Hello, AngleWyrm
"And what is a logarithm? log_x(x^y) returns y, the number of
dimensions. Taking the log of something implies that it has
multiple dimensions/variables."
In my example experience is calculated as:
Exp = Ta*K, K=const.
-- just a value directly pro****tinal to the time the unit has
spent fighting. It is neither multi-dimensional nor consists
of several variables...
"The assumption I am making is that the center 'diagonal'
produces the highest number. It could also be called the
optimum price/performance ratio."
It's a fact, not an assumption. What you assume is that the
various stats are correlated (hence every point is close to
the diagonal) and that the overall fittness function is a
product thereof (so that being on the diagonal means being the
best). I don't think either of these assumptions applies to a
considerable number of games...
"Which happens in a lot of games. Most of the 4X space games
are an early race, the the entire game is decided within the
opening moves. Some of them are decided even before the
opening moves, by the random layout of the terrain."
You think that's due to lots of stats? In your 'article' you
said a great number of stats did the opposite thing, didn't
you?
The opposite situation would be if no early gained advantage
could have any effect, which'd be more absurd, right? So the
question is, how to find the point between the two poles:
self-accelerating provess and self-deceletating process,
negative or positive feedback...
Common sense tells that every advantge (gained during the
opening moves or in the middle of the game) should of course
have an effect, but also it shuld not be too strong. What
middle point is chosen is decided by how the game models the
Friction Forces (as Klauzevitz called them)
Another assumtion of yours that I don't like is the existence
of a single fittness ****ntion that summarizes a untit's
effectiveness. Think of Stone-Scissors-Paper. A mojority of
strategy games implement this principle, better or worse, and
your 'diagonal' strategy doesn't work because the stats are
negatively correlated (good against infantry but can't resisst
against airctaft). So, such a unit cannot be characterized by
a single statistic.
"This happens if pieces of magic armor offer multipliers, or a
character can buff their weapon with several multipliers."
True ONLY if the multipliers are correlated, but why shoul
they?
"Also, as the number of stats increases, the product hangs
around the bottom until the very end. The situation devolves
into a set of boolean maxed/not-maxed prerequisites, making
the individual stat ranges rather pointless."
Not only this, but also the overall value of X^n starts to
behave as a boolean. But that'd be so only in case of highly
correlated variables, which'd mean they might be reaplaced by
only one variable!
In a good model the variables are not correlated and you
graphs loose all sense.
And replacing naturally analogous values by booleans is bad
irregardless of the model and number of stats therein, because
that creates lack if information. I may wiels the swor
skightly better than you, and some other guy, a bit better
than me. With a boolean this difference cannot be accounted
for.
Anton
P.S.: Deciding about the number of stats before designing a game
model is like choosing the number of screws before desig-
ning a car.
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