It's a long post but I've done my best to explain it thoroughly, given the shot doesn't necessarily mean advantage has materialised (although many referees and players mistakenly think so).
This is actually an excellent question and goes to the heart of understanding what advantage means. We talk about advantage not meaning '2 bites at the cherry', but what does that mean?
Now, in all scenarios where we're looking at a potential shot, we're probably doing a 'wait and see' - but if the shot comes off and goes out we may well consider that to have the advantage. The outcome of 'no goal' doesn't
necessarily mean there's no advantage.
Let's change the original scenario.
1) Keeper fouls an attack on the edge of the PA, but he regains his feet. Has full possession, takes a controlling touch. There's no defender, completely open goal. Attacker has a completely open goal right in front of him - skews the kick, and kicks it out. Has advantage materialised or not?
Next up, is a scenario I had:
2) Attacker running onto goal. Defender next to him, keeper in goal, nobody else, running straight onto goal. From 30 yards out defender has a hold of his shirt and it affects the attacker's movement. Foul...but the attacker keeps running. Into the PA. Shirt pull is still quite firm and definitely affecting the attacker's movement, but defender still can't/won't make the tackle. Attacker does the right thing and tries to take a shot. Taking the shot while his shirt is being held puts him off balance, and he falls as he takes the shot, with the shot going straight to the keeper. He took a shot - so advantage or not?
The reason for these 2 is that I believe the OP's scenario fits somewhere in the middle.
And this comes down to the advantage equation:
Advantage = Possession + Opportunity
Taking a shot is always possession, but not always opportunity. In the first scenario, the attacker had the ball (possession), and had an open shot on goal and was no longer being affected by the foul. So, the opportunity was clearly there. No longer influenced by the foul, so if he stuffs it up it's his tough luck. Going back to the foul would be '2 bites at the cherry'. (Also, no RC for the keeper has the OGSO has been maintained). Ask yourself -
why did the shot miss? - here, nothing whatsoever to do with the foul.
For the second scenario, the attacker had the ball (possession), but despite taking a shot, this was largely out of desperation or because he was supposed to - he was affected by the foul at the time of the shot so he never really had a clean opportunity to make the most of it. So, possession but no opportunity, despite the shot. PK + RC (holding began outside and continued inside). There was a chance he could do a miracle kick which is why I held the whistle, but given that the shot missed, I then need to ask -
why did the shot miss?. In this case it was due to the foul. Thus, go back to the foul.
I hope I've begun to demonstrate the concepts thus far.
Let's go back tot he OP as written. A clear DOGSO foul has occurred. Attacker has regained his feet and possession of the ball. Full control, full balance. He takes the shot, but a defender blocks the shot.
Why did the shot miss?
On one hand, the attacker failed to get it past the defender. But look at it another way:
At the time of the foul there was only the keeper. No defender to beat.
After the foul the attacker has suddenly had an
extra player to beat. The attacker has still found himself in an inferior position - that is, with less opportunity - as a result of the foul. The time it took for the foul to occur, the attacker to regain his feet, control the ball and look up to check where the goal was permitted the defender to come across and block the shot.
Take the foul and the foulling player out of the equation and there was an open goal with no defender. Foul occurs, attacker reclaims possession, and this has allowed the defending team to put another defender in place.
The attacker always had an inferior opportunity. He didn't miss the shot because he blew it like scenario 1 - he missed the shot because he did the right thing (like scenario 2), but the foul left him in a poorer situation.
Thus, in my opinion, the correct decision is to 'wait and see' if he manages to get it in the goal anyway, but with the ball having been saved by that defender, it must go back to the original foul. Had it been a clear miss of the goal then you could say the defender hasn't had an impact so you don't go back (or you could say that his mere presence has changed how he's had to take the shot - he had to 'shoot' rather than tap it in - and go back to the foul anyway). But original foul. Red card the keeper.
The skill of the referee is in recognising the number of factors that affect 'opportunity'. It may well be that there's been the chance for a defender to come across who wasn't there before. It may be that the foul has resulted in the ball being difficult to control. Or previously unmarked teammates are now marked. Or angles being closed off. So on and so forth. There are many ways that opportunity can be removed or restricted, and you need to take a 'bigger picture' approach and look beyond the player himself to understand how the foul has actually affected the field position, the likelihood of control, and the secondary opportunities (the opportunities his teammates have) - if the attacker was going to pass it to a teammate on a perfectly timed run through the defence, and after being fouled the teammate is now in an offside position and the attacker doesn't really have anything useful to do with it, do you still want to play advantage there? Probably not! It's not often that scenario comes up though.....usually the pass to the offside player will be a decision the attacker has made unaffected by the original foul, so offside, but we need to make sure that our decision isn't forcing the pass to the offside player to be the only option. But I'm digressing - of course we can't explore every possible scenario in a thread otherwise we'll get bogged down. Important thing is to ensure the concepts are understood.
If you blew your whistle and gave a foul, it would have been a penalty - so in my mind, the only way a more advantageous situation can occur from letting play go on is if a goal is scored. The fact he got his shot off means it almost certainly can't be DOGSO, but the fact the ball didn't go in the net suggests the offended-against team would be better off if you gave the foul.
Penalty and a caution for me (and even that depends on how good a clearance it is), but it's a bit of a grey area and tricky to sell regardless of what is given.
I think you're over complicating the relationship between DOGSO and 'no advantage'. Waiting and seeing is the referee exploring the possibility of the OGSO being retained. If you declare there is no advantage and you go back to the foul, then you're simply stating that, after a brief experiment, the OGSO wasn't actually retained thus the foul did, in fact, deny the OGSO. The DOGSO foul doesn't become nullified because the referee 'waited and saw' then decided no advantage - the 'no advantage' decision is precisely what declares that the foul was, in fact, DOGSO! Hope that makes sense there Graeme