Formulae Guide (by Xeno and Kingpin)

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): making multiple skill synergies ((C) xeno, 2004) (it’s somehow similar to skill sets with partial and full set bonuses);

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:



[missile? miss? (both do not work)](‘’.),

where , and stand for ISC, MS and SK string entries (they MUST be written in single quotas, e.g. stat(‘level’.accr) or skill(‘Holy Shock’).edmn) and is a reserved word which indicates the particular property of stat, skill or missile, we want to reference. You can see the list and detailed descriptions in the Appendix B.

Complicated formulae (more general case) are formed from simple ones with the usage of arithmetic operators (which include :'-', :'+', :'-', :'*', :'/' and :'^'. Other c-style operators don’t seem to be working :( ), standard functions (see Appendix C) and, of course, parentheses. Examples:

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:


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

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[url=]Knowledge Base - Formulae Guide (by Xeno and Kingpin)[/url]