I think the primary issue here is that you are calling the lowest ranked cards "underpowered" and the highest ranked cards "overpowered", which is taking too much from just ranking. By taking the top and bottom 25%, you are immediately assuming that 50% of all cards are unbalanced. If you must choose an arbitrary cut-off, it would be better to use a smaller number.
So which number would you use? 10%? 15%? 5%?
I wouldn't even use a percentage. I'd do what Donald said and make the judgement call myself. For simplicity, maybe look at top and bottom of each of the ranked lists and choose a cut-off. So for example, let's look at the $4 cards.
Scout, Thief, Feast, Coppersmith, Treasure Map... OK, Coppersmith is sometimes a powerhouse payload, but that happens very rarely. I think it's fair to say that it's underpowered. Treasure Map is weak but I don't think it's underpowered. It's supposed to be high variance. So I'll put the cut-off there.
Sea Hag, Tournament, Remake... well, I don't think any of those are really overpowered. But Sea Hag and Tournament can be pretty centralizing, so maybe I'll put those through. Remake definitely isn't overpowered though (especially with Shelters), so I'll cut it off there.
From 57 cards, I ended up with the bottom 9% and the top 4%.
I did a new analysis with different cut-offs:
Cut-offs:
Cost 2: Pearl Diver (20/22), Hamlet (4/22)
Cost 3: Great Hall (32/34), Steward (4/32)
Cost 4: Bureaucrat (50/57), Jack of All Trades (4/57)
Cost 5: Madarin (57/66), Witch (5/66)
Cost 6+: Expand (14/16), Goons (2/16)
Underpowered:
Base (32%):
$3: Chancellor, Woodcutter
$4: Bureaucrat, Feast, Spy, Thief;
$5: Mine
$6: Adventurer
Intrigue (20%):
$2: Secret Chamber, Great Hall;
$4: Coppersmith, Scout;
$5: Saboteur
Seaside (15%):
$2: Pearl Diver;
$3: Navigator, Treasure Map
$5: Explorer
Prosperity (15%):
$5: Contraband, Counting House, Royal Seal
$6: Expand
Cornucopia (8%):
$5: Harvest
Hinterlands (16%):
$2: Duchess
$5: Cache, Mandarin
$6: Farmland
Dark Ages (3%):
$5: Graverobber
Guilds (0%):
Overpowered:
Base (8%):
$2: Chapel
$5: Witch
Intrigue (12%):
$2: Courtyard;
$3: Masquerade, Steward;
Seaside (15%):
$3: Ambassador, Fishing Village;
$4: Sea Hag
$5: Wharf
Prosperity (12%):
$5: Mountebank;
$6+: Goons, King's Court
Cornucopia (23%):
$2: Hamlet
$4: Tournament, Remake
Hinterlands (8%):
$2: Fool's Gold;
$4: Jack of all Trades
Dark Ages (6%):
$5: Rebuild, Cultist
Guilds (0%):
Most overpowered set:
CornucopiaMost underpowered set:
Base Dominion (runners-up: Intrigue, Hinterlands)
Most balanced set:
Guilds (runners-up: Dark Ages)