AngleWyrm,
"The term 'log' in the above example is a bit ambiguous. Are we
taking the log with a base of e, 2, 10, or some other value?
Log_10 (1000) is 3. This means 10*10*10 = 1000. This is just
the degenerate case of X*Y*Z. A square is still a rectangle,
and a cube is still a box."
The base doesn't matter much. And calling somethng "just a
degenerate case" is a bit illogical because the particlar
inherits the properties of the general, but not vice versa!
A rectangle is not a square and a box is not a cube! You can't
project the properties of a particular case onto the general
case (at least, without applying induction correctly).
"And perhaps this is the correlation you speak of, where the
same dimension is being used multiple times."
Yes, it's absolute, 100% correlation.
"wouldn't it be more interesting to use b*c*d -- a box?"
Now that the variables are different, to assume their high
correlation becomes ungrounded.
"Such as Character Level, Armor class, Damage output, etc.
Perhaps you'll invent a replacement for these."
In your 'article', you never mention several functions and all
your statements won't work with more than one because you keep
thinking of the variables as highly correlated (hope you know
what it means) and different functions would allow for the
Scissors-Paper-Stone principle which, by definition, destroys
correlation by incor****ating unit's specifications,
professions. Not only in strategies but also in RPGs: like a
mage working on the improvement of magick skills or a warrior
that has to train strenglth, stamina, weapon-wieldiing...
I said: "In a good model the variables are not correlated and
your graphs loose all sense."
And you commented:
Here is where I suggest a small change:
"and your graphs lose all _common_ sense".
True: Common sense does not work for this problem space.
Why did't you react to my real criticizm instead of turning it
to something totally different and commenting on the modified
version, which has nothing in common with I wanted to say?
"Unless you multiply many of them together. Because when
multiplying many of them together, the result is that max
dwarfs everything else. In other words, the game winds up
having only one good armor/gun/whatever."
I have said why it is always bad to use booleans for analogous
values. Also I have said why your logic is incorrect. Why do
you repeat it here? This way you won't convince anybody,
neither will you let anybody to convince you, even if you're
wrong.
I can only repeat that what you propose leads to nothing else
than making some information not accounted for in the model.
For example:
S = X^4;
x1 = 0.0008
x2 = 0.0009
x1/x2 = 8/9 ~ 1
S1/S2 = (8/9)^4 = 0.624
That's the difference (between S1 and S2) that you don't wonna
take into consideration. Using booleans only creates noise.
"In other words, the game winds up having only one good
armor/gun/whatever."
Yes, but also a lot of bad armors/guns, which can also be
compared. And if you replace them with booleans, you'll get
only random noise ditributed between only two values.
"Putting the cart before the horse are we?
Deciding about the number of stats _is_ designing the game,
and in my opinion it is a step up from pound-and-observe."
I think you're puttin it in front of the horse. The number of
stats is only a corollary of design. Designing a game is
creating a model of the game's inner physics such that it
meets the designer's needs (in terms of the external,
observable behavior, not the number of stats...). No matter
how many stats are used. One may create a model with only two
stats, and another designer -- with ten ones. And both the
models will be great as long as they'll be what their authors
wanted them to be.
Anton
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