Formulae Guide (by Xeno and Kingpin)
Description: This tutorial (or guide rather) will teach you how to properly use the powerful formulae calculations now possible in D2.
Categories: Tutorials (1.1x) - Skill Mechanics
A short intro. Some days ago I realized that in Blizzard text files one can use not only immediate numeric values (e.g. 150 or 3.14), but also formulae, which will be interpreted in the execution time, so being much more flexible (you can see examples below). This discovery was a great shock for me, because I couldn’t even imagine all the possibilities, versatile gameplay changes, when can be implemented due to using such formulae (skill synergy from clvl, “reduce casting delay” or “increase curse effectiveness” affixes, anyone ;) ) I became very interested in this theme, maybe because professional (programmer) motives. And so I decided to research this aspect of game mechanics and to write a guide on it in order to clear out all the things and to consolidate all the info about formulae syntax in one topic.
This is my first guide at the Phrozen Keep. I’m a bit anxious about it :lol: But I know that our senior colleagues will correct and append this post if necessary. [I've marked my questions with color] Sorry for my poor English in advance. So it begins…
[1.10] Formulae guide
1. What is the benefit of using formulae in txt files?
The main idea of my answer to this question is that using formulae (i.e. through soft coding), one can implement things that for sure seem to require code editing. Some examples of such ideas:
a) various softcoded skill system changes, e.g. Char’s skill system (d2:elements mod), i.e. each skill requires [slvl] skill points to advance to [slvl] level, and the first skill point always costs required character level (e.g. 12 for Zeal or 30 for Frozen Orb), so you need hard investments into the skill to maximize it. I can also mention Will’s ideas (take a look through “One skill point per two levels, per skill...” post in General Mod Making);
b) even more deep skill interdependencies: 1)adding and ability of Skill Masteries to reduce casting delay, increase missile speed, widen aura range, e.t.c. only for particular skills, 2)making your minions using and gaining benefits from your passive abilities and active skills, 3)adding and modifying skill synergies not only for damage but also for versatile (each possible in the game) skill-specific parameters;
c)
et cetera, et cetera... (listing of such ideas is worth hundreds of separate posts in the appropriate forums).
2. What files are used for this and what files allow using formulae?
You’ll need to look through ItemStatCost.txt (ISC), Skills.txt (SK), Missiles.txt (MS) for identifiers (string entries) plus MissCalc.txt (MSC) and SkillCalc.txt (SKC) for using predefined internal functions. I guess almost each file, where immediate numeric values are applicable, allows using formulae. But to know this for sure, I’m now going to test some of them, including the most important: SK and MS.
3. Formulae description.
Now I’ll try to give a recursive definition (sounds scary, yeah?) and detailed description (examples are included, too) of Diablo II-formulae. Such formulae consist of some simple parts. So let’s study them firstly.
Simple formula is:
1) an immediate integer or real value.
2) a reference to a predefined (i.e. hard coded) formula from SKC or MSC (such references can ONLY be used in SK and MS, respectively). [can we define our own formulae in these files?] Detailed description of available formulae is available in Appendix A.
3) a reference to a property of skill, stat or missile. [I bet we can also reference monster props or particular item props, but I haven’t found it out yet] Such reference can be written in one of the three possible ways:
stat(‘
skill(‘
[missile? miss? (both do not work)](‘
where
Complicated formulae (more general case) are formed from simple ones with the usage of arithmetic operators (which include
Skill(‘FireStorm’.clc1)*(Skill(‘FireStorm’.edmn)+ Skill(‘FireStorm’.edmx))/2 stands for average effective damage of firestorm skill (number of snakes * average dmg);
[Default value]/((100+Skill(‘Fire Mastery’)*5)/100)) If placed into “delay” column and appropriate skill row the skill’s casing delay will be reduced by Fire_Mastery_slvl*5 percent;
Stat(‘nextexp’.accr)-Stat(‘experience’.accr) stands for the your experience rest to level-up.
But all formulae syntax wouldn’t be SO flexible, if we can’t use conditional formulae. Let’s proceed by studying them.
4. Conditional formulae. Conditions are special types of formulae, but with one important difference: their values are interpreted in a special way: 0 means “false”, and 1 (and any non-zero value) stands for “true”. Both conditions and formulae can be very complicated and both of them consist of several simple parts. Let us study them firstly. Simple condition is:
1)an immediate numeric value (zero stands for “false”, and any non-zero value stands for “true”);
2)a relation of two expressions, formed using ‘>=’, ‘<=’,’>’,’<’,’==’ (means “equal”) and ‘!=’ (means “not equal”). Again, other c-style operators don’t seem to be working :( ;
Complicated conditions consist of simple ones with the usage of logical conjunctions: OR & AND (‘+’ and ‘*’, respectively. C-style syntax: ‘&&’ and ‘||’ doesn’t work :( ). Simple maths shows us that complicated conditions cover all possible variants of conditions in txt-files. Examples:
(stat(‘level’.accr)>=54)*(stat(‘strength’.accr)>=25)*(stat(‘dexterity’.accr)>=136)) if this condition is true, then the character can equip Phase Blades (he has at least 54 clvl, 25 str and 136 dex simultaneously);
(skill(‘Cold Mastery’.blvl)!=0)+(skill(‘Fire Mastery’.blvl)!=0)+(skill(‘Lightning Mastery’.blvl)!=0) this condition is true, if at least one of sorceress masteries has at least one skillpoint invested.
Conditional formulae have the following format:
condition?cfla1:cfla2.
Then this formula has a value of cfla1 if the condition has a value of “true” (has non-zero value), else it has a value of cfla2. Keep in mind that both condition and formulae can be conditional formulae, too. Examples:
(stat('item_cannotbefrozen'.accr)!=0)?(dm34+50):dm34 if placed into column “aurastatcalc1”, row “Resist Cold” of SK, aura “Resist Cold” will grant player additional 50% Cold Resist, if he can’t be frozen;
(lvl<3)?3:((lvl<5)?4:((lvl<7)?5:((lvl<9)?6:((lvl<11)?7:((lvl<13)?8:((lvl<15)?9:((lvl<17)?10:((lvl<19)?11:12)))))))) if placed into column “skpoints” and appropriate skill row of SK, this formula will make the skill require 3, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12… skill points to advance to 0..20th skill level (view details in “One skill point per two levels, per skill...” post in GMM);
Appendix A. MS and SC formulae.
These formulae allow referencing to certain columns in Missiles.txt and Skills.txt, respectively, so that you can, for example, use some skill-specific parameters to adjust skill damage or increase passive skill effectiveness, using active skills’ stats. They are mostly self-explanatory, so I’ll describe only not so obvious and some details. Also I don’t want to duplicate Skills.txt and Missiles.txt guides, so there won’t be a detailed explanation of these files.
SkillCalc.txt formulae (MissCalc.txt ones are analogical):
par# References skill function parameter (“param#” columns of SK);
ln## LiNear (not logarithmic) formula. Returns value of (par#1)+[slvl]*(par#2), i.e. ln12=par1+lvl*par2. Gives a constant level bonus to a stat (e.g. firestorm’s number of snakes: 3+lvl*0);
dm## DiMinishing returns. Has a value: (110*[slvl] * (par#2-par#1))/(100 * ([slvl]+6)) + par#1, i.e. dm34=(110*lvl*(par4-par3))/(100*(lvl+6))+par3. Used, when you need greatly decrease level bonus to a stat, if the skill have been heavily invested (e.g. resist cold resist bonus: (110*lvl*(150-35))/(100*(lvl+6))+25);
lvl, blvl Effective (modified by items) and Base skill level (e.g. all synergy bonuses (except ones from Prayer) use “blvl” – number of physically invested skill points);
ulvl Unit LeVeL. Stands for player or monster level. Syntactically equals to stat(‘level’.accr);
clc#, ast#, pst# References to SK’s columns “cltcalc#”, “aurastatcalc#” and “passivestatcalc#”, respectively;
skpt Required SKillPoinTs property (“skpoint” column in SK). Allows adjusting how many skillpoints do you need to invest in a skill in order to advance in it (see examples for conditional formulae);
Appendix B. Qualifiers for “stat”, “skill” and “missile?”.
With “stat” keyword one can use the following qualifiers: (thanks to adamantine):
base BASE (unmodified) value for the stat. Consult ItemStatCost.txt for more details;
accr Effective (modified by items) value;
mod Modification value. Equals to stat.accr-stat.base;
Qualifiers for skills and missiles are contained in SK and MK, respectively. Consult Appendix A for more details.
Appendix C. Standard functions.
(quoting adamantine)
rand(#,#) selects random number from two choices (don’t seem to be working);
min(#,#) always uses the lowest number;
max(#,#) always uses the highest number;
Appendix D. Formulae calculations.
Integer values. Each step of formula calculations operates only with integer values. If a temporary result has a non-zero fractional part, it is truncated. So, it’s erroneous to use “1/3*lvl” formula (it’ll always return zero). Instead of this use “lvl/3”.
Integer overflows. Game stores every temporary result in a signed dword (-2147483648…2147483647). And if the number doesn’t lie in these bounds, we get a rollover (e.g. “2147483647/1000000000” equals 2, but “2147483648/1000000000” equals -2). After calculating the final result game engine tries to store it in the appropriate variable. But the problem is that its size may be less than dword, so we’re likely to get a rollover then. Consult ISC for determining exact stat size or simply make some experiments.
Errors in formulae. 1) If game finds erroneous function, e.g. “man” instead of “min”, it doesn’t change the parameters and returns the last parameter; 2) If game can’t recognize an operator (e.g. if we’ll try to use c-operator ‘++’), it considers the whole formula to be erroneous and sets its value to zero; 3) Division by zero will return zero (e.g. “50/0” equals zero and “50/0+10” equals ten(!)); 4) Referencing self in a formula (e.g. “10+ast1” in “aurastatcalc1” column) will surely crash the game.
Appendix E. Known bugs.
1)Diablo II formulae cannot be more than 255 symbols length (the rest of the formula is truncated). But you can make a clever trick, using predefined formulae from MSC or SKC or defining your own in unused param# fields.
2)Sometimes you can get a rollover due to an arithmetic overflow (see Appendix D).
3)Some cells in text files may not recognize formulae properly (e.g. “Vel” column in MS).
4)Sometimes stats, modified by formula aren’t refreshed correctly, until your reset the skill or save&exit.
Appendix F. Calc Fields (by Kingpin).
Here is what fields that is calc fields in 1.10.
missiles SrvCalc1
missiles CltCalc1
missiles $HitCalc1
missiles CHitCalc1
missiles DmgCalc1
missiles DmgSymPerCalc
missiles EDmgSymPerCalc
skills prgcalc1
skills prgcalc2
skills prgcalc3
skills auralencalc
skills aurarangecalc
skills aurastatcalc1
skills aurastatcalc2
skills aurastatcalc3
skills aurastatcalc4
skills aurastatcalc5
skills aurastatcalc6
skills passivecalc1
skills passivecalc2
skills passivecalc3
skills passivecalc4
skills passivecalc5
skills petmax
skills sumsk1calc
skills sumsk2calc
skills sumsk3calc
skills sumsk4calc
skills sumsk5calc
skills cltcalc1
skills cltcalc2
skills cltcalc3
skills perdelay
skills skpoints
skills calc1
skills calc2
skills calc3
skills calc4
skills ToHitCalc
skills DmgSymPerCalc
skills EDmgSymPerCalc
skills ELenSymPerCalc
skilldesc ddam calc1
skilldesc ddam calc2
skilldesc p1dmmin
skilldesc p1dmmax
skilldesc p2dmmin
skilldesc p2dmmax
skilldesc p3dmmin
skilldesc p3dmmax
skilldesc desccalca1
skilldesc desccalcb1
skilldesc desccalca2
skilldesc desccalcb2
skilldesc desccalca3
skilldesc desccalcb3
skilldesc desccalca4
skilldesc desccalcb4
skilldesc desccalca5
skilldesc desccalcb5
skilldesc desccalca6
skilldesc desccalcb6
skilldesc dsc2calca1
skilldesc dsc2calcb1
skilldesc dsc2calca2
skilldesc dsc2calcb2
skilldesc dsc2calca3
skilldesc dsc2calcb3
skilldesc dsc2calca4
skilldesc dsc2calcb4
skilldesc dsc3calca1
skilldesc dsc3calcb1
skilldesc dsc3calca2
skilldesc dsc3calcb2
skilldesc dsc3calca3
skilldesc dsc3calcb3
skilldesc dsc3calca4
skilldesc dsc3calcb4
skilldesc dsc3calca5
skilldesc dsc3calcb5
skilldesc dsc3calca6
skilldesc dsc3calcb6
skilldesc dsc3calca7
skilldesc dsc3calcb7
weapons len
weapons calc1
weapons calc2
weapons calc3
weapons spelldesccalc
armor len
armor calc1
armor calc2
armor calc3
armor spelldesccalc
misc len
misc calc1
misc calc2
misc calc3
misc spelldesccalc
magicsuffix mod1param
magicsuffix mod2param
magicsuffix mod3param
magicprefix mod1param
magicprefix mod2param
magicprefix mod3param
automagic mod1param
automagic mod2param
automagic mod3param
uniqueitems par1
uniqueitems par2
uniqueitems par3
uniqueitems par4
uniqueitems par5
uniqueitems par6
uniqueitems par7
uniqueitems par8
uniqueitems par9
uniqueitems par10
uniqueitems par11
uniqueitems par12
sets pparam2a
sets pparam2b
sets pparam3a
sets pparam3b
sets pparam4a
sets pparam4b
sets pparam5a
sets pparam5b
sets fparam1
sets fparam2
sets fparam3
sets fparam4
sets fparam5
sets fparam6
sets fparam7
sets fparam8
setitems par1
setitems par2
setitems par3
setitems par4
setitems par5
setitems par6
setitems par7
setitems par8
setitems par9
setitems apar1a
setitems apar1b
setitems apar2a
setitems apar2b
setitems apar3a
setitems apar3b
setitems apar4a
setitems apar4b
setitems apar5a
setitems apar5b
gems weaponmod1param
gems weaponmod2param
gems weaponmod3param
gems helmmod1param
gems helmmod2param
gems helmmod3param
gems shieldmod1param
gems shieldmod2param
gems shieldmod3param
runes t1param1
runes t1param2
runes t1param3
runes t1param4
runes t1param5
runes t1param6
runes t1param7
Link to this article: Select all
[url=https://www.d2mods.info/forum/kb/viewarticle?a=371&sid=893316c56e51db7ac9f8be1d42ae6155]Knowledge Base - Formulae Guide (by Xeno and Kingpin)[/url]