Must say I love this thread.
I think how long it takes depends on whether the players the system uses are suited to that style, and there may also be a period of time where players take on board something new depending on how adaptable they are.
If we look at Liverpool, Rodgers is trying to implement something there and it is going to take time for that to bear fruit. They've already dropped points a couple of times because of mistakes made. Against Emirates Marketing Project, Skrtel wasn't used to the way of playing, of always trying to keep the ball. In the position he was in for Tevez's goal, he probably would have preferred to clear it. But he has been drilled to take risks at all costs to keep possession. But he was uncomfortable, played the ball back in a poor pass and City lost a goal. That's an example of perhaps a player being unsuited, but also not really having had the time to get used to what is being asked of him yet.
Similarly today, it was very obvious what they were trying to do, before Podolski's goal. They had a goal kick, played it short, kept the ball, managed to play it out wide and had acres of space to move into because of how well they worked it, with players capable of doing that such as Sahin and Allen receiving the ball from defence. But then it came to Gerrard, who's natural inclination is to force passes through quickly. He tried it, Arsenal intercepted, broke quickly with Liverpool's players out of position and scored. There's an example of ideas needing to bed in, but also the problem of some players not being suited. They worked it from the goal kick well, Allen and Sahin are suited, and you saw the benefit of them playing the goal kick the way they did, because once they worked it out wide, they had so much space because Arsenal had tried to press them. But it came to Gerrard, who isn't suited, and lost it. So it's the awkward mix of an unsuited player playing with suited ones, meaning they will all get caught out of position and concede chances, because they are set up to play a way only 7 of their players probably can.
So how quickly will Rodgers do it? I think it may take a while before they are really firing in the way he would like them to. It may take the time that it takes to move Gerrard out of the club. They needed someone like Sig or Dempsey, someone who is used to being more patient and waiting for the right chances, so they don't get caught out while trying to support their front players. He was absolutely right to move Carroll out, because no matter what his talents are, he would have been absolutely useless playing the way Rodgers wants them to play. They should have got another striker in, but Carroll had to go. They may get some good results and performances over the season, as Emirates Marketing Project showed, and because they do have some good players. But because of the fact they have influential players that aren't suited to the system such as Gerrard, and not much money to strengthen, it really is a tough situation for them.
How quickly can Laudrup do it? From what he has said, his style is broadly similar to that of Rodgers except that he wants to be a bit less patient when the right opportunity arises. So it was a fantastic appointment, even though his record is only average. They can do that, because they have had years of playing a certain way that the players already know. They have Martinez to thank for wanting to build something long term there. And they have a very clever chairman that knows exactly what he is doing in terms of preserving continuity. It's that kind of planning that means they don't need a DOF, because hopefully every manager they hire should at least be able to make use of the players at his disposal in some way.
Lambert? I'm not sure he is a system manager as much as a tactically flexible one that changes from game to game. But they put in an impressive performance at Saudi Sportswashing Machine today. His approach requires him getting the right tactics for each match, and making sure the players can carry it out. As long as the players are confident, they should be able to take on that way of working pretty quickly, even though there will be inconsistencies over the season.
AVB? It's interesting, because I thought with a whole pre-season to work with he would have been able to get us going with a system he wants us to play straight away, and was handed some good fixtures to get the results to back it up, especially considering our squad seemed much more suited to his ideal football than Chelsea's. So why haven't we stormed out of the traps? Maybe because for a lot of pre-season, he didn't actually have a lot of players he intends to use to make his system work, and has instead focussed these early games on trying not to disrupt things too much, adding some ideas but keeping it pretty simple. Keeping us solid, and hopefully not losing. Against Saudi Sportswashing Machine we seemed to press high and played it well but against West Brom and Norwich it seemed that we didn't quite know what we wanted to be.
In pre-season he has not had the goalkeeper he wanted, which is actually pretty important. He's had no real ball carrier in central midfield, except for Tom Carroll (Huddlestone is a passer rather than a carrier) and he hasn't had many strikers. He also gave games to players that seemingly wouldn't suit his ideal system in Rafa, Bentley, Dawson, Friedel, Huddlestone etc. So he's been forced into playing a way that accommodates some of the existing patterns of play in the squad, while seemingly adding some bits, but not wanting to go all the way with his ideal. That's meant maybe not pressing as high as he would like because he doesn't want to leave Friedel exposed. We've still had no ball carrier in midfield. He played Rafa against WBA, which was probably actually a Harry system performance considering he knew he would let Rafa go. So we haven't actually played the way he wants yet IMO.
I think now he has his keeper, now he has Dembele and Dempsey, and Ade will be fit after the break, we could start seeing what he really wants us to do. He doesn't want us to play negative football, I'm sure of it. But he's also not wanted to upset the squad. So he's tried to play them in a hybrid system, and tried to keep us solid (maybe what Santini was trying to do?) while he recruits the players for his system. And now they have been given a chance, he has allowed himself the opportunity to drop some players because they can accept a change is needed. Playing Rafa showed me he hasn't gone full whack with his system yet - where to me it's obvious Rodgers is already doing it for example.
We will now see more of what he wants us to play like IMO, and it will also take the players getting used to it. There are so many differing factors at each club that it is tough to say exactly how long a system takes to implement. But I think the key is simply getting the players that are capable of playing it. Laudrup has a nice situation, because he knows his guys already can. Rodgers has to play certain players that aren't suited due to political constraints and AVB was maybe waiting to get his business done before deciding exactly how to set us up this season. I simply can't believe he wanted us to awkwardly force it through to Defoe, and have rigid movement in midfield. He must have known what was going on against Norwich, because it was so obvious. But maybe he knew it was possible, and it was best to not lose games while he waits for the right time to properly do what he wants to do.