I must mention that I have NO experience with Baratheons in full, 8 player games as of March 2019 My opinions are speculative in nature and I'd like to hear your thoughts on the matter - especially if you had opportunity to play Mother of Dragons with GOT veterans, or at least semi experienced players.
HOUSE BARATHEON IN BASE GAME
Although Stags are the most likely winners in 4p and 5p competition, 6p games show much different results. The win ratio on Thronemaster is 18.2%, which is much closer to 16.7% than any other faction. A good argument could be made for Baratheons as the best House in terms of balance.
Pros and cons (vanilla, 6p):
+ good power generation
+ good access to strongholds/castles
+ Iron Throne, 1 star order
+ additional ship
+ unraidable Blackwater Bay
+ relatively safe position thanks to Salladhor and reasons mentioned earlier
- poor supply
- inferior House Cards deck
- 4 neighbours
As much as I hate it, Baratheons have unanimously the worst deck of all. It's common knowledge at this point, judging by opinions on this forum, Boardgamegeek, Reddit etc. Limited number of icons, inflexibility and reliance on conditional power pumping are cited most often. There are three cards with variable combat strength, but House Greyjoy does this trick much better, with more swords and faster cycling.
It's hard to pull out a win with these cards alone and random position games seem to back it up. I don't have stats (if anyone has, please post a link!), but games I browsed show that Baratheon performance in less advantageous positions is usually abysmal.
The conclusion is self-explanatory: decent win ratios for House Baratheon result from juicy position on the board and manageable influence tracks. Change it a bit and all balancing may crumble.
HOUSE BARATHEON IN MOTHER OF DRAGONS
Now enter the new expansion. Imagine we play a full, 8p game - with Targaryens, Essos, Iron Bank, but no vassals. Probably the "ultimate" experience boardgame has to offer. All houses are affected to some extent, but Stags face completely different setup now.
1) No star orders.
That's right, Baratheon loses his lone star so Tyrell gets one. It means that two most common openings: double CP/muster and King's Landing bull rush are no longer viable. And even if Tyrell faced early Doran, Stags don't improve much (Arryn gets a star instead).
2) House Arryn blocks northern expansion.
The North was a favorite target for many Baratheon players. Not every Stark played March +1 in Shivering Sea, and even if he did, less careful/lucky players had their butts handed to them on Narrow Sea quite often. It's a big prize in vanilla game: not only you gain access to the Vale and its barrels, but you also control the Neck and may effectively finish House Stark before it solidifies its position.
Now with House Arryn and its 3 Knights so near, Baratheon will find himself on the defensive and may even struggle to keep Cracklaw Point in early game. It seems that blitz tactics favor House Arryn big time.
3) Baratheons are in the middle of the map, literally.
Shipbreaker Bay used to be fairly safe for Bara. As long as there is no Web of Lies, Blackwater Bay provides steady, firm support of 2-4 value every turn. Careful Baratheon could defend SB effectively. In Mother of Dragons expansion with Essos map, Shipbreaker borders 4 other sea areas, including two native seas of House Targaryen. It's not hard to imagine Bara neighbours getting additional 3-4 points of support from dragon faction. Or Targaryens invading it themselves.
4) House Targaryen has plenty of tools from the get-go.
OK so I already mentioned: I haven't played this out so I might be talking out of my *** here... BUT one could wonder if there are any means of defense against malicious Targaryen at all. They start with more ships, troops, they have 4 march orders and possible Viserys + Khal combo, effectively a 5 power card any time they wish. There are better openings for Targs, granted, but how many players will resist the urge of capturing your arch-rival's capital on Turn 1/2? I mean it WILL happen a lot, at least as often as we see aggressive Greyjoy openings. And even GJ needed a serious amount of luck to pierce Lannisport defenses on Turn 2, right?
I'm afraid Baratheons gain basically nothing from the expansion (even Lannister got a new ship in port, please check out the latest FAQ & Errata) but lose most advantages of their rich but flexible position. Does it mean that the most well-balanced House in the game was nerfed too hard, while thirtypercenters (Greyjoy) thrive with new shiny sea orders?
IS YELLOW THE NEW RED?