Another thing is that he did not build the game from scratch he tweaked an existing balance that has been explored greatly.
Yup, that's, um, a little easier.
I have a more serious idea, if you math-heads want to explore it.
Instead of analyzing balance of a RTS in terms of sterile unit / unit interaction, perhaps the more accurate way is by modeling probability spaces
What do I mean by this term? Well, it's very complex, I could probably write a whole book about it at this point... but here's a non-mathematical way to describe it:
Within X minutes, most RTS games worth playing are at a critical junction
in time. X is a variable that's going to be hard to pin down, without adequate mathematics for any one game.
In P.U.R.E., for example, on the maps that shipped with the game, it's between 6 and 8 minutes. It depends on the faction and the map. That's the most accuracy I can give anybody.
At this critical junction point in time, certain things have happened, or not happened, that tend to have profound effects on the outcome of the matchup. These factors include, but aren't limited to, the following:
1. Resource income, both ramped (i.e., delta change / time) and total (how many units of XYZ have been available).
2. Unit income- a description of what units are available within timespace X given the resource income. I think it's a more accurate treatment of units to treat them as a form of "income" that derives from the total units of Resources available, instead of looking at them merely as chunks of combat power. That they remove resources from the pool is irrelevant- if you aren't spending those resources on units, you're effectively not using your resource income, and you're going to lose.
3. Spacial control, defined in strictest terms by how much map area can be accurately described as defended against a higher cost in unit income. Usually, this is a surprisingly-small surface area.
4. Spacial sprawl, defined by how large of a surface area must be "in use" to ensure resource income or unit income.
5. Total overhead, or the costs of all unit income over time. In *A games, this is rarely relevant anymore, but it used to be a bigger factor in OTA, and in P.U.R.E., it's a big part of the macroeconomics of it all. How much Power does a unit income eat, really? Well, you need to apply each unit to the current income in as it occurs. There's a point where further unit income is eating into resource income. This is an entirely separate issue from "choke", which is basically improper use of the given resource income trading for unit income.
When you look at things this way, you can see where things get really complex, when we try to apply them outside some sterile math.
For example, you'll never
see ideal numbers. This isn't Chun Li vs. Guile- there is nothing like that level of sterility in a RTS environment.
Even perfectly played, you won't ever see the theoretical ideals. Which is a good thing, generally speaking, because the ideals are surprisingly large, and the difference between a theoretically-ideal economic curve and typical curve is pretty big.
Moreover, this kind of analysis, while it can never be perfect (it's always an estimate because the real world is rarely going to allow for more than 75% efficiency or less, depending on the game design and time constraints), is a more accurate way to look at real play
, as opposed to unit / unit matchups, assuming that no one unit has combat power that is unattainable by any others (i.e., it's just obviously OP and can do all real jobs).
IOW, focusing on what units are OP today is fine and good. But it's not a good way to balance an entire game design.
The growth of economies is "fungal math"- it's complex, may include chaotic elements (such factors outside player control as pathfinder choices, etc., which have subtle effects throughout the outcome IRL vs. a model), and most importantly... it may be interrupted
by a number of factors that cause the model to run into serious problems.
For an example of "serious problems", here's one from P.U.R.E.. Power growth over time, theoretical time-hack vs. reality, can take several non-linear curves, depending on player choices (and there's no way that I can tell you what's ideal atm, that's a difficult thing to answer conclusively).
But weapons fire in P.U.R.E. is never
free. All of it costs Power. This was done for several reasons, mainly economic, and are really difficult for people trying to analyze a game strictly using DPS methods to appreciate.
So, in my model, if you get into heavy combat, you're trading Power with your opponent. Depending on the frequency of events on each side, you may be losing more, or gaining some, every time the relevant unit income becomes involved- an additional complexity.
I hope that this little example shows you where your attempts to model things break.
It's not possible to just do unit analysis and arrive at definitive answers. I've already shot that one down, and I don't see the point in returning to it, unless you'd like me to shoot more of it down, and prove to you guys that you can't really arrive at better than a fuzzy approximation. But your attempts to model anything aren't going to be worth much if they are outside the economic circumstances that deeply influence the real
You may win a given battle
, given unit / unit dichotomies, but you're probably losing the war
due to mechanics that aren't even included in your models. I suggest that if any of you are serious about this stuff, you might want re-examine your assumptions, and maybe build better models. I know modeling economic curves (and where they increasingly become chaotic and unpredictable, because it certainly happens) isn't fun or sexy, but that's far more serious game-design.