Evaluating the positional advantage, how can I do it?

I had crushing advantage after 1. e4 e5 2. Nf3 Nc6 3. Nc3 Nf6 4. Bc4 Nxe4 5. Bxf7+ Kxf7 6. Nxe4 d5 7. Ng3 e4 I had strong center like I played halloween gambit. White tries Bxf7+ desperado, but it removes defender piece of white(weakening white squares) and helps black build strong center and develop pieces, whereas the advantage of exposing the king has little value with their underdevelopment.

Then I played 11... Bg5? thinking that queen is actually trapped, thinking that white can't 12. Qxg5 since white need to defend c2 square with their queen. so I thought 12. N1e2 was forced.

But stockfish actually suggests white Actually counter black's advantage by accepting Qxg5.(-3 -> -1) It is kinda counter-intuitive while white material being 3 points down after the exchange.

Why I think this move was wrong...

1. Ne4 Knight has already great outpost and also great attacker. You don't really want to exchange it with a1 Rook, which is not developed at all.
2. By the exchange black's great attacker is now gone, losing their initiative.
3. after the exchange white king is somewhat safe and black's attack is now done.
4. somehow black is 3 materials up, but a1 Knight is actually trapped and you will need to Nxb3 desperado later, leaving only small advantage with +1 material.
5. black king is not safe, there is chance of white's counterattack if white develop their pieces in time.

This is my analysis, but still playing Bg4 considered blunder is somewhat counter-intuitive. how can I evaluate such advantage during the game?

It does not really matter.
11...h5 may be stronger, but 11...Bg4 wins just as well.

Quit thinking positionally, do a ton of tactics, thats how you get strong lik bull

It's hard to analyze a position with such awkward placement of the king, but fortunately the basic analysis of Qxg4 is not complicated:

Let's forget about the smaller things like a pawn loss or the queen development, then what remains seems rather attractive for white, especially from a place with nothing to lose.

White removes two developed pieces (the B is gone directly and the N is either lost or long trapped in a useless spot) and only loses a rook on a1.

@plopsky said ^

It's hard to analyze a position with such awkward placement of the king, but fortunately the basic analysis of Qxg4 is not complicated:

Let's forget about the smaller things like a pawn loss or the queen development, then what remains seems rather attractive for white, especially from a place with nothing to lose.

White removes two developed pieces (the B is gone directly and the N is either lost or long trapped in a useless spot) and only loses a rook on a1.

So it's like Bg4 only works when the opponent don't want to get forked and plays N1d2, which completely blocks queen's d1-h5 diagonal, putting their king in danger.
And actually best defense is just remove two attackers of black and simply get forked, in compensation white buys time to recover from their underdevelopment.

11... Qh4 looks also very nice

@Druismat said ^

11... Qh4 looks also very nice

That was actually top engine move, white can't really go castle long due to their underdevelopment and repeling the queen with g3, Nf3 is virtually impossible because of g3 knight, and black e4 pawn.

@prehevil said ^

Quit thinking positionally, do a ton of tactics, thats how you get strong lik bull

I want to understand the position better, because to perform tactics I should consider which threats of mine/opponent are actually valid or invalid in given position, so understanding the position is part of my study in tactics. thank you