Well, I value by 300 turns. Game almost always lasts that long if you want it to, without losing.
Fine, snow day over here, so here's the math:
Russia = 10(avg value of horse/iron tile) x 6(avg # of such tiles in a 6 city empire, my compromise between tall and wide play) x 250 (turns) = 15000 gold (not savings, but actual flexible gold) over the course of the game (in this game, raw gold is worth at least double gold savings, at it's worst valuations, and is usually worth 4x); and
2.5(avg hammer gained per city) x 6 (cities) x 150 (average of turns remaining in game after obtaining resource) = 2250 hammers.
Total = 15000 gold, 2250 hammers.
Greece = 5x8x250 (250 turns for 8 CS of gold savings) + 5x8x200 (200 turns for the rest, because you actually have to find them, and then complete a quest; actually optimal CS play to wait for consulates to clear at this point, so that's 25 turns after discovery) = 18k of gold saved over the course of the game.
Total = 18000 gold saved.
Sweden:
In mid game+, 90 influence = 1k gold (or 1.25k gold without the quest). You should also be using your spies, to knock down the competitor's influence too. In any case, even if coups were not an option, you're basically selling your GWAMS for 1k gold each. I'm going to assume you open Honor, and ignore how bad the tree is. This is the most beneficial calculation for Sweden.
So, what's the worth of extra GGs? They're not worthless, as they expand your territory, and provide defense. How much would an aggressive game pay for a GG (once you already have 1)? I'd say 500 gold (would cost 250 gold each for ~6 tiles in the outter ring/unbuyable area; assume you only want 2 of those tiles, for 250 gold). Admirals are a bit more worthless, maybe 300 gold. Prophets are certainly not useless, especially with your faith pantheon, but let's say you found and enhance a religion, then gift the rest. Prophets are worth at least the gold/faith it takes to get them (or else you wouldn't), so 500, 800, 1200, 1700 faith. Faith is worth more than gold (e.g. they trade on a 1:4 ratio with gold when used to purchase faith buildings), I'm going to be generous to Sweden and say they're only worth double (since you'll be getting a ton of faith anyway). Next, you get to spread 3 times before gifting, so the value lost is 25% of that. I'm going to gift all four. 250, 400, 600, 850 = 2100
So, the total cost of gifting 5 GGs, 2 Admirals, 4 Prophets = 5200 gold.
Now, GWAMs. Let's say you generate (with your UA) 9, 8, 7 of W, A, M in the course of the game and gift all of them. Note that this bakes in the UA (I'm basically taking my stats from games I play with Aesthetics opener, presuming that Sweden won't be able to go for Aesthetics early while doing Honor Patronage and Rationalism). Anyway, the value of a golden age is going to surpass 1000 gold (it does so on just 4 cities, and gets ridiculous with more cities), so gifting artists is bad. Quite frankly, you're not going to finish Honor, Patronage, Rationalism and Autocracy tier 3 in a timely manner without some great works. We're ahead of your 20-GP curve anyway. So, let's say that you pop or GW the writers to have enough culture to finish this. Your first and only gifted writer is You have 7 GMs, which are worth whatever +2 culture / +2 tourism is worth to a war civ (not much). Since you would probably still build a 2 culture building that costs 2 gold upkeep in your cities, I think it's worth at least (150 turns x 2 upkeep = 300 gold + 300 gold for discounted hammer cost equivalents; to being worthless at the end). So, we'll set the value of the average GM over the course of the game at 300 gold.
7 musicians = 2100 gold.
Subtotal = 7300 gold.
Your CSs will send you random GPs. Out of 9 options, at a once per 20 turn clip, starting turn 160 = 6 GPs. Out of 9 late-ish game options, the only ones you'll keep are GSs, GAs, GWs, GMs (you'll get a better gold/influence total by actually using the thing) and GEs. The other 4 will be gifted. Trust me on the math on this, you'll end up with 1200 total gold cost and ~3 gifted GPs.
Total GP gifted = 21
Total gold value from gifts = 21000
Total opportunity cost of gifting = 8500 gold.
Net total gold saved= 12500 gold saved on CS influence.
Remember, Greece is at 18000. It also gets the bonus that CS influence recovers at twice the speed, which makes stealing a worker and failed coups less painful for Greece.
So, played by warring the ENTIRE game, and not taking into account any costs of war, Sweden gains 67% what Greece does. It will also generate GSs, GAs, GWs ~30% faster. (assuming you war with 1-2 civs, and still manage to be friends with more than half the other civs, because you own diplo hard).
To sum up:
Russia = Clearly better, in almost every way compared to Sweden and Greece. My math was for 6 cities to match Sweden's lowest diplo cost play style, but more cities means more benefits, and even at 4 cities, Russia's bonuses would still crush Greece/Sweden.
Greece = Pretty bad overall, but no tundra start.
Sweden = Has bonuses that cumulatively outrank Greece, very very slightly. But, starts in Tundra. And, is also premised on starting Honor, and fighting all game, while keeping good diplo. Only with this very specific strategy does Sweden get a tiny bit better than the absolute (by a mile) worst civ in the middle tier. This strategy Sweden needs is also comparatively difficult to pull off in BNW's war and diplo mechanics. On the other hand, you can start Tradition/Liberty, and lose out on a couple of GGs, which then basically makes you a worse version of Greece who is forced to fight all game to grind GG/Admirals. This is also all heavily premised upon actually getting a religion, which is not a guarantee, even with the tundra start (although, very likely). Sweden without the Great Prophet trick is awful.
So, I get that Sweden looks very similar to Greece, and as you see from the math above, it IS very similar to Greece. But, that's because Greece sucks, and is by far the worst civ on the mid tier. You can't really compare either to Russia. It's like when you do Rome math. Russia doesn't ever look powerful, but everything adds up to be a rather huge bonus.
Now, instead of moving Sweden up, is anyone convinced that we should move Greece back down? It's UA basically gives less than half the bonuses Russia's UA does for 6 cities, and about 2/3rds Russia's bonus for 4 cities.
