So many folks want to flip a switch and magically become agile. They want all the benefits without any of the hard work that comes along with really transforming the organization. People think that just because they read a book... or took a few days of training... that they can expect instant productivity. They don't realize that agile methods only show you your problems... it is still up to you to fix them.
I'll often see this thinking manifest in questions like "how many iterations until I can expect my team's velocity to start going up". There is so much underneath a question like that, it's hard to give a solid answer. Is there a prioritized product backlog? Is there a product owner grooming the backlog and available to the team? Is the team cross/functional? Are they dedicated to the project? Do they have everything they need to be successful? Are there external dependencies?
All those things matter... and right out of the gate.. you are not quite sure the kind of impact those answers will have on the team's ability to deliver.
My recommendation is generally to look at team performance in three phases. The first goal is to measure what is... to establish a performance baseline. Next start thinking about getting stable... stable performance is key to running a predictable agile project. Once you are stable... now you can start thinking about getting faster. Adopting agile is a learning process and you can't improve a system when you don't understand what is broken.
And that is really the key... it isn't about getting a better velocity. It's about fixing the broken parts of your organization. It's about looking at where you are and comparing it against where you would really like to be. It's about understanding the impediments standing in your way and dealing with them in a meaningful way... in a way that really, truly helps the team get better. It's about getting more efficient at creating value and really improving the processes that allow value to be created.
Those kinds of answers don't translate into a great marketing pitch. How long will it take to get agile? I don't know... how many iterations will it take to remove the organizational impediments that are slowing the team down? How many iterations until you are willing to fix what is really broken? How many iterations until we are ready to stop applying labels and start REALLY transforming the organization?