From: Rannou@info.polymtl.ca (Patrick Rannou)
Subject: Re: Why are their level limits?
Organization: Ecole Polytechnique de Montreal, Canada
	<1992Aug26.181636.12337@miavx1.acs.muohio.edu>
	<1992Aug26.220054.695@ccsvax.sfasu.edu>
Distribution: na
Date: Sat, 29 Aug 1992 01:32:24 GMT

In article <1992Aug26.220054.695@ccsvax.sfasu.edu> z_copeab@ccsvax.sfasu.edu writes:


[...]
	   But neither of these are 'realistic' penalties. Level limits have no
   justification outside of 'game balance' (what an ugly phrase).

Huh? Gigax and T$R got it all wrong here!!! Level limits AREN'T AT ALL A
GAME BALANCE THINGIE!!!

YES! Maybe it's what it is INTENDED for, but tlet's think about it a
little, shall we?

1) What is game balance ???

"IMHO, game balance is the concept according to which a character having N
XPs should be just as "powerful" as another character who has ALSO N XPs.
By "powerful", I do not limit myself to combat but to the overral
usefullness of the character in the campaign."

Since I like the concept "level" to fit with "power", too, then it would be
reasonnable for a GM rewriting the rules to think that...

"IMHO, game balance is the concept according to which a character having N
LEVELS should be just as "powerful" as another character who has ALSO N LEVELS.
By "powerful", I do not limit myself to combat but to the overral
usefullness of the character in the campaign."

In short, IMHO, it should take the SAME amount of XPs to get up a level
WHATEVER YOUR CLASS IS. Sure, if you want to play a young adult dragon, go
for it, but you don't start at level 1, you start at level, say, 15. At
level one the dragon has just hatched, and is just as powerful than a 1st
level character of ANY kind.

Note also that I've made the monsters be considered as characters also.
This means uniformisation, less "it's a monster so let's just kill it" and
more rolelplaying, and also a chance to play something other than
human/elf/darf/gnoime/hobbit without having to rewrite the rules or feeling
too confined. Mostly, it allows for "Oh, that bugbear is level 3. That
means that a single level 3 character can take him".

Also, a good thing would be to make the difference of "power" between any
two levels be small and as much homogenous as possible. A 0 level character
going up to level 1, or a level 1 going up to level 2, or from level 2 to
level 3, receives a humongous power boost. That isn't balanced. The
difference in power from level to level should also be fairly constant, so
it should surprise some when they meet a level 200 monster. It simply means
that 200 level one monsters will be a match against it. Well, it's not as
simple as that because after the fight the 200 level one monster will have
many of them killed anyway, so to balance things out either we let it at
that, or say thjat each indivudual entity in a group count for say one
level, and thus it should take 100 level one characters/monsters/entities
to have 50-50% chances to kill the 200 levels monster. But that's only
another possibility. Anyway, in short, after all calculations are made, a
tough monster of X XPs should be just as tough to deal with/kill than many
tiny monsters totalising X XPs. Or replace XP by levels, depending on the
premisce you started with. After all, what is XP or level but a measure of
the experience/power a character got? If even at this most basic stage the
simple concept of XP isn't linear, then everything else will not be
balanced and you might just as well kick game balance out the window and
NEVER talk about it again.

And there is also the matter of the stats humonmgous effect of the "power" of
a character, be it fighting or other tasks. If you want to have a balanced
game, then the only way to accept it is to make the stats bonus themselves
worth XPs, and thus say a character starting with low stats could start at
a slightly higher level and be worth the same amount of XPs. That's if you
don;t think that the level concept should represent true power. If you do,
then the stats themsevles count as bonus on the level, so finally you get
two characters of the same level anyway: one is more experienced, the other
inexperienced but have more natural talent to do it. Result = both perform
equally.

Gee, this starts looking like GURPS or something...


So I'll stop now and limit myself to the "AD&D crippled game-balance"
concept only.

In that sense, i'll resume fast: Level limit are NOT game balance, if

"IMHO, game balance mean that any two characters are equally as
vauable/powerful, in a stable fashion".

Why the "stable" thing? Well, balance require stability, right? Let's have
an example: if you had a dice with three 6 and three 1 written on it, the
mean value would still be 3.5, but would you say that the dice is balanced?
Me, I'd say it is balanced OVER A LONG NUMBER OF ROLLS. I.E. It is balanced
on the MEAN value of the dice. But any roll itself ISN'T balanced, there
just is too much difference between the rolls. Say, suppoise you got two
dices like that, one is called "PC #1", and one is "PC #2". Now, suppose
you compare how they are balanced one compared to the other by rolling and
noting the difference between the two rolls, and adding it to a "point
total" for the winning PC. Now, if you roll enough times, you will discover
that the difference of the point totals become more and more negligible
comapred to the mean value of these point totals. So the dices are balanced
one compared to the other WHEN YOU ROLL OFTEN. You will notice also that
when you compare your results to the ones you would have recieved had you
rolled with two NORMAL dices, they tend to become more and more similar as
the number of rolls increase, showing that ANY dice whose mean roll value
is 3.5 (by mean value I mean "you roll an infinite number of times"), will
give you a ""PC #X" that is just as balanced as the other ... when you roll
enough times...

Now, if you roll only once, then you will notice that you obtain a
difference. Either 5 or 0. If you roll only a few times, say 2 or 3, and
you keep only the following value: you make the avbsolute value of the
difference between the point totals from each side, divide by the mean
value of those point value of each side, and thus the result is expressed
as the "typical displacement". Now, you repeat the same experiment many
times, and make a graph of the number of typical displacement of each value
possible.

Notice that here you are not making results that are based on the
mean value (mean value is given over an infinite numebr of rolls, and each
experiment will always give you the same result even if you try an infinite
time to get the mean value by an infinite numebr of rolls, BECAUSE the mean
value was given by an infinite numebr of rolls in the first place!), so you
aren't making results based on an INFINITE number of experiments each based
on an INFINITE number of rolls, but you are making results based of an
INFINITE number of experiments each based on a FINITE number of rolls. Big
difference. So, you do it for the "1 or 6" dices, and you do it for the
normal pair of dices, and what do you get?

You get the repartition of all "typical displacements" possibles, and you
then notice that with the normal rolls the shape of the associated "curve" is
strongly "pushed" toward high-density for zero, like this:

+ Normal dice
* Special dice
@ both dices.

|+
|+
| +
| +
| +
|*+
|* +
|* +
| * +
|  **@**
|     ++@*******
|       +++++   ********
|____________+++++++++++___________>
0

I.E. While both curves have the same surface area. If we account for the
fact that the special dices can only give values stepped by 5, because the
difference between the two dices os always exactly 5, and thus leaving 4
difference values empty every 5 possible difference value. To correct it,
we simply divide by 5 and assume the curve goes through all the intervening
missing possible values. If we assume that "Game Balance", as taken in our
definition, doesn't include Diversity or results nor Gradual change from
one result to the other. If you include these, then of course the special
dice is less balanced than the other, but the ultimately balanced dice
in that case would be one with 3.5 written on erach side, and that would be
boring, so that's why I excluded diversity of results in the "Game Balance"
concept. Also, I don't want to limit ourselves to just one kind of die: the
standard one (D6), because that means that, using the "PC #X" denomination
of the dices themselves, we would arrive at the conclusion that the only
way to make the game balanced is by having ALL PCs be exactly the same,
which would be just as boring as having 3.5 on each side of a dice.
Diversity is needed, but isn't the same thing as Game Balance. RTo convince
you of it, make a special dice with 0.9, 1.0, 1.1, 5.9, 6.0, 6.1 written
on it. The mean value is still the same, the curve from earlier will look
to be nealy the same as the * one in the graph above, but there will be as
much diversity of results as with the standard dice. That shows the two
concepts are not directly related, although they cabn be inderectly related
(in the case of the "mean" dice with 3.5 on each of his 6 sides, we get NO
diversity, and the "Absolute" game balance. Thus we could create a third
concept, say "Perfection", which would be taken from Diversity and Game
Balance, say A * Game Balance value + B * Diversity Value + 
             C * Game Balance Value * Diversity Value.

Anyway, back to the graph... We notice that at low typical displacemnt
values, a normal dice has more density than the special dice, while at the
higher attainable values, the special dice has more density. Since we
previously stated that "game balance" result from near-0 difference betwen
the two dices, then the normal dice is effectively more balanced.

Im general, dices with straight UNIFORMLY REPARTITED values are at the
same time MORE balanced have more Diversity, and thus when we comnbine both
values we find that the standard dice is better than eother the special
"sides go from low to high in a straigth single step" and the "sides all
have the same value".

Now, all this was on dice, but I always have kept real PC classes in mind
the whole time. If we compare the numbered values on the sides, which are
tagged from "start" to "end", and assume the value on the side is the
absolute "power" level of the character at that moment in his adventuring
life determined by the "side" valuewhen you compare him to other characters
at the SAME moment in his life. I.E. A 6 on the "start" side means "very
powerful comapred to a reference powwer value for that level" and a "1"
mean "very weak when compared to the same reference value". Now, sure that
means that a 6 on the "start" side/moment is less powerful than a "1" onthe
"near retirement"  moment, but since when we evaluate the WHOLE power
level/value of th character class along the entire life of the PC, then it
doesn't really make any difference if we say the character is more powerful
than the norm at the start of his life and less powerful at the end of his
life, or the reverse. When you compare along the entire life of the PC, you
lose the meaning of time, so the numbers can be switched any way you want
and what you obtain is our initial dices which we talked about before. I.E.
A character growing in power regularly, according to the reference of each
level, will be a "standard dice" PC, etc...

Then we find that the standard PC, with power gradually going up from his
beginning of play to his retirement, is more diverse than a PC whose power
level would stay the same from start to end (as in most monsters are
currently depeicted in AD&D), and more game balanced than a PC whose power
level would start higher than the normal PC and finishes more limited than
the standard PC, or the reverse (starts less powerfull than normal,
finishes more powerful).

Sure, over the ENTIRE PC life, the mean values stay the same, but our
previous results from the dice graph are based not on "the whole life mean
value of the PC taken as a whole", but on the "whole life mean values of
the PC life taken bits by bits". And we conclude that a PC with regular
power level increase offers more diversity than one with the same power
level whtefver his level (that one was easy), and is more game balanced
than the PC which starts more (less) powerful and end up less (more)
powerful. 

The latter conclusion can easily be reached by two ways: first, the wrong
one: "Sure, you'll get this result not because it's true but BECAUSE you
defined game balance as having the same level of power for two PCs of the
same XPs". It's true, yes, but it doesn't let us learn anything new.
The second way to look at it is seeing game balance not from the whole
perspective over the whole life of the PCs, but from the PLAYERS
perspective, who live these events thorugh time, i.e. to see game balance
as the sum of all the tiny little perspective taken separately of every
adventuring moment.


Then it's VERY EASY to realize that having a player who kicks everybody's
butt when he's level 1 through 5, is just as powerful as any other player
between level 6 through 10, and becomes a wimp from level 11 to 15 will
produce this game balance:

a) from level 1 to 5, no game balance since he's much too powerful for
   the party. Game balance A = 0%
b) from level 6 to 10, there is game balance. Game Balance B = 100%
c) from level 11 to 11, there is no game balance either since he's a
   drag for the party. Game Balance C = 0%

Total game balance = 1/3 A + 1/3 B + 1/3 C = 33.3%, which is BAD.

That's why Level limits are BAD. And that's why non-human races being so
much better than human at low levels is BAD too.



	   I want penalties that make sense, not penalties that are slapped
   together for 'game balance' (that ugly phrase again) so that T$R can claim that
   game worlds would be humanocentric.

Game Balance is an ugly word only because Gigax and T$R never understood
what game balance means.



	   I want penalties to balance out the advantages of each race, so that no
   race is inherently weaker or stronger for PC use.

THAT'S game balance. Taking into account the time factor gives game
balance. Taking only the mean value over a long period of time is no
game balance.

	   I want specific penalties for each race, that are (more or less)
unique to that race.

Yeah!

	   Yeah, I want a lot. I want the game to make sense and to be balanced in
   a better, more logical, way.

   Brandon Cope

No, you're only asking a MINIMUM of common sensed, IMHO. But T$R isn't
reputed for common sesne, are they?


Pat.








--
/---------------------------\
| Patrick "Paradak" Rannou. |
| Rannou@info.polymtl.ca    |
\---------------------------/