21 years ago I got a C in geometry. That is the extent of my math mastery.
I'd like an opinion from the experts, though. It seems to me that these marginal differences we are discussing end up being trivial considering how easily a DM can adjust an encounter. Or, to look at it another way, a poorly made encounter can make the added bonuses from the Expertise feat irrelevant.
Well, for starters, to say that a DM can adjust for something is to tacitly admit that there is a problem in need of adjusting. Consequently, I rarely accept "the DM can fix it" as a good solution for a game design or development issue.
Moving to the example at hand, if all of the scaling were consistent, then it'd be relatively easy to simply adjust monster levels up or down as needed. Unfortunately, player AC scales about the same as monster stats, but differently than player NADs or player hit rates in the absence of the feat "taxes" we are discussing. Which means you have this weird situation where monsters with attacks against AC don't have an appropriate level point, ever. Either it's too hard for the players to hit the monster, or it's too hard for the monster to hit the players. This can still be fixed by the DM, but the easiest way to do so is to grant free Expertise and free Improved Defenses and move on with on-level opponents as a standard.
But let's say the DM doesn't like that solution, and is willing to do a bit more work. Then the potential arises for the other problem created by the feat "taxes" existing as feats: namely, when people already optimizing for combat have them, and people running at system baseline do not. This makes it much more difficult for the DM to present a reasonable array of challenges for the party. It's easily possible for an enemy that one character hits normally to be one that another character either rarely hits or rarely misses. In the absence (or ubiquity) of Expertise, it's much more difficult to achieve this level of discrepancy. Ideally, you'd like everyone's hit rate to be within 10-15% of each other (i.e., 2-3 points on the die, with attacks against AC an extra 2 higher than attacks against other defenses). When the difference reaches 30%, it is very noticeable in play, and that kind of difference generally detracts from player enjoyment. Expertise is singlehandedly the entire ideal gap and half of what might be considered the start of problematic gaps*.
This kind of analysis is where you get statements like: "either the feats are necessary and shouldn't be feats, or they're overpowered and shouldn't exist". Because they're demonstrably overpowered, and it's not hard to show how that power level has the potential to create problems. If they're necessary, then the power level is justified, but their existence as an optional game element is questionable. If they aren't necessary, then the power level isn't justified, and their mere existence is questionable.
Add in various designer comments, both on record and merely reported, and it's easy to see why many have come to the conclusion that the designers consider them necessary, and have therefore opted for some kind of houserule fix like giving the feats for free (which is what all designers we know about do in their home games).
t~
[sblock=*problematic gaps]At a 30% gap, you're talking about 6 points on the d20, or a third of the available space. The same third, I might add, occupied by the suggested level range of creatures the party should encounter: level -2 to level +4. Given the system baseline of hitting an even level opponent on a 10, that means you should be somewhere between hitting on an 8 to hitting on a 14. If your characters have a 6 point hit gap, then there is exactly 1 level of monster that gives both characters a challenge that lies in that range. Go a level up, and one character needs a 15. A level down, the other hits on a 7. This has the effect of constraining the monsters a DM can use. He has one level band to present a reasonable challenge to both characters. He can present higher level monsters to one character, but has to make sure that it's an appropriate monster for that character to deal with; he can present lower level monsters to the other character, but should avoid making them things that the higher power character would want to deal with. Surmountable? Yes (it takes a 9 point gap to get into scenarios where you really can't challenge both characters simultaneously--but I might add that without Expertise, 6 is the max you reasonably get, and Expertise boosts that to 9). More trouble than you encounter when the baseline math is consistent? Absolutely.[/sblock]