Depends at what stage you're taking that snapshot.
At the point where you choose, of course, I thought that was fairly clear. The 65 arrays that can be built with 5e PH point-buy is 64 more arrays to choose from before arranging than standard array or random give you.
Before I roll any dice I've potentially got a huge boatload of stat lines
None of which you can /choose/. I suppose, to be fair, if we step it back a bit, Array gives you 1 choice, point-buy 65, and random 0.
Another way to look at it is the number of different arrays you actually have in the party as a whole, when you're done.
In standard Array, it's 1.
In Random it's up to the number of players, depending on how the dice fall.
In point-buy, it's up to the number of players, depending upon their individual choices.
When playing Monopoly (a typical board game) no-one expects you to create an alternate character to role-play, and wonder if the particular capitalist pig you are playing this time is the kind of guy who would bulldoze four houses and evict the poor tenants just to build a luxury hotel for the bourgeoisie!
You are not playing a character
No one expects it, but it doesn't mean you can't....
; you are you, trying to win a boardgame according to the rules of that game.
A not particularly good boardgame, but yeah. Getting your favorite token and attaching a personality might make it less boring... and you can still play to win while doing so. :shrug:
Part of the rules of that game are that each player starts with the same amount of money. No-one expects to have a random roll to see how much money they start with, because realism has absolutely nothing to do with the game.
The game evokes it's own myopic vision of a capitalist reality. Some of the places on the board are real places, for instance, some of the cards refer to laws, traditions, sayings &c of the day when it was created. It's not a realistic simulation anymore than LIFE is of modern life, or chess or go are of warfare, or D&D is of the middle ages, though. FWIW.
But if we were DMs trying to create a believable world in which to have adventures, then it would be totally unbelievable for each person to have the exact same amount of money. That every entrepreneur has to receive the exact same 'starting' cash from Daddy (as if everyone 'starts' at the same time!), and their natural talents are divinely mandated to be equal.
Not impossible to arrange. Maybe they're the top 4 graduates from Harvard Business that year, and have been given money and challenge by an eccentric millionaire (because a million was a lot of money back then)?
So we have a spectrum: at one end is the 'just a game, therefore everything must start equal' attitude of a mere boardgame. On the other end is the 'reality sim' attitude.
Fairness is critical in competitive games, the higher, arguably more nuanced bar of 'balance' is critical in cooperative games (sure, you can have a cooperative game where one player is the only one who's play actually matters, and everyone still 'wins' if he does - but everyone else might as well have gone in the next room and played Monopoly). 'Everything is identical' is a simple way to achieve fairness, but 'everything is random' is, too.
Neither, however, deliver balance.
Random generation (like your move is 2d6) would be fine for a competitive tactical board game, as would everyone playing identical 'playing piece' characters. For a cooperative board game, though, it'd be better if each player had a different 'playing piece' with different characteristics, but still equally important to winning the game - but it'd still be fine for those playing pieces to be chosen from a limited set or randomly distributed.
In an RPG, though, you have both a cooperative game to play, and a role to play, and not just choosing, but creating that role can be an important and rewarding part of that process....
For those of us who hold 'realism' as more important than 'only a game', then 'realism' is more important than 'fairness' in character generation. Therefore, rolling is more attractive than point-buy or standard array.
Though I sorta agree with the conclusion, I find your rationale less than satisfying. Fairness isn't really an issue in comparing the character generation methods - they're all fair, as long as you're all using the same method, achieving fairness is trivial, really. Realism of the two 'RAW' methods in the PH, OTOH, is minimal, the difference between choosing to arrange either a standard array or a random array (weighted towards results that average the same as the standard array), or arrange one of 65 point-built arrays (built on the same points as the standard array), is barely meaningful. Roll-in-order would be significantly more realistic, though, especially if combined with random determination of other factors beyond the character's influence - random methods, in general, can be a lot more realistic than point-build methods, but the specific one in the 5e PH, not so much. FWIW.
For those of us who hold 'only a game' as a higher priority than 'realism', then a fair/balanced PC generation system is more attractive than one with realistic variation. Therefore, rolling is less attractive.
Again, fair isn't an issue. Balance is, of course, because it's a cooperative game. But, for 'only a game' attitude, balance can/should be fairy tight and limited, only enough distinct roles to give one to each player are required, and what that role is will not be that important. There's not a lot of fine-tuning involved. Pre-gens, as in the days of Tournaments, or Standard Array would be ideal, then.
But, those two extremes aren't the only options. Players who want to engage, play, and enjoy the game, and /also/ want to engage, play & enjoy their role, need more than mere fairness, and more than a handful of cookie-cutter roles. They need more options in choosing/customizing their exact role in the cooperative game and it's imagined setting, that requires greater balance and more flexibility & choice than either random or array can provide... that's when point-buy makes more sense. It's also when the other player-facing sub-systems of the game are under the most stress/scrutiny, because if a player chooses a certain role and that role chronically under-contributes for mechanical reasons, he can be all but excluded from the game...
One reason that this thread is so long is that human nature leads us to treat the way we like things as the way things should be, and find it weird when we see people making the opposite choice. I see people who treat RPGs like a board game and my knee-jerk reaction is that they are having fun wrong. I don't get it. It seems to me like they are throwing away the best part of this extraordinary hobby just so that they can play a rather complex boardgame
Nod. And, you're clearly at the other end of the spectrum you see it. GNS sees a more complex pattern with 3 extremes rather than the two of a simple spectrum, with story as an emphasis in addition to the 'game' and 'realism' dimensions you see.
Doesn't change anything: whether you focus on one of two extremes or one of three extremes, and the incompatibilities of one with the other, you're denying the middle, the synthesis where things actually happen. An RPG is both playing a role and playing a game, you can do one or the other, but it's not really an RPG at that point - no one who shows up to discuss an RPG is likely to be that extreme, and painting others that way is usually little more than making a straw-man of them. (I'm sorry if I'm just repeating your point, BTW, I'm just going off on a similar tangent in my own words.)
You can can also emphasize one or the other while still doing both, and, in that emphasis, de-value the aspect you're paying less attention to until you think it doesn't matter. That probably happens, and it's problematic.
Thus, I think it's a good idea to cut the other side some slack in these debates and look at it from their side, too. If the advantages of one technique seem obvious, think harder about the disadvantages, you might gain some insights you've overlooked. If the down-sides of a technique seem overwhelming, go digging for it's strengths and try to understand them, you might reap a similar benefit.
Long, circular, and pointless as a thread like this can seem, there's a chance, however small, someone might benefit from it...
