There are numerous studies showing that visualization improves performance, often nearly as well as actually doing the thing in question. It never gets better results by itself, but in practice you'd be adding visualization to your normal activity, not replacing your activity with it.
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What I think is lacking is a proper understanding about the limitations of visualization and how it can be used most effectively. If you have no experience with the thing you're visualizing, for example, it won't do you much good. The more experience you have with it, the more vivid your visualization of it will be. The more vivid your visualization is, the better your results will be.
Also, if the activity you're trying to visualize has a lot of dynamic variables, visualizing is going to be much less effective, because it requires a lot more brain power. So when you visualize something, you should be isolating it to just a very simple part, and something you have a good amount of experience with.
For example, with the 3-point throw from basketball, there aren't many variables which significantly effect your throw. It's just you, the ball, and the basket.
For kickboxing, you can take that idea and work on small pieces of your game. And I would specifically look at things that occur frequently, because those are the things you're going to be able to visualize most effectively.
Combinations are okay to work on. They're small enough that you can visualize them. But I'd say chop them up even smaller. Ask what the most important thing is about that movement. Usually it's what happens before you throw the first punch. You're looking at subtle "tells" from your opponent's body language and movement to determine how to move, and then the combo technique follows from there. So concentrate your visualization on this part. It will cue your subconscious muscle memory to react more quickly. That's going to give you the biggest bang for your buck as far as visualization is concerned, in my opinion.
Another question that hasn't really been answered by the research is whether or not visualization combined with doing the thing you're visualizing will make more improvements than either alone. I would imagine it's not going to hurt and probably would help, but I can't say for sure.
Hope that helps.