A couple points... In reverse order...
Some analysis can serve an overall analysis by micro zooming on on individual elements but it can also harm the large analysis if it paint a cockeyed picture.
Doesn't eliminate analysis as a useful tool. ...
An egregious example would be focusing on damage but ignoring hit chance.
Thats why larger system tests in actual play conditions are better.
That'd be testing playtesting, obviously, which is also helpful. Testing will find a problem, analysis will isolate the root cause, and point to possible solutions.
About not being about weighing flex vs restrictive... You listed maximizing the choices you have etc options which seems to be about flexibility but added while blah blah is met seems restrictive.
What we have, here, is a failure to communucate...
So, games present players with choices. The more choices at each choice point and the more choice points, the greater the potential depth of play.
But just adding choices doesn't always help. The classic example is the token in monopoly, you may like being the shoe, but it makes no difference in play. That's not 'meaningful' - RPGs add nuance to 'meaningful,' though (that you 'want to play a shoe' might carry some weight).
Another is the worthless choice - there's a variation of rock-paper-scissors that adds 'well' rock & scissors fall in the well, paper covers it - it obviates rock, so once both players realize that, the variation is back to three viable choices.
At absolute minimum, a viable choice must not have an alternative that is better than it in all ways. Again, RPGs add a lot of nuance to that.
If your top best output choice as a martial is 50. Then you have two 43s Then a half dozen at 35 then plenty in the 20-30 where is the not viable line drawn?
Depends on how much heavy lifting that DPR has to do, in context (of the system), and what, if anything the other alternatives have going for them.
For instance in the assumed 6-8 encounter day with 5rnd encounters, 1500-2000 vs 1290-1670 vs 1050-1400 vs 600-1200. If for the sake of illustration, a profoundly simplified Mike Mearls style balancing of the games hypothetical full caster's slots, with cantrips filling in additional rounds, were equivalent to 1500-1650, then the 50 dpr martial balances at 6 encounters & is OP at 8, while the 43 dpr is below par at 6, but balanced at 8.
But, on a off-label 4 round day, the martials throw down 1000, 835, 700, & 400-600, while the caster, down 10 rounds of very hypothetical 15 dpr cantrips, is at 1350.
So it's not just "is it balanced?" In an RPG it's also balanced for what sort of campaign?
And, again, theres nuance. If you really like the style of a weapon that takes you down from 50 to 47.5 or 43 to 41.5, why not go for it? (Effing half-point on average differences.)
Of course, that's a D&Dish example, other games are less sensitive to day length.
As in **outside of minmaxing** viable does not mean "best or close to it"
Even on the OP board it doesn't mean that - optimization is a specialized exercise, it needs parameters. Usually optimized for a specific thing.
In an absolute sense, 'not strictly inferior,' should be viable, keeping in mind that relatively minor and highly situational qualities can save you from strict inferiority.
In an RPG, 'not consistently overshadowed in the scope of play' might be closer. Though, you'll note, thats a higher bar.
Balance is more important in an RPG, where play is ideally cooperative, and 'meaningful' can be independent of mechanics, than in the narrower scope of a board/video and/or competitive game.
and i suggest that in 5e most any even,moderately straightforward build that is not crippled by contrary choices is "viable".
Depends on day length...
And pillar emphasis...
And that gets into another aspect - balance can be robust, or fragile...
In a TTRPG each and every campaign is very different, each party is different and so the things on the need side are not static.
Exactly. D&D traditionally copes with that by balancing to particular play expectations - a dungeon crawl with other adventurers waiting in the wings to jump your claim, new monsters moving in every day, old ones leaving with their hoards, &c; or 6-8 encounter/2-3 short rest days - it hasn't always been clear about those expectations or successful, of course.
One ed's lack of success at balancing classes led to sorting classes into Tiers by the power that mattered most in the highly variable context of an RPG: Versatility. Its still a useful tool to think about in 5e. Fighters lack versatility, but are solid tanks, Tier 4. Sorcerers have a potent spell list and cast spontaneously, but limited spells known that are hard to change, Tier 2. So, of course there's a corner case where the sorcerer can grind damage like the fighter, while in other scenarios going all in on some other spell.
Thats just one of many aspects where we look for **balanceability** instead of equality.
Its important to remember that balanced doesn't mean identical. If all weapons do d6 (and no other qualities) theres no meaningful choice of weapon, if the wizard, sorcerer, and Psion all have the same slots, and identical spell lists, and trivial 'ribbon' class features, theres only one caster. Add or change something, give weapons different die types, proficiency, grits, damage types; give casters completely different spell lists, etc, and you avoid that, and re-eintroduce some balance, if you do it well.
