Where did White go wrong?

I play against this opening and I think 3.Bd3 is unnecessary. You can play Be2 instead. 12.Rd1 isn't a good move. Nd2 is much better. I think you didn't develop your queen side pieces well and to be precise, you lost this game coz of a single black bishop sitting on g7 square.

Bd3 is one of the main moves, and 12. Rd1 was played in a game by a 2182 player that led to a draw against a master (per 365chess.com's database); I think your fine at this point.  12. ... B4 is the first novelty, but seems extremely logical.  In fact, it poses a real question as to how the heck your going to develop your knight without losing the c or (if you play d4) d pawn.  I dont really like your position, but Stockfish feels your equal if you play 16 bb5.  After that, you make a series of less than optimal moves, such as 18. qb2 which gradually increase the awkwardness of your pieces.  (Stockfish liked 18. qe2 instead, keeping your disadvantage minimal.)  So...it wasnt one mistake, it was a bunch of small ones which gradually built a very uncomfortable position.

Your opponent seems to have played a very strong game imho.  You chose the Alapin, and got a position that the computer deems equal after 12 moves are done, but looks awkward for a human to play.  I just dont really understand what your plan should have been to complete your development, and Stockfish seems to be coming up with extremely computer-esq plans.

So...while you got outplayed in the middle game, the opening, despite the lack of any clear mistakes, didnt give you a good position.  Rather, even if Stockfish says it was equal, you got a position that was much easier for a human to play for black.  There is a reason the Alapin isnt terribly popular -- this sort of thing can happen.   

I think your opening is not very accurate:

2. Nf3 is perfect in normal sicilian lines in supporting the 3. d4 push. However you are not playing d4 here but playing c3, the Sicilian Alapin, therefore making Nf3 questionable. The correct Sicilian Alapin has 2. c3 and for very good reason, in that white can respond to 2 ..Nf6 (the main line) with 3. e5, and after Nd5 either d4 or Nf3 with good position. In your position you can't play e5 and the knight is always looking at your e pawn.

4. Bd3?! is a concession due to the inaccurate opening in that the bishop is misplaced. Here I think 4. Qc2 is more accurate so that you can develop the bishop to a better place.

After 6. Qxf3 Nc6 black is at least equal (if not already better) because white's development is terrible (bishop blocks pawn which blocks the other bishop etc.) and I don't see any threats. White will need quite a few moves to untangle which you don't want to do in a sicilian. Looking at Black's position it is very solid and I don't see any problems or weaknesses.

After that there were some repositioning moves by both sides. The moves themselves were okay but I think white should have developed the knight (instead of 12. Rd1 for example) and then get the rook out of the bishop diagonal, because it is very difficult to play the queenside with the pin/x-ray. 14. d4?! is not very good and I think it is a concession (you could have played d4 almost anytime but now you are kind of forced into it) and weakens the queenside structure.

After 15 ..Qa5 comp saids equal but actually white is in a difficult spot. Comp saids 16. Bb3? is a mistake and recommend 16. Bb5!, which I don't think anyone would play and I don't think I understand the recommendation fully. The general idea is that the bishop on b3 is actually loose (because of the loose rook on a1) and it is actually quite difficult to defend the position properly. With best play black will be better because white will have a clump of pieces on the queenside which will be difficult to untangle.

I don't think you played the rest of the game badly, just that the open queenside was really difficult with the monster bishop.

Bd3 looks silly, but it's perfectly fine. Even GMs play this sometimes.

I see you followed the database pretty far. I don't like how white seems to be rushing for d4 (Be3, Rd1, even Ba4). I don't know when exactly things went wrong, but I think 18.Qb2 is a sign something's gone wrong. The queenside is open and under pressure and the knight is still on b1. And the queen is on both a tender file and diagonal.

So I think whatever 2200 or 2300 you were following has started guessing by that point.

In fact, a quick look at the database, and no one over 2500 is playing d4 before the b1 knight is on d2 or f3.

One problem may be your mindset. This opening is under the solid/passive category. And black's play is pretty easy. You should have equality and defense in mind for a long time even though you're white (for that reason this opening may be a poor practical choice for you).

I think Bd3 is fine if the pawn structure is something like a e6 sicilian (so for white that would be c4, d2, and e3). That way the bishop actually is on a good diagonal looks at the kingside, specifically h7.

But in his position the bishop on d3 is worse in that it is blocked by his own pawn and he is not going e5 anytime soon. I think there is a difference here from the normal Bd3.

Although I play against this line, I fail to understand why do you even need to play 4.Bd3 or Qc2? Please share your ideas. Thanks!

Bd3 is a poor move as wrathss indicates. Black instantly has an equal game or a little the better of it.

It does not matter if a master played the move or a grandmaster played the  move or a supergrandmaster played the move--it is still a poor move.

Black played very well, he had a plan, a queenside attack or pressure.

What was your plan?  Bd3?! makes it hard for White to develop a good plan. 

well, the e4 pawn hangs otherwise.

4. Be2 Nxe4 5. Qa4+

e4 is a bait as skotheim2 pointed out. You can develop a piece rather than waste tempo to protect that pawn.

@VibrantMoves Not really e4 continues to hang and you have to defend your e4 pawn sooner or later. Say 4. Be2 Nc6 (or the less sharp and simple Bd7) white face the exact same problem.

You can choose to not protect e4 directly and there are a lot of sharp tactical lines that require careful analysis. Qc2 overall is much cleaner.

Actually your 3rd move...3. c3 is a mistake.  3. c3 does not work well after

1. e4  c5  2. Nf3  d6

Yes, I know and that's why I'm interested to know why would you play Qc2 so early. :) Nc6 is what I play.

Say 4. Be2, 4 ..Nc6?! is very sharp and not accurate for black due to 5. d4! cxd4 6.cxd4 Nxe4 7. d5! Qa5+ 8. Nc3 and it is incredibly sharp and white has the advantage. 

4 ..Bd7 is better and white does need to address the pawn now with either Qc2 or d3, and it is an equal position.

if you want to play Qc2 why not use my bullet system?

premove all the way

Why 7...Qa5? I like black here. I'm very comfortable with this position. Black has numerous choices. But again, it all depends on how we proceed.

For someone who wrote a book on the ponziani you seem to unduly criticize a move simply because it gives black equality in the opening.

Although I agree this isn't a practical choice, at least for amateurs, because white will be passive for a long time.

c3 in this line has nothing to do with the Ponziani. I criticize 3. c3?! because it is a bad move in this position.

You said Bd3 is bad no matter who plays it because it gives black equality.

Maybe I could say the ponziani is poor no matter who plays it because it gives black equality.