Although inventions are typically expected to occur within firms with the most related specific knowledge and history, they sometimes arise in less-anticipated competitors. We measure competitive technology dynamics between firms with a new approach, considering each patent as a competitive arena with each competitor given propensities or expectations to “win” that patent. We use this method to give empirical evidence to theories of positive and negative competitive effects of agglomeration of related firms. We find patent ownership is highly predictable by considering relative relevant knowledge stocks between competitors, showcasing the measure's validity. We then show that when leaders lose a patent to a less-predicted firm, the lost patent is 76% more likely to be geographically collocated with the leader than otherwise expected, showing evidence of spillovers that the leading firm would consider significantly negative. The firms driving this effect are less than half as expected to get the patent as that patent’s leader. Leaders lose patents by collocation with concentrations of relevant experts with focal patent expertise, but are not hurt by concentrations of unspecific inventors of competitors, showing the requirement of regional absorptive capacity for spillovers.