This definition that you use here fits your definition of bounded accuracy, but is dramatically different from Rodney Thompson's definition, which is: "The basic premise behind the bounded accuracy system is simple: we make no assumptions on the DM's side of the game that the player's attack and spell accuracy, or their defenses, increase as a result of gaining levels.
BA is a design philosophy, not a prescription of how you must run your game. The DM's side of the game is mak'n stuff up.
Instead, we represent the difference in characters of various levels primarily through their hit points, the amount of damage they deal, and the various new abilities they have gained
Minor flaw in that is 'special abilities' aren't exactly comparable among classes. OK, other than casters... Ok, who are most classes... OK, and share lots of spells. OK, minor problem with my 'minor problem' there.
So, genuinely minor problem with the 'special abilities' dodge is that there's a sub-class or few that don't really get much of any - they do get plenty of hp/damage scalling, though. So if we want to be fair to all (sub)classes, that's what has to carry the burden of scaling.
... Now, note that I said that we make no assumptions on the DM's side of the game about increased accuracy and defenses. This does not mean that the players do not gain bonuses to accuracy and defenses. It does mean, however, that we do not need to make sure that characters advance on a set schedule and we can let each class advance at its own appropriate pace."
Hmmm... that last bit is off. There's only one pace of advancement for bonuses in 5e: proficiency. You advance or you don't. OK, expertise doubles it, but that's the only exception that comes to mind. Monster bonuses do scale with CR, as well. So it's not really classes advancing at their own pace, but advancing in their own areas. :shrug:
Tony's definition: assumes a narrow gap between best and worst d20 bonuses.
Which the game delivers: it doesn't overwhelm the d20.
Rodney's definition: avoids making assumptions about d20 bonuses.
I think we're missing some context for these quotes. About 15 years of context, against which BA is being contrasted, there.
In 3e, scaling was rapid and very uneven. Skills advanced by spending 'ranks,' that you gained as you leveled, so an in-class skill could be level+3+stat Mod+feats+items(items were assumed), while a cross class skill started at half-level, if you put a rank in it every level, and there were simply more skills than any class could get ranks, so plenty languished at 0. Those bonuses could exceed 20, even long before 17th level, and that created circumstances in which challenging the specialist PC, meant using DCs the other had /no chance against/. The same applied to a lesser degree with attack bonuses, full BAB classes with optimized AB could hit ACs on a 2 that other characters might miss on a anything short of a natural 20 (the way itterative attacks worked mitigated against that being a serious problem, but that was still common complaint). Then there were saving throws. The DCs scaled with spell level and caster stat mod - and feats &c - and could be optimized to the point even 'good' save bonuses had little chance vs a top-level spell. Bad saves were abysmal. But, there were at least only 3 of them, so it wasn't as impossible to try to cover them all, just a losing battle vs the casters' (and monsters, all the same options were open to them) optimized DCs.
That was a pretty appalling situation, and 5e BA is, in part, a reaction against it.
It's also, in larger part, a reaction against the 4e solution to that same problem, because it also did something pretty damn appalling: it worked.
4e simply put everyone on the same basic advancement: 1/2 level. Instead of variable BAB and DC optimization and 'bad saves' and ranks resulting in swings of 23+ overwhelming the d20 and making it impossible to set DCs that'd keep everyone relevant, 'training' granted a +5, proficiency a +2 or +3, and good saves +1 or +2 over 'bad' saves - and named bonuses were curtailed and also pegged to progression via feats and 3e-style wealth/level & make/buy, reducing the impact of optimization. Challenges - monster level, skill DCs, etc were rated relative to that progression, so they'd be fairly consistently challenging when 'level appropriate.' The result was a 'treadmill,' because the game remained consistent, balanced, and functional at all levels: at-level challenges could be taken on with confidence, higher level with increasing difficulty, around level+4 or 5 it got very deadly, much below level -1 or 2, trivial. But, advancement was rapid, all 'expected' bonuses factored in, it was about a +1/level at anything you were trying to be reasonably good at, and numbers were /big/. The game spanned from low 'heroic' levels to 30th at the end of epic. So towards the end, you'd be looking at numbers above +20, the same as were overwhelming the d20 in 3e, the difference being that the low end wasn't languishing at 0 at those levels. (Just as with 3e, mitigations like that were ignored when the game was criticized).
Also, tellingly, the way 4e handled it's equivalent of ASIs meant that PCs were mostly channelled into maxing out two stats and letting the rest more or less languish (one way it which it very much wasn't a treadmill), that meant that at least one non-AC defense (the 4e equivalent of save bonus), was going to languish a bit, net getting 'worse' relative to the attacks you'd be weathering at high level. There were ways to shore it up, feats, selective use of stat increases and build tricks, but that required system mastery and diverted build resources, and the gap still wasn't going to be huge, it's just enemies might be hitting your worse non-AC defense on a 4 rather than a 9 at very high level - and, the consequences of being 'hit' by an attack, even one that's modeling some nasty spell of past editions, really were a lot less severe - and generally included some hp damage, anyway - the effects might last a turn or be 'save ends' (and saves were a duration mechanic, 55/45 - nothing like repeating a save you need a natural 20 to pass, or can't make, at all).
I can't begin to get across the horrors and excesses of the edition war, but the upshot for Next/5e and BA was that it absolutely had to avoid certain things that became rallying cries. Big numbers. Long combats. Fighter casting spells (whoops). Etc... It also kinda needed to avoid returning all the problems 3e had had. OTOH, the problems of the classic game were prettymuch OK to return to.
Nostalgia, y'know, 'brand identity.'
So when Mr. Thompson briefly alludes to 'not making assumptions' on the DM's side, he means there's no wealth/level or make/buy, no uneven, uncontrolled rapid scaling, and no prescribed progression of challenge to keep pace with scaling, even if it were controlled, slow, and even.
When BA works, it means the DM can drop a challenge out of the blue that's of a very different nominal level than the PCs, and they'll have shot (maybe a pretty slight shot) at making relevant checks. It doesn't mean they'll have any chance against it if its much higher level. It just means that d20 isn't overwhelmed by specialization /nor/ by level. Instead, numeric scaling is mostly contained in hp/damage. The much lower-level enemy in a battle might be missed now and then, might hit now and then, but will not be able to keep up in the DPR-based race-to-0-hps of D&D combat. He's able to participate, but he's gonna lose. Likewise, a higher level combatant has to be pretty badly outnumbered to be taken down, because he has so much resilience from his massive pile of hps.
Now, characters do also 'progress' or 'become better,' in a sense, by getting to do new things, as well as being much tougher and hitting harder, and doing the few things they were particularly good at just slightly better. Getting to do a new thing is not the same as being able to survive a Meteor Swarm because you just have that many hps. It might be, in the case of casters, because they get to accumulate so many new things to do and have so much flexibility in which thing they do when, and may be able to apply this or that spell as a 'win button' in this or that situation, but it's not the same thing. It's breadth. It's nice, but it's not necessarily going to help you stand up to something of CR close to your level the way having a pile of hps and dishing a pile of damage will.
Where BA falls down is when the system depends on one or two d20 checks to resolve some level-CR-rated 'challenge,' instead of on something, like hp/damage, that actually scales. Saves are the most evident example.
Trying to create something akin to a 'skill challenge' or rate a non-combat challenge for exp to a degree similar to what's done in encounter building, would run into similar problems. Precisely because designs don't allow for workable assumptions about bonuses scaling with level, and the other two pillars have little to hang their 'challenge' on beyond DCs...
