Why is Ba4 an inaccuracy here? Why is Bd3 the best move?

Question

I played this game recently as white: https://lichess.org/b7B16RLF/white#18

[FEN ""]

1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. d3 Bc5 5. Be3 Bxe3 6. fxe3 d6 7. d4 Bd7 8. Nc3 O-O 9. Qe2 a6 10. Ba4 h6 11. O-O-O Qe7 12. h3 b5 13. Bb3 Rab8 14. g4 h5 15. g5 Nh7 16. Rdg1 Ra8 17. Nd5 Qd8 18. Qg2 f6 19. gxf6 Nxf6 20. Qxg7# 1-0

On move 10 I played Ba4 to protect my Bishop from the attacking a file pawn while continuing to target the black knight on c6. But according to Stockfish, this is an inaccuracy and that the best move is Bd3.

I want to understand why.

Answer 1

If you follow the suggested virtual variants with an engine on, you can see the reason immediately.

If it still goes over your head: Your tactical instincts should scream danger. Your K and Q idle around on the e-file. Black will attack with exd4 and Re8. Now, only the e pawn is in the way of doom, and Black will win it, if necessary by Nxe4 and d5, or with b4, driving away the Nc3, also if necessary, N-a5xb3 (if Bb3 tries to protect d5, Black exchanges the last defender). It's a pretty straightforward case of pins and mobbing the weakest point.

Example variant: 10.Ba4 exd4 11.exd4 Re8 12.Bb3 Na5 13.O-O Bxb3 14.axb3 Nxe4! 15.Nxe4 d5.

In contrast, Bd3 overprotects e4 and gives you time to get your royal stuff out of the line of danger.