My company has a web application that uses lots of windows. My boss forces us to set all "y" window positions to "0" (top) instead of the default center. To me, it's a pain in the *** to manually return windows to the center of the browser. I'm pretty sure most users agree but don't complain because it's not a big enough deal to waste time on processing complaints. If anyone has statistical proof (or anything useful) it would be of much help to persuade him.
You can probably find statistical proof for arguing both cases, because it really comes down to the nature of the application and how people use it. In an environment where there are multiple screens and multiple windows open, placing a window in the centre of the screen by default might not be the best thing.
Is it not possible to allow the user to set a preference for the position of the window, or perhaps allow them to pin/dock the window in a certain position?
Trying to find proof or support for your point of view is encouraged, but the ultimate proof will come from the users because any other data will be based on the context of another application being used by a different group of users with perhaps different intentions.