The Mana World - User contributions [en]

User talk:Zao

2007-11-05T17:27:56Z

Zao: /* maximums */

==Formula Ownage==

Here are my own notes for keeping on top of the consistency and balance of formulas.

===Consistency===

you want to own the formula, you don't want it to own you, so you have to make sure it behaves
how you want for all the conditions the formula allows (based on it's independent parameters)

For instance, if you're making a formula for a roll based on multiple attributes, you'll want to
consider the case of the balanced character, the physical character, the magic character, the
dexterous character.

===Balance===

We also don't want our formulas for the fighter's physical skills to grow faster than the formulas
for the mage's magical skills. This is tough to factor in, since the mage can cause effects on their
opponents that don't exactly equate to damage. This is why you have lots of handy expressions in
formulas that can be used to manipulate it for your needs.

===Tools===

Here are some handy expressions and concepts to wreak pwnge on your equations:

====Constants====

constants are handy for scaling. Whether they're in front of a term or buried inside a me complex
expression, they can help bring balance to an equation. For instance, if you have a skill that relies
more on dexterity than strength, but you want it to rely on both, you can make the success go as:

S = a*str + b*str

where a and b are arbitrary constants that you can scale to strengthen the growth of a particular term
In our case, we could take (a = 1) and (b = 2) to make strength dominate the equation

====Function behavior====

=====maximums=====

if you want your formula to stop climbing after a certain point, the logarithm is ideal.
The logarithm climbs fast when the dependent variables are closer to 0, but as they approach
a given value (depending on what base you chose for the log) they begin to climb much slower
as the function levels out. It has the form:

y = log(x)

here's a base 2 log function.
[[Image:Log.png]]

:''Comment: Note that this function doesn't really has a maximum. It will reach any y-value at some point. As an alternative I would recommend using a function of the form ''y = a - a / (x + 1)''. This results in a function that approaches ''a'' but never reaches it. --[[User:Crush|Crush]] 11:49, 5 November 2007 (CET)''

here's the formula Crush suggested if it more fits your needs:
[[Image:Negoverx.png]]

:''Yeah, I thought about this. Since everything here should be numerical it shouldn't be a problem. But your formula is probably more user-friendly because you don't have to figure out what base to use for your log function; instead your max is simply decided by "a". The thing about -a/x is after it hits the "bend" it doesn't increase much anymore, whereas at higher levels, the characters will still get gains from the logarithmic function (just not as large of gains). I need to rename this section something besides "maximum" but I want it to be intuitive to non-math peoples." --[[User:Zao|Zao]] 4:10 5 November 2007 (CET)''

=====exponentials=====

exponentials climb or fall really fast. They have the form:

y = c^x

where c is an arbitrary constant greater than |1|

I can't think of a use for them off the top of my head
in a game, but here's what the positive one looks like:

[[Image:Posexp.png]]

and a negative:

[[Image:Negexp.png]]

File:Negoverx.png

2007-11-05T17:26:36Z

Zao: a - a/(x+1)

a - a/(x+1)

User talk:Zao

2007-11-05T17:22:14Z

Zao: /* maximums */

==Formula Ownage==

Here are my own notes for keeping on top of the consistency and balance of formulas.

===Consistency===

you want to own the formula, you don't want it to own you, so you have to make sure it behaves
how you want for all the conditions the formula allows (based on it's independent parameters)

For instance, if you're making a formula for a roll based on multiple attributes, you'll want to
consider the case of the balanced character, the physical character, the magic character, the
dexterous character.

===Balance===

We also don't want our formulas for the fighter's physical skills to grow faster than the formulas
for the mage's magical skills. This is tough to factor in, since the mage can cause effects on their
opponents that don't exactly equate to damage. This is why you have lots of handy expressions in
formulas that can be used to manipulate it for your needs.

===Tools===

Here are some handy expressions and concepts to wreak pwnge on your equations:

====Constants====

constants are handy for scaling. Whether they're in front of a term or buried inside a me complex
expression, they can help bring balance to an equation. For instance, if you have a skill that relies
more on dexterity than strength, but you want it to rely on both, you can make the success go as:

S = a*str + b*str

where a and b are arbitrary constants that you can scale to strengthen the growth of a particular term
In our case, we could take (a = 1) and (b = 2) to make strength dominate the equation

====Function behavior====

=====maximums=====

if you want your formula to stop climbing after a certain point, the logarithm is ideal.
The logarithm climbs fast when the dependent variables are closer to 0, but as they approach
a given value (depending on what base you chose for the log) they begin to climb much slower
as the function levels out. It has the form:

y = log(x)

here's a base 2 log function.
[[Image:Log.png]]

:''Comment: Note that this function doesn't really has a maximum. It will reach any y-value at some point. As an alternative I would recommend using a function of the form ''y = a - a / (x + 1)''. This results in a function that approaches ''a'' but never reaches it. --[[User:Crush|Crush]] 11:49, 5 November 2007 (CET)''

:''Yeah, I thought about this. Since everything here should be numerical it shouldn't be a problem. But your formula is probably more user-friendly because you don't have to figure out what base to use for your log function; instead your max is simply decided by "a". The thing about -a/x is after it hits the "bend" it doesn't increase much anymore, whereas at higher levels, the characters will still get gains from the logarithmic function (just not as large of gains). I need to rename this section something besides "maximum" but I want it to be intuitive to non-math peoples." --[[User:Zao|Zao]] 4:10 5 November 2007 (CET)''

=====exponentials=====

exponentials climb or fall really fast. They have the form:

y = c^x

where c is an arbitrary constant greater than |1|

I can't think of a use for them off the top of my head
in a game, but here's what the positive one looks like:

[[Image:Posexp.png]]

and a negative:

[[Image:Negexp.png]]

User talk:Zao

2007-11-05T08:53:10Z

Zao: formula formulation formula

File:Negexp.png

2007-11-05T08:50:17Z

Zao: negative exponential

negative exponential

File:Posexp.png

2007-11-05T08:49:09Z

Zao: positive exponential

positive exponential

File:Log.png

2007-11-05T08:45:09Z

Zao: logarithmic function

logarithmic function

Archive talk:Combat system

2007-11-03T20:58:11Z

Zao: /* Special Attacks*/

== Ultima Online ==
This is how Ultima Online handles combat calculations:
http://uo.stratics.com/content/arms-armor/combat.php

==Length of Attacks==

Theory:

We want attack speed to depend on 1) weapon speed and 2) dexterity
so that positive weapon speeds and dexterities contribute positively
to the speed of attack (or negatively to the length of the attack)

(i use the words positively and negatively not mathematically, but
from player's perspective)

''1) weapon speed''

if there's not a system for weapon speed, you could simply make it
inversely proportional to weight so that:

ws = c/w , where c is some constant (generally 1)

so bigger weighted weapons would be slower.

This might also need to be augmented by strength, so that heavier
weapons are faster in the hands of stronger peoples.

perhaps:

ws = c*s/w where s is strength and w is weight of weapon, c a constant

''2) dexterity''

assuming a player with better dexterity will have a quicker swing,
dexterities contribution could simply be the players dexterity multiplied by
an arbitrary constant:

b*d (b constant)

''Swinging Speed''

swinging speed, denoted SS can then be equated to 1) and 2) by

'''SS = c*s/w + b*d'''

where c and b are constants that can be adjusted to balanced
between strength-based characters and dexterity-based characters

''Length of Attack''

L = 1/SS

so that the Length of time is infinite when
chracters have 0 swinging speed.

-Zao

:''The problem with these formulas is that they would cause a huge difference between the combat behavior of low-level and high-level characters. A character with 100 in both strength and dexterity would have a swinging speed that would allow it to attack 10 times as often as a character with 10 in both attributes. With these formulas it would be impossible to balance the attack speed in a way that it wouldn't be pure button-mashing for high-level chars or long waiting times for the next attack for a low-level char. To have a better control over the feel of the combat system the influence of attributes on the attack speed should be less strong. Personally I would in fact prefer when the attack speed would be a weapon constant.--[[User:Crush|Crush]] 05:21, 3 November 2007 (CET)''

"perhaps we could incorporate an logarithmic scale into it so that the rate of increase decreases as you get into the higher numbers of dex and str
so that:

SS = c*log(str)/w + b*log(dex)

if we take c and b to be 1 and w to be 5, here's what I get (using Matlab):

for str=dex=10:

SS = 2.76

for str=dex=100:

SS = 5.53

Now 100 swings only twice as fast as 10

We can put constants inside the ln functions too for further manipulation --[[User:Zao|Zao]] 3 Nov 2007"

===Special Attacks===

=====Lunge Attack=====
speed: one combat turn
prerequisite: Dexterity

jump forward a square or two and engage an enemy, doing 1.5x damage (an extra 30%). Requires a dexterity of n. Can only be used to start combat.
If you are already next to an enemy you're lunging towards, you will push them to your new square as you lunge. Accuracy is reduced slightly.

=====Wild Swing=====
speed: one combat turn
prerequisite: Strength

Character's defense goes to half but their attack damage is x2.

=====Tactical Roll=====
speed: one combat turn
prerequisite: Dexterity

Character rolls behind opponent in one turn, during which his defense is doubled. Opponent is then stunned for one turn figuring out what happened and turning around. Character can use a suprise/engagement/first strike move during this moment.

=====Dash=====
speed: half a combat turn
prerequisite: Dexterity

Character dashes forward a square without any focused attack. The chance to hit with a dash is good (100?), with a Str% chance of knocking opponent down. Opponent spends one turn recovering, getting back on their feet. Can only be done to two legged creatures.

=====Spin Attack=====
speed: 1.5 combat turns
prerequisite: dexterity

Character harvests rotational energy (well, a longer path length to build up speed anyway) and swings on his enemy. For the moment, his defenses and accuracy go down dramatically, but he scores 3x the damage on his opponent when (if) he connects

=====Upthrust=====
speed: 2 combat turn
prerequisite: strength

Character more-or-less uppercuts with his weapon, knocking opponent into air for 1.5x damage. Wares characters out*.

*what's the chances of having a stamina bar, especially for special attacks and running. My idea here is that we
don't have to put as many consequences on special moves if they can't be used infinitely.

User talk:Zao

2007-11-03T05:23:49Z

Zao: /* 2nd Header */

=Learning=

Just learning how to use the wiki editor.
I see now, how the titling is done, though

==2nd Header==
[tex]y = e^{2x}[/tex]

\startformula
c^2 = a^2 + b^2.
\stopformula

<math>\vec F = m \vec a</math>

<math>y = x^2</math>

=====Header Three=====

User talk:Zao

2007-11-03T05:18:19Z

Zao: /* 2nd Header */

User talk:Zao

2007-11-03T05:17:47Z

Zao: /* 2nd Header */

User talk:Zao

2007-11-03T05:17:16Z

Zao: /* 2nd Header */

User talk:Zao

2007-11-03T05:16:19Z

Zao: /* 2nd Header */

=Learning=

Just learning how to use the wiki editor.
I see now, how the titling is done, though

==2nd Header==
[tex]y = e^{2x}[/tex]

\startformula
c^2 = a^2 + b^2.
\stopformula

:<math>F = ma</math>

User talk:Zao

2007-11-03T05:15:52Z

Zao: /* 2nd Header */

User talk:Zao

2007-11-03T05:15:22Z

Zao: /* 2nd Header */

User talk:Zao

2007-11-03T05:12:47Z

Zao: /* 2nd Header */

=Learning=

Just learning how to use the wiki editor.
I see now, how the titling is done, though

==2nd Header==
[tex]y = e^{2x}[/tex]

\startformula
c^2 = a^2 + b^2.
\stopformula

User talk:Zao

2007-11-03T05:08:32Z

Zao: /* 2nd Header */

=Learning=

Just learning how to use the wiki editor.
I see now, how the titling is done, though

==2nd Header==
[tex]y = e^{2x}[/tex]

User talk:Zao

2007-11-03T05:06:03Z

Zao:

=Learning=

Just learning how to use the wiki editor.
I see now, how the titling is done, though

==2nd Header==

Archive talk:Combat system

2007-11-03T04:59:25Z

Zao: /* Length of Attacks */

Archive talk:Combat system

2007-11-03T04:58:26Z

Zao: /* Length of Attacks */

Archive talk:Combat system

2007-11-03T00:30:22Z

Zao: /* Ultima Online */

=== Ultima Online ===
This is how Ultima Online handles combat calculations:
http://uo.stratics.com/content/arms-armor/combat.php

---------------------------------------------------------
========================
'''Length of Attacks:'''

Theory:

We want attack speed to depend on 1) weapon speed and 2) dexterity
so that positive weapon speeds and dexterities contribute positively
to the speed of attack (or negatively to the length of the attack)

(i use the words positively and negatively not mathematically, but
from player's perspective)

''1) weapon speed''

if there's not a system for weapon speed, you could simply make it
inversely proportional to weight so that:

ws = c/w , where c is some constant (generally 1)

so bigger weighted weapons would be slower.

This might also need to be augmented by strength, so that heavier
weapons are faster in the hands of stronger peoples.

perhaps:

ws = c*s/w where s is strength and w is weight of weapon, c a constant

''2) dexterity''

assuming a player with better dexterity will have a quicker swing,
dexterities contribution could simply be the players dexterity multiplied by
an arbitrary constant:

b*d (b constant)

''Swinging Speed''

swinging speed, denoted SS can then be equated to 1) and 2) by

'''SS = c*s/w + b*d'''

where c and b are constants that can be adjusted to balanced
between strength-based characters and dexterity-based characters

''Length of Attack''

L = 1/SS

so that the Length of time is infinite when
chracters have 0 swinging speed.

-Zao

Archive talk:Combat system

2007-11-03T00:29:49Z

Zao: /* Ultima Online */

=== Ultima Online ===
This is how Ultima Online handles combat calculations:
http://uo.stratics.com/content/arms-armor/combat.php

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

'''Length of Attacks:'''

Theory:

We want attack speed to depend on 1) weapon speed and 2) dexterity
so that positive weapon speeds and dexterities contribute positively
to the speed of attack (or negatively to the length of the attack)

(i use the words positively and negatively not mathematically, but
from player's perspective)

''1) weapon speed''

if there's not a system for weapon speed, you could simply make it
inversely proportional to weight so that:

ws = c/w , where c is some constant (generally 1)

so bigger weighted weapons would be slower.

This might also need to be augmented by strength, so that heavier
weapons are faster in the hands of stronger peoples.

perhaps:

ws = c*s/w where s is strength and w is weight of weapon, c a constant

''2) dexterity''

assuming a player with better dexterity will have a quicker swing,
dexterities contribution could simply be the players dexterity multiplied by
an arbitrary constant:

b*d (b constant)

''Swinging Speed''

swinging speed, denoted SS can then be equated to 1) and 2) by

'''SS = c*s/w + b*d'''

where c and b are constants that can be adjusted to balanced
between strength-based characters and dexterity-based characters

''Length of Attack''

L = 1/SS

so that the Length of time is infinite when
chracters have 0 swinging speed.

-Zao

Archive talk:Combat system

2007-11-03T00:28:11Z

Zao: /* Ultima Online */

=== Ultima Online ===
This is how Ultima Online handles combat calculations:
http://uo.stratics.com/content/arms-armor/combat.php

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

Length of Attacks:

Theory:

We want attack speed to depend on 1) weapon speed and 2) dexterity
so that positive weapon speeds and dexterities contribute positively
to the speed of attack (or negatively to the length of the attack)

(i use the words positively and negatively not mathematically, but
from player's perspective)

====================
1) weapon speed

if there's not a system for weapon speed, you could simply make it
inversely proportional to weight so that:

ws = c/w , where c is some constant (generally 1)

so bigger weighted weapons would be slower.

This might also need to be augmented by strength, so that heavier
weapons are faster in the hands of stronger peoples.

perhaps:

ws = c*s/w where s is strength and w is weight of weapon, c a constant

=====================
2) dexterity

assuming a player with better dexterity will have a quicker swing,
dexterities contribution could simply be the players dexterity multiplied by
an arbitrary constant:

b*d (b constant)

=================
Swinging Speed

swinging speed, denoted SS can then be equated to 1) and 2) by

SS = c*s/w + b*d

where c and b are constants that can be adjusted to balanced
between strength-based characters and dexterity-based characters

=================
Length of Attack

L = 1/SS

so that the Length of time is infinite when
chracters have 0 swinging speed.

-Zao

Archive talk:Combat system

2007-11-03T00:26:59Z

Zao: /* = */

=== Ultima Online ===
This is how Ultima Online handles combat calculations:
http://uo.stratics.com/content/arms-armor/combat.php

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

Length of Attacks:

Theory:

We want attack speed to depend on 1) weapon speed and 2) dexterity
so that positive weapon speeds and dexterities contribute positively
to the speed of attack (or negatively to the length of the attack)

(i use the words positively and negatively not mathematically, but
from player's perspective)

=1) weapon speed

=====================

if there's not a system for weapon speed, you could simply make it
inversely proportional to weight so that:

ws = c/w , where c is some constant (generally 1)

so bigger weighted weapons would be slower.

This might also need to be augmented by strength, so that heavier
weapons are faster in the hands of stronger peoples.

perhaps:

ws = c*s/w where s is strength and w is weight of weapon, c a constant

=====================
2) dexterity
=====================

assuming a player with better dexterity will have a quicker swing,
dexterities contribution could simply be the players dexterity multiplied by
an arbitrary constant:

b*d (b constant)

=================
Swinging Speed
=================

swinging speed, denoted SS can then be equated to 1) and 2) by

SS = c*s/w + b*d

where c and b are constants that can be adjusted to balanced
between strength-based characters and dexterity-based characters

=================
Length of Attack
=================

L = 1/SS

so that the Length of time is infinite when
chracters have 0 swinging speed.

-Zao

Archive talk:Combat system

2007-11-03T00:26:36Z

Zao: /* = */

=== Ultima Online ===
This is how Ultima Online handles combat calculations:
http://uo.stratics.com/content/arms-armor/combat.php

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

Length of Attacks:

Theory:

We want attack speed to depend on 1) weapon speed and 2) dexterity
so that positive weapon speeds and dexterities contribute positively
to the speed of attack (or negatively to the length of the attack)

(i use the words positively and negatively not mathematically, but
from player's perspective)

=====================
1) weapon speed
=====================

if there's not a system for weapon speed, you could simply make it
inversely proportional to weight so that:

ws = c/w , where c is some constant (generally 1)

so bigger weighted weapons would be slower.

This might also need to be augmented by strength, so that heavier
weapons are faster in the hands of stronger peoples.

perhaps:

ws = c*s/w where s is strength and w is weight of weapon, c a constant

=====================
2) dexterity
=====================

assuming a player with better dexterity will have a quicker swing,
dexterities contribution could simply be the players dexterity multiplied by
an arbitrary constant:

b*d (b constant)

=================
Swinging Speed
=================

swinging speed, denoted SS can then be equated to 1) and 2) by

SS = c*s/w + b*d

where c and b are constants that can be adjusted to balanced
between strength-based characters and dexterity-based characters

=================
Length of Attack
=================

L = 1/SS

so that the Length of time is infinite when
chracters have 0 swinging speed.

-Zao

Archive talk:Combat system

2007-11-03T00:25:39Z

Zao: /* Ultima Online */

=== Ultima Online ===
This is how Ultima Online handles combat calculations:
http://uo.stratics.com/content/arms-armor/combat.php

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

Length of Attacks:

Theory:

We want attack speed to depend on 1) weapon speed and 2) dexterity
so that positive weapon speeds and dexterities contribute positively
to the speed of attack (or negatively to the length of the attack)

(i use the words positively and negatively not mathematically, but
from player's perspective)

=====================
1) weapon speed
=====================

if there's not a system for weapon speed, you could simply make it
inversely proportional to weight so that:

ws = c/w , where c is some constant (generally 1)

so bigger weighted weapons would be slower.

This might also need to be augmented by strength, so that heavier
weapons are faster in the hands of stronger peoples.

perhaps:

ws = c*s/w where s is strength and w is weight of weapon, c a constant

=====================
2) dexterity
=====================

assuming a player with better dexterity will have a quicker swing,
dexterities contribution could simply be the players dexterity multiplied by
an arbitrary constant:

b*d (b constant)

=================
Swinging Speed
=================

swinging speed, denoted SS can then be equated to 1) and 2) by

SS = c*s/w + b*d

where c and b are constants that can be adjusted to balanced
between strength-based characters and dexterity-based characters

=================
Length of Attack
=================

L = 1/SS

so that the Length of time is infinite when
chracters have 0 swinging speed.