Jack Hughes wrote on 12/16/19 at 00:24:23:
One point to keep in mind is that if you intend to meet any a2-a4 lever with ...Bb7 rather than ...Rg8 then you are advised to play 5... Bc5 instead of 5... b5. The point is that after 5... b5 6. Bb3 Bc5 7. a4 Bb7 white has not committed to c2-c3, which gives white the chance to play the more useful Nc3 instead. The resulting positions have more commonly arisen via the old Archangelsk move order of 5... b5 6. Bb3 Bb7 7. d3, which is a line that has been out of fashion for some time now. Of course the resulting positions are objectively defensible, and have even proven quite solid for black in correspondence chess, but the general thinking is that white should have a dream d3-Spanish with the b7-bishop typically just misplaced in these lines.
I think this is the reason why 5..b5 6.Bb3 Bb7!? is considered inferior to 6..Bc5 - because white can save the h3 tempo and play for a quick d3, Nc3-e2-g3 et al. .. However in your line whites a4-move can
maybe help black to organize his counterplay more efficently. I recently looked at the Ruy Lopez from the white perspective and decided against a4 in conjunction with d3+Nc3. The line I did not want to allow goes as follows :
1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.0-0 b5 6.Bb3 Bc5 7.a4!? {forcing black to show his intentions, Arkhangelsk or Moeller guy ?} 7..Bb7 8.d3 0-0 9.Nc3 {in my opinion black should not play ..d6 here, this would play in whites hands because the bishop on b7 is just misplaced and has nothing to do on b7. But the point of 8..0-0 was to keep the option of going d7-d5 in one go !} 9..Na5!? 10.Ba2 (10.Nxe5) {would be another logical choice but after 10..Nxb3 white has to take back with the c-pawn - a potential downside of a4 - black will play ..d5 next with murky play} 10..b4 {and black will play ..d5 next even at the cost of a pawn. b4-b3 in order to disrupt whites coordination even further is another idea}
I do not say that this is bad for white - Maybe white even can claim an edge with precise play ? But I would not enjoy these positions over the board with white.
an ordinary chessplayer wrote on 12/16/19 at 02:54:12:
1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Ba4 Nf6 5.O-O b5 6.Bb3 Bb7 7.d3 Bc5 8.a4 {the line mentioned by Jack Hughes} 8...O-O 9.Bg5 h6 10.Bh4 d6 {the chessgames move order} (10...g5 11.Bg3 d6 12.Nc3 {was the P/E move order, without ...d7-d6 white cannot sac 11.Nxg5 because black still has ...Bc5-e7, not to mention ...Nc6-d4}) 11.Nc3 (11.c3 {!? would transpose to Tauromachie's line}) (11.axb5 {leading to unclear "Ubilava" P/E}) 11...g5 {! P/E} 12.Bg3 b4 13.Nd5 Na5 14.Nxf6+ Qxf6 15.Ba2 (15.Nd2 {"Dorfman" P/E}) 15...b3 {! P/E} 16.Bxb3 Nxb3 17.cxb3 Qe6 {with compensation P/E}
Black should really take his chance here and play 10..g5, not allowing 10..d6 11.c3!? I guess
Tauromachie wrote on 12/15/19 at 11:48:16:
14. Qf3 Nb8 15. axb5 axb5 16. Rxa8 Bxa8 17. Na3 Nbd7 18. Nc2 Rg8 19. Ne3 Kf8 20. h4 Rg6 21. Nf5 Bb6 22. Bh6+. White seems to be winning at the end. Black has various opportunities to jettison another pawn in this line (e.g. 15...Nd7, or 20...d5), maybe one of those is the way.
I came to realize that chess is a cruel game ! What did black do wrong deserving being lost after 13 natural moves ?

It goes against my chess philosophy and logic but there is little point in arguing with the all-knowing computer.. However it would be a shame if this piece sac just refutes the whole line since the pawn sacrifice idea with 12.Bg3 Ne7 13.Na3 Ng6!? looks very cute.
Your line seems both very straightforward and convincing to me. I underestimated this piece sac with the semi-closed centre. Black has no counterplay like in the c3-d4 lines and just has to sit and wait for white to organize his forces.
The Rg8-idea does not seem to work, at least I (but maybe another member of this forum will?) could not come up with an improvement - sorry
But there is another defensive-setup we could try for black.. maybe Rh8!? with the idea of Qg8 and possibly Kf8-Qg6. We also gain the possibility to play ..Rh6 to defend the knight and tempt white to take the rook, thereby reducing whites attacking potential.
My lines are certainly not conclusive but maybe it is a way to put up more resistance at least :
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. O-O b5 6. Bb3 Bc5 7. c3 d6 8. a4
Bb7 9. d3 O-O 10. Bg5 h6 11. Bh4 g5 12. Nxg5 hxg5 13. Bxg5 Kg7 14. Qf3 Nb8 15.
axb5 axb5 16. Rxa8 Bxa8 17. Na3 Nbd7 18. Nc2 Rh8 19. Ne3 Qg8 20. h4 (20. Nf5+
Kf8) (20. Ba2 Bb6 21. b4 Qh7 22. Bh6+ {looks scary at first but black seems to
survive} Kxh6 23. Nf5+ Kg6 24. Qg3+ Ng4 $8 25. Qxg4+ Kf6 26. h4 Qg6) 20... Bc6
$1 {Looks a bit cryptic at first but it is actually a multi-purposed move !
Black defends his knight on d7 and could prepare ..Qa8 which could prove to be
useful against whites plan to mobilize his kingside-pawns by playing g4-Kg2.
With the queen on a8 and the king on g2 white has to watch out for ..Nxe4 !} (
20... Rh7 21. Qf5 Bc6 22. Bxf6+ Nxf6 23. Qg5+) 21. Bc2 $1 (21. Nf5+ Kf8 22. Ra1
(22. Nh6 Rxh6 23. Bxh6+ Ke8 24. Bg5 Qg6 25. g4 Kf8 26. Kh2 d5 27. exd5 Bb7 28.
Kg2 e4 29. dxe4 Nxe4 30. Qf5 Qxf5 31. gxf5 Nd6) 22... Qg6) (21. g3 Rh7 22. Kg2
(22. Qf5 Kf8) 22... Qa8 23. Kh3 Qf8) (21. Ba2 Bb6 22. b4 (22. Bb3 Rh7 23. Ba2
Qa8 24. Bb3 Qe8 25. Ba2 Ng8 26. Nf5+ Kh8 27. Ra1 Nc5) 22... Rh7 23. Bb3 Qf8 24.
Nf5+ (24. g4 Ng8 25. Nf5+ Kh8 26. Ra1 Ndf6 27. Ng3 Qg7 28. Kg2 Bb7) 24... Kh8
25. Ra1 Bb7 26. Rf1 c5 27. Ra1 cxb4 28. cxb4 d5 29. Ne3) (21. g4 Kf8 22. Bxf6
Nxf6 23. Qxf6 Bxe3 24. fxe3 Qxg4+ 25. Kf2 Qxh4+ 26. Qxh4 Rxh4 27. Bxf7 Ke7 {
bespite of being half a pawn down black should be able to hold the balance.
The rook is ready welcome the white king on the second rank while e3 remains a
weakness.}) (21. Qf5 Qh7 $1) 21... Bb6 $5 (21... Bxe3 $6 22. fxe3 Nh7 23. Bb3
$1 Nxg5 24. hxg5 {Seems to dangerous for black. I will give one example line :}
Qe8 25. Qf5 Qe7 26. Qg4 Rf8 27. Qh5 Bb7 28. Qh6+ Kg8 29. g6 {#3}) 22. d4 (22.
g4 Kf8 $1 23. Bxf6 Nxf6 24. Qxf6 Bxe3 25. fxe3 Qxg4+ 26. Kf2 Qxh4+ {
transposition}) (22. b4 $5 {Is however another critical move which needs to be
analyzed}) 22... Qh7 23. Bh6+ {As far as I can see this is the critical line} (
23. d5 Bb7 24. Nf5+ (24. Bh6+ Qxh6 {transposition}) 24... Kf8 25. Bh6+ Ke8) (
23. dxe5 {Gives black more breathing room. Black can reroute his knight do d6
and pressure the e4 pawn} dxe5 24. Bh6+ Qxh6 25. Nf5+ Kf8 26. Nxh6 Rxh6 27. g3
Nc5 28. Re1 Nb7 $44) 23... Qxh6 (23... Kxh6 {Is in comparison the worse queen
sacrifice because the black king is more exposed than in my mainline} 24. Nf5+
Qxf5 25. Qxf5 Kg7 26. d5 Bb7) 24. Nf5+ Kf8 25. Nxh6 Rxh6 {Black has 3 pieces
for the queen and - very important - will not be lost immediately in the next
3 or 4 moves to come !} 26. d5 $1 {Closing the position seems reasonable as
the e4 pawn is no longer a liability. Now the b6-Bishop gets some fresh air
nevertheless.} Bb7 27. g3 {At first I thought black had to play for ..c6 in
order to get some play but maybe black should leave his pawns as they are and
try for full-scale piece play on the kingside instead} Nh5 $5 {Black plans
Ndf6, Rg6 , Bc8 to include all pieces to the attack - watch out for Nf4 or
Nxg3-cheapos !} (27... c6 $5 28. Rd1 cxd5 29. exd5 e4 {Is interesting too but
I have higher faith in 27..Nh5}) 28. Kg2 (28. Qf5 Ndf6 29. Ra1 (29. Kh1 Ng7 30.
Qh3 {no way white is better with a queen on h3.}) 29... Nxg3) 28... Ndf6 29.
Qe2 Rg6 $1 {Pawns are irrelevant by now} 30. Qxb5 Nf4+ 31. Kh1 Nh3 32. c4 Nxf2+
$1 {attack !} (32... Bc8 {was my first try but white seems to be close to
winning after} 33. c5 Bd7 34. Qxd7 Nxd7 35. cxb6 cxb6 36. Kh2 {trapping the
knight and at the very least remaining a pawn up in the endgame}) 33. Rxf2 (33.
Kg2 N2g4 34. Rf3 Bc8 35. c5 Bd7 $1 36. c6 Bc8 {in a practical game I would
even take black here. White has no counterplay on the queenside anymore and
black will allways have chances against the weak black king. The Bishop on c2
is atm a very sad bystander too.}) 33... Bxf2 34. Kg2 Bxg3 35. Qxb7 Bxh4+ 36.
Kf1 Nh5 37. Qxc7 Nf4 {White has a massive material advantage with queen + 2
pawns for rook and knight but the black counterplay should give black a
perpetual. SF 10 gives 0.00} 38. Bd1 Kg7 39. Qb7 Rg2 40. Qd7 Rf2+ 41. Kg1 Rg2+
42. Kh1 Rg6 43. Qf5 Rg5 44. Qd7 Bf2 *
Do not get me wrong - I am certain there are improvements for white earlier but it is fascinating stuff and very much fun to look at nevertheless
Edit : Can someone please put the analyses in a clickable diagram ? More user friendly this way