EPTThere is no good way to define balance.
It's not something that I realized right away, but it is something that, after many attempts to do just that, I realized that is as true as can be. And if we can't make a good definition that is testable, then we're just wrestling with philosophy. Sure, I could go whip out my old playbook of philosophical logic and philosophy of science and have a fun little talk in the process, but as I've found over the years, any philosophy debate always ends in some nice little discussion but then a realization that you can't prove anything, you can't logic your way into anything, and you all just agree to have your little inconclusive talk then go about your business. That's not what any of us want; all that will lead to is just folk leaning to the feel-good, but rather misguided, solution that either the game is close to perfectly balanced, or that balance doesn't matter, neither of which are good conclusions based on the results compiled in my two articles. But I'm not sure we can do better.
Another individual on this forum who was really into posting long diatribes about balance (among other things) is letmelose, who takes a fairly different approach to it all. You can feel free to read through his blogs or his various posts; there are plenty to look through. While I don't know if I could really pin a specific style on him, if I had to try then I would put it as "eclectic" in that he seems to take a lot of rather different approaches to proving a point, and showing how a certain range of indicators prove a certain point. With regards to Terran and their place on the top of the rankings, this post is a good sample, showing how many different indicators show the same thing. It's not exactly proof and yet, whenever I disagreed with a point made this way (such as here), it was hard to figure out exactly why or how it was or wasn't true. It just seemed to be perfectly valid from a completely different definition of balance.
I also corresponded with another individual around these parts - Jealous / fanatacist - who was interested in trying to use my data to look at the problem with different methods to gain a more useful result. I did give him all the datasets I worked with, but it seemed like he got stuck in that neither he nor any of his sources could make sense of it either. This post seems to suggest as much as well. And my own posts were a fairly simplistic analysis of line graphs and histograms, because I too felt that there was no way to frame the problem better.
I could easily prove that Terran has the best results overall, that Protoss have pretty bad results all around, and that Zerg are somewhere in the middle and buoyed by large quantities of players. I've done it before with one method, letmelose has done it with other methods, and I could dig up any number of further indicators that will show that it is so. It's not hard; the data clearly shows it to be the true. But that's not enough to close the case. It might give one explanation as to why, but it's not necessarily more valid than any other explanation. I personally focus on the way that the TvT matchup supports the advancement of better players rather than dice-roll mechanics and that the TvZ/ZvP/PvT spread clearly favors Terran. But there are other ways to show similar results that follow a completely different, and perhaps partially contradictory, train of logic. It doesn't show that this is an essential reality rather than an accident of how the professional BW scene developed, and the argument could be made with reasonable accuracy that either the map choices over time or the metagame influenced the results and that a different evolution would have given different results. And so on and so forth ad infinitum, ad nauseam.
What would really be the holy grail that would allow this to work is if we could agree upon one single definition of balance, a testable idea which we could evaluate to say that something either is or isn't balanced. With that in hand, it would be little more than a task of writing a mathematical proof, or at least a highly suggestive statistical analysis. But without that in hand, there really is nothing that we can do. If we use the same term "balance" but we can't agree what it means, then we can do all the analysis we want but it won't make a bit of difference because we are just essentially talking past each other. And for all the effort I've put into it, and for all the people I've queried, no one definition really seems to make sense, so I can only conclude that we're talking mere philosophy rather than mathematics.
That being so, I've been forced to come to the conclusion as listed in the title: balance is an intractable problem. We can't define it, so ultimately we're just going to end up going in circles talking about it, without ever coming to a suitable final answer.
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