Excellent!
I can't see that you explicitly accounted for the fact that the fighter has no resource management:
It was probably somewhat of a mistake, but how I was working the analysis was in part built on the resource of time.
As the wizard uses up his spell slots, his power curve will obviously invert; you're comparing them in a static (fully rested) state-- which is fine, but neither is it negligible from a design standpoint. You have a pretty complex problem to solve and it's going to require a calculus that includes dT (change over time). After 5 rounds, the wizard's power has changed; after 5 encounters, the wizard's power has changed dramatically. Conversely the fighter doesn't suffer any loss of power/resources. (They both have to worry about hit points as a resource; I'm happy to drop them out of the equation but, if not, I'll simply note that the fighter has more.)
One of the principles that I was working with is the notion that on average a combat encounter lasts on average five rounds. So as the wizard goes up in levels the number of spells increases to the point past which you can realistically use in any given encounter.
In the realpolitik of a gaming session, it would seem really difficult to run through five encounters simply because turns take far too long with lots of iterative attacks and high powered spells and powers being flung about, so a 20th level wizard who has 55+ spells prepared is going to have more resources than the game is likely going to push them to expend.
So even though the fighter has less resource management, the limited time of needing to be expending them ends up favoring the wizard more and more.
Still, all of that is very broad in assumption, and fine tuning really is needed.
Furthermore, I would only count the wizard's top 3-4 levels of spells, as spells below that (regardless of how he tries to optimize) will dramatically fall off in utility with respect to combat power (which, ultimately, is what folks seem to want to compare).
I'd agree that it is the top few layers of spells that are going to have the most impact, though the issue of Quicken Spell, along with scrolls and other magic items (which I wasn't accounting for) is another layer that seems to favor the wizard even more. At the highest levels the wizard is going to be able to burn mid level spells to get some of the new still effective low level spells (like grease) to be cast in the same round that a high powered spell is being flung, thus pushing the limited time factor of "rounds per day" even father into wizards corner.
I didn't take those factors into account, seeing them more as a buffer in, what I have to admit, was not as rigorous of a methodology as you'd been using.
You should probably also "value" the spells quadratically-- so that if a 1st level spell has a value of X, a 9th level spell could have a value of 81X; but you seem to have valued them linearly (4x spell level). The power of spells doesn't actually scale quadratically, I don't believe; but something in the wizard's arsenal needs to be valued quadratically or his power won't actually scale quadratically. Something in there needs to be valued as the square function of our known variable, Level.
Your graph-- ergo your methodology-- seems to show the 1st level wizard starting out with power in excess of the 1st level fighter. That's definitely not the case so I'd send you back to the drawing board.
I agree. The math is a bit too ham fisted. I started plugging numbers in and went back to your class rebalance section and followed your and Craig's method.
Now the thing that I'm kind of scratching my head over is that both of you decided to average out the class features over 20 levels. I'm not sure why this was done because it seems like it just flattens the power curve, when that really needs to be highlighted to show the disparity between spellcasters and martial characters.
Plugging all of the numbers in that you and Craig used (and using the .005 value for spell factor multiplication), but not doing the averaging I got:
The numbers for the graph are:
Now, the Wizard was higher that the fighter right from the start mainly because of the familiar being stated out and added to the wizard, rather than just giving the wizard a +0.2.
But the main issue is with the high levels of play. There the the gulf opens up between the wizard and the fighter. But with these new numbers I'm not too sure how to use them. Just by the factors alone a 20th level fighter and 20th level wizard are 162.95 "feats" apart (assuming the 0.2 value for a feat) which if people think 45 feats is too much, would think this factoring absurd.
I know that one avenue would be to try and work out the value of feats as they progress over the levels. A feat gained at first level probably isn't going to be as potent as one that has a level 16 prerequisite. However even there the disparity in power isn't that great compared to 1st level spells vs 9th level spells.
Overall though, I just wanted to get this concept out onto the boards because I haven't found anyone trying to do a quadratic fighter concept. It seems obvious that the fighter's 11 extra feats are inadequate, and so if you just go withe the concept of a fighter being a "feat wizard" then it really just comes down to trying to figure out how many feats should roll out at certain levels.
In the most broad thematic view, the idea is to emulate the AD&D fighter which was more of the "total package" guy who'd gain a large number of proficiencies in weapons. Rather than hyper specializing and becoming a one-trick pony, the fighter can pretty much pick up any weapon and be deadly with it. So if you pack enough feats onto a 3.5 fighter then they have something similar in terms of diversity.