to everyone.

That's good. At least he wasn't lying to me tongue.gif

EDIT: Newest news straight from DA himself:
QUOTE
Actually now that you mention it, I believe I have the source, it's just
backed up on a tape from 1995.  I don't even know where I'd find a drive to
read it, so I don't really think of it as accessible.  If Jesus came to me
and said that he needed the source code, I might be able to recover it, but
that'd be about the only reason I could think of to try and restore it :-P

Anyone know Jesus' home phone number? help.gif
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aardless
post Apr 3 2005, 07:46 PM
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laugh.gif, cool. cool.gif I had a bit of trouble to find the link in the page, I thought I had stumbled on the wrong one. tongue.gif

QUOTE (Straxx)
And what use is Magical Skill? Thieving and Fighting are easy to figure out but shouldn't total magical skill enter into things as well?


I don't have a clue. biggrin.gif It may be that the ugly Log part is in fact a function of magical skill, but apparently it's not needed to infer the darn thing before applying it to the formula, so why bother?

Fighting is easy to figure out? blink.gif I'm mightily interested, cuz I haven't been able to. All I know is that fighting skill doesn't enter _linearly_ in the hand-to-hand damage formula.

QUOTE (unleashed)
how can you calculate the damage cone to a monster?? Monsters have resistance to magic and also are resistant to a type of spell....
You may be able to calculate the damage you should be inflicting.. but not for a specific monster.

If i'm wrong, please say so. i'm quite interested in this...

You're right, the formula I proposed only calculates the max-min damage range. There's a random factor involved, so nothing better can be done. sleep.gif (Well, apart from the usual statistical things, anyway)


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A. J. Raffles
post Apr 3 2005, 08:37 PM
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QUOTE (Straxx @ Apr 3 2005, 03:00 PM)
Anyone know Jesus' home phone number?   help.gif

Greg should know. tongue.gif

Edit: And what on earth does he mean by tape? Surely there were already CDs around in 1995? Or at least 3.5'' floppy discs?


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