The question is actually simpler: Does the player list require interaction from the user (i.e selecting players) or are the big lists just for display purposes?
Button placement depends on the users flow. In the case of a typical form for example, the flow is this:
input required data > button indicates the action to take when complete
Does the user have any interaction with the big lists? or is that just displaying all available players?
If the lists require interaction:
The button needs to be presented after the input (selecting players etc), and so below the lists is fine. To avoid it getting lost, perhaps consider fixed positioning (i.e always at the bottom of the screen, but they can scroll up and down the lists)?
If the list DON'T require interaction:
Placing the button above the table is perfectly fine, and it will be down to the final design to solve the grouping (i.e making sure the user instinctively understand that the button is a function he can perform on that 'data').