I see quite a few comments addressing the fact that there's no way to directly measure 'productivity' of a programmer. And there's also the questioning of whether the 10x figure is made up or not (Its not. There's research that attempts to measure productivity, but its always by some proxy measure, usually time to complete a task. There was a post not too long ago that collected various articles on the origin on the 10x number).

So far I haven't seen anyone point out that there are lots of abstract concepts that we measure and rank without having a specific measurable quantity. Art is the first thing that comes to mind. What makes someone a 'good' artist? Even in things people might normally consider numbers based like college football rankings aren't purely objective.

The to deciding some ranking and relative comparisons is to ask people familiar with the subject to compare to instances of the set. In this particular case I could see having the team rank each other member or assign some numeric score representing their opinion. Giving this and some brief written reasoning for the scoring it seems like management would be able to get a clear picture of who the most 'productive' programmers are. There'd be obvious chances for pitfalls and politics in such a system, but if it were applied with some sanity it seems like it could work.