Mistakes review

Hello !
I wanted to analyse a game I just played, and I don't understand one of stockfishes suggestion... can you guys explain me what was wrong with my move, and why stockfishes one is better ? I'm sure it is, but sincerely I can't see why 😳

My move :
http://www.bayimg.com/091f6d2b48e14c9599a26b1fcbdab97543bdd633.jpg

Stockfishes suggestion :
http://www.bayimg.com/802d13b18f292681402d834e8aaf91ee640e6d85.jpg

By the way, I've always wondered what those "+0.2", "+2.5"... meant ? It seems that the bigger they are, the dumbest was my move, but how is it calculated ?

Sorry for my English, I hope I stayed understandable. Have a nice evening, and thanks for reading 🙃

Bxd5 wins a piece but your move leads to N+R vs Q.

I have not evaluated this with Stockfish, but here are my thoughts:

If you go Rxb3 you will only win a quality as white has a Zwischenzug.
It should go something like this:
16. ... Rxb3 17. Nxe7+ Qxe7 18. Nxc6

Now your rook is still hanging and your queen is attacked. You can still get a better position, but you could have done better than that.
18. ... Qxe1+ Rxe1 19. Rxb2 (You've won the quality)

Sidenote: You shouldn't try to hang on to your queen because after
18. ... Qd6 19. Ne7+ Kh8 20. axb3 (...)
you "only" have a queen for a rook and a knight in a -with correct play- I guess equal position.

In the correct variation you win the bishop because it still comes with a tempo on the queen and there is no Nxe7+ anymore.

The numeric values "+0.2" etc. are the engine evaluations. + is white and - is black. "+1" means that the position would be equal if black had another imaginary, positionally "neutral", pawn, and that white is currently up a(n) (imaginary) pawn. This does not have to be a real "material pawn" , but it can also be a positional advantage (in fact losing a knight will often result in a +5 rather than in a +3 because the position gets a lot worse too). So basically the evaluation tells you how many "calculated" pawns white or black is better or if the position is equal. Note that this value is estimated by an engine and engines brute force their combinations - there are positions where the engine will tell you white is winning , however, it might be super hard for white to find the correct moves which lead to the winning position. That's why chess commentators often evaluate "from a human perspective".

P.S.: #n means there is a forced mate in n moves for white, #-n means there is a forced mate for black in n moves.

Below is the entire game in question:

The numbers are Stockfish's way of evaluating a position. It first determines the value of all of the pieces left on the board, then looks at where they're located (giving more points to a pawn that's about to be promoted, or of a Knight is in position to fork to pieces, and so on).

They're called "pawns" or "centipawns". (For instance, +1.4 would be 14 centipawns). Stockfish then weighs what it considers the value of each player's position to be against the other's. If it is a positive number, Stockfish considers the player with the White pieces to have an advantage. If the number is negative, Stockfish considers the player with the black pieces to have an advantage.

What Stockfish (or any chess engine, for the matter,) considers "right" doesn't necessarily mean it's right for you, or against your opponents.

For Example, Stockfish doesn't think I should sacrifice a pawn, a bishop, a knight, and a rook just for my opponent's queen. When I'm playing my friend Tim over the board, I happen to know that if I manage to take his queen, even with such a big sacrifice, he will lose his will to play, and will make poor moves, or sometimes even give up.

In your example, taking the queen with your rook led to an easier endgame for you to manage, even if Stockfish thinks it knows better.

Thank you all for your explanations ! 👌🙂