I've been working on a 'balanced' formula and on a 'physical/special' formula too, but I'm a bit stuck on what the definition of these should be.
Let's start with 'balanced':
1) I think Speed isn't an issue on whether a Pokemon is balanced, offensive or defensive, but maybe I'm wrong. So, am I wrong?
2) I agree, in part, that the higher attack stat from Atk and SpA should be more responsible for the 'offensive' part of the formula than the lower attack stat. For example, Hariyama has 120 Atk and 40 SpA, and surely it will only use its Atk. However, Salamence has 135 Atk and 110 SpA, and both can be used fine. I've been kinda stuck as to how I should intepret the attack stats.
3) For defenses, however, I don't agree that only the higher of Def and SpD is taken into account, as the Pokemon will be using both during a battle, whether it likes it or not.
4) Because of this, I think my formula will take into account HP, Def and SpD, and a heavily biased trend on the higher between Atk and SpA.
For physical/special:
I think I misunderstood Time Mage's definition. Is there a separate disparity between physical/special offense and physical/special defense, or are both offense and defense taken together?
This is what I had in mind: First, in the style poll, we choose if the proficiency of the pokémon is at attacking, defending, or a mix of both. That's why I proposed comparing the
highest attack stat to the
highest defense stat: When attacking, the highest attack stat is the most likely to be used, and when defending (and understand, defending as in "sent out to absorb an attack", not as "every pokémon, when battling, takes a hit") it will use its highest defense stat, too: You're not switching your Steelix on a Starmie, you switch it into a CB Tyranitar. Also, you nearly always (predictions and sacrifices not counted) retire your Steelix if they send a Milotic. Yes, you will take some hits from the less optimal side from time to time, but just as a good battles doesn't use the lower attack if there isn't a reason to do so, a good battler avoids taking hits from the weakest defensive side if possible.
That's concerning offensive/defensive/balanced. But we all know that there are offensive threats of any kind (physical, like Garchomp, special, like Porygon-Z, or mixed, like Infernape). The same can be said about defensive pokémon. There are some that take physical hits like nothing (Steelix), others that eat special attacks for breakfast (Blissey), and others that are comfortable taking hits from both sides (Cresselia). What makes those pokémon do better in one department or the other is, aside from typing and movepool, the difference between the corresponding physical and special stats. Gliscor's defense is much higher than its special defense, so it's obvious it is a physical wall. Both Rhyperior's physical stats, offense and defense, are much higher than the special counterparts, and both are relatively equal, so he is balanced and physical, meaning that he can equally take damage and dish it out in the physical side, but is horrible at both in the special side. There are many other examples, like Gallade, who is balanced (SDef and SAtt are very close), but is physical in the attacking department and special in the defensive department. As you can see, this way of classifying pokémon allows for most if not all types of pokémon to be taken into account.
Sorry it took too much, but I felt I had to clarify exactly the meaning of the style and build categories.
Finally, regarding your first 4 points:
1) I agree... Somewhat. I've been thinking about this for a while, and the speed chart you posted made me think more about it. Does speed counts for offense? In some cases, it's obvious, frail pokémon with high speed and attack are clearly offensive, but then, we have things like Tyranitar, who is fairly slow but also very offensive. Why? Because it can afford to take a hit or two, and dish out much more in return. The lower the speed, the more important the HP (since it affects both defenses) becomes. Factoring in both the speed factor and the HP in the offenses should do the trick. Something in the lines of: HA*SF + 4*HP*(1-SF). HA is the Highest Attack, SF is the Speed Factor, HP is Hit Points. Comparing that to 2*HP*HD/(HP+HD), being HD the highest defense, and adding the 2 and the /(HP+HD) so it can be compared with the offensive term. This is a rough draft, but I think that this method of taking both speed and HP into consideration when measuring the offensive prowess can solve a lot of problems.
2) Again, maybe weighting each stat according to its own power would do the trick? In terms of statistics, the lower the attack stat, the lower the chances that it will be used, so if instead of using HA we use something like PA*PA/(PA + SA) + SA*SA/(PA + SA) for the calculations, it will have a better meaning.
And regarding 3) and 4), I've reasoned abut them in my first two paragraphs.
Phew, sorry for the long post.
EDIT: All stats are the normalized ones, of course. And because of that, I'm changing HP to 4*HP in the offensive power calculation: Since I am adding the weighted Attack and HP stats, and not multiplying them, the 1/4 factor the HP term has in the normalized base stats does influence the outcome here.
And of course, this is all a draft. I still have to make more numbers and some other considerations to make this thing work properly. The biggest problem is normalization, in fact, not all terms are comparable right now.