Old Guild penalty information
 
Note: This information is only correct for versions up to Infinite Worlds.  For any releases after the Infinite Worlds beta, this information will be drastically incorrect!!!

When your character joins multiple guilds, they gain different skills from each of these guilds.  Because you have skills from various guilds, a penalty on both the experience and gold required to level is applied to certain guilds.

WARNING: This section gets moderately mathematical, so if you are not very good at mathematics, the following could be confusing.
 
All studies are based on real multi-play character data or hex-edited single character data.  This document only addresses various statistics associted with the game. It is not intended to give you direct guidence on how to actually play the game. However, the statistics will help you greatly decide your game play strategy! I am sure some of you hardcore Demise fans will love to know about them. :)

I have divided this report into 2 sections:
1) How is guild experience related to race, guild, penalty, and level?
2) How is guild penalty related to guild and level?
 

Vamp has a couple of  spreadsheet penalty calculators (In different Excel formats - I think) available for download at his website http://www.geocities.com/Tokyo/Field/1288/
 

Section 1)
How is guild experience related to race, guild, penalty, and level?
================================================

This study confirmed the formula I last posted. The exp required to go from level L to level L+1 is:

ExpForNextLevel(L) = Constant * RaceFactor * GuildFactor * (1 + Penalty) * L

Total exp required for level L is:

TotalGuildExp(L) = Constant * RaceFactor * GuildFactor * (1 + Penalty) * (L * (L - 1) /2 )

Constant is around 22.0.
RaceFactor is 1.000 for Human(3), 1.0582 for Yeti(4), 1.1055 for Dwarf(5), 1.1471 for Ogre/Troll(6), 1.1854 for Elf/Giant/Gnome(7), 1.2217 for Saris(8). All four digits are correct values.
GuildFactor is the ExFt from the official Guild Statistics. It is 8 for Artisan, 16 for Warrior, 32 for Cleric etc.
Penalty is your guild penalty.

This formula is tested on pure character. The character only joins one guild and level that guild to level 100, 200, 300, and 400. This formula is very accurate, with a relative error of less than 1%.

Section 2)
How is guild penalty related to guild and level?
================================================

Penalty is the most difficult, and yet, most interesting part of my study. The result actually turns out to be pretty simple.

Many of you have guessed that penalty is closely related to guild abilities. Your guess is correct. First of all, let me put some official guild abilities statistics. Note that ''Guild Abilities' for penalty is different from the guild abilities you see by pressing F7.
 
 
Guild
Thieving
Backstab
Critical Hit
Multi Swing
Fighting
Perception
Language
Total
Artisan
5
 
 
 
7
3
1
16
Warrior
2
 
9
5
12
2
2
32
Paladin
2
 
5
2
10
3
4
26
Ninja
7
2
5
8
10
6
2
40
Villain
6
4
1
3
8
4
5
31
Explorer
3.5
 
3
 
9
9
6
30.5
Thief
9
9
 
 
6
5
3
32
Barbarian
7.5
5
 
1
7
3
2
25.5
Magi
2
 
 
 
5
3
7
17
Sorceror
2
 
 
 
5
2
7
16
Wizard
2
 
 
 
5
2
8
17
Cleric
2
 
 
 
5
2
6
15

 
The formula for Penalty for your guild G at level L is realy simple:

Penalty(G) = PenaltyConstant * (TotalAbilities - GuildAbilities(G, L))
Penalty Constant is a constant around 0.030. TotalAbilities is your total abilities from all guilds you join. GuildAbilities is the abilities contributed only by your guild G at level L.

The formula for GuildAbilities(G, L) is:

GuildAbilities(G, L) = GuildTotalAbilitiesFactor(G) * L / 100
GuildTotalAbilitiesFactor(G) is the last column in my guild ability table. It is 16 for Artisan, 32 for Warrior, 30.5 for Explorer, 17 for Warlock, etc.

For instance, if you have a Warrior at 100, then your guild abilities from warrior are:
GuildAbilities(Warrior, 100) = 32 * 100 / 100 = 32.

The formula for TotalAbilities is a little complex. It is the sum of all your 7 abilities.

TotalAbilities = MaxThieving + MaxBackstabing + MaxCriticalHit + ... + MaxLanguage

MaxThieving is the maximum thieving ability from all your guilds. Note that your thieving ability is not added from various guilds, but the max of them. Suppose you are guild G1 at level L1, guild G2 at level L2, ..., guild G_n at level L_n.

MaxThieving = Max(ThievingGuild_1, ThievingGuild_2, ..., Thieving Guild_n).

ThievingGuild_1 is the thieving ability contributed by your guild G1 at level L1. It has a linear relationship with respect to guild level L1.
ThievingGuild_1 = Guild1ThievingFactor * L1 / 100.
Guild1ThievingFactor is the thieving factor for your guild G1. It is from the guild ability statistics table. Thieving is 5 for artisan, 2 for warrior, 3.5 for explorer, 9 for thief, etc.
To sum up the formula for TotalAbilities, Suppose you are guild G1 at level L1, guild G2 at level L2, ..., guild G_n at level L_n.

TotalAbilities = SUM (MAX (GuildAbilityFactor(i, j) * Li / 100) )

GuildAbilityFactor(i, j) is the ability factor for guild Gi for ability j. Li is the level of guild Gi. The SUM() is for j (for all 7 abilities). The MAX() is for i (for all guilds).
Some examples. If you only has one guild, then your total abilities is exactly the same as the abilities contributed from your only guild. So
TotalAbilities = GuildAbilities
The penalty for your only guild is 0:
Penalty = PenaltyConstant * (TotalAbilities - GuildAbilities) = 0
This comes at no surprise.
If you have a Warrior 100, and Artisan 1. Then almost all your abilities come from your Warrior. Your warrior will get 0.0 penalty. Penalty for your Artisan 1 is:

Penalty(Artisan) = PenaltyConstant * (TotalAbilites(Warrior, Artisan) - GuildAbilities(Artisan))
= 0.03 * (WarriorAbilities(100))
= 0.03 * (32 * 100 / 100)
= 0.96

So Warrior 100 gives your Artisan 1 a penalty of 1.0! It equals to the actual number form character data!

Things get interesting when you have multiple guilds. Suppose you have a Warrior 100 and a Thief 100.

WarriorAbilities = 32 * 100 / 100 = 32
ThiefAbilities = 32 * 100 / 100 = 32

The following table is for guild abilities and to calculate total abilities.
 
Guild
Thieving
Backtab
Crit Hit
Mult Swing
Fighting
Perception
Language
TOTAL
Warrior
2
0
9
5
12
2
2
32
Thief
9
9
0
0
6
5
3
32
MAX
9
9
9
5
12
5
3
52
 

So TotalAbilities = 52

Penalty(Warrior) = 0.03 * (TotalAbilities - WarriorAbilities) = 0.03 * (52 - 32) = 0.60 (Actual penalty is 0.5)

Penalty(Thief) = 0.03 * (TotalAbilities - ThiefAbilities) = 0.03 * (52 - 32) = 0.60 (Actual penalty is 0.5)

Penalty(Other Guild) = 0.03 * (TotalAbilities - OtherGuildAbilities) = 0.03 * (52 - 0) = 1.56 (Actual penalty is 1.6. Suppose the other guild is low level around 1.)

If you are a Warrior 100, Wizard 200, then:
 
Guild
Thieving
Backstab
Crit Hit
Mult Swing
Fighting
Perception
Language
TOTAL
Warrior 100
2
0
9
5
12
2
2
32
Wizard 200
4
0
0
0
10
4
16
34
MAX
4
0
9
5
12
4
16
50
 

TotalAbilities = 50

Penalty(Warrior) = 0.03 * (TotalAbilities - WarriorAbilities) = 0.03 * (50 - 32) = 0.54 (Actual penalty is 0.5)

Penalty(Wizard) = 0.03 * (TotalAbilities - WarlockAbilities) = 0.03 * (50 - 34) = 0.48 (Actual penalty is 0.4)

Penalty(Other Guild) = 0.03 * (TotalAbilities - OtherGuildAbilities) = 0.03 * (50 - 0) = 1.50 (Actual penalty is 1.5. Suppose the other guild is low level around 1.)

One final example, for Artisan/ Warrior/ Explorere/ Thief/ Wizard/ Cleric. All level 100.
 
 
 
Artisan
Warrior
Explorer
Thief
Wizard
Cleric
Estimated Pen.
1.35
0.87
0.92
0.87
1.3
1.38
Actual Pen.
1.1
0.7
0.8
0.8
1.2
1.2
 

For most samples I calcuated, the errors range between -5% to 15%. The error is caused by the 1-2 digit accuracy in the official guild abilities table. They probably used a table that is slightly different to calculate penalty.

Recall the penalty formula can be written as

G= 0.0003*(GiLi - GF*L)

Here are the Guild Factor's ranked in order

Guild Factor(GF)

Ninja 40
Warri 32
Thief 32
Villa 31
Explo 30.5
Palad 26
Barba 25.5
Magi 17
Warlo 17
Sorce 16
Artis 16
Cleri 15

The higher the GF, the easier it is for you to level out of a penalty, as your GF*L factor increases. So the ninja is easiest to level out of a penalty, and cleric is worst.  So, try and level up in those guild which have a low GF first, otherwise they will suffer a heavy penalty - increasing as the GF gets lower.