I present a positive feedback model to explain why media attention to SMOs is so unequal, volatile and unpredictable. Receiving some degree of media attention helps groups to receive still more--a cumulative advantage, or rich-get-richer, process. The model presents two empirically verifiable implications: (1) levels of media attention will be power-law distributed across SMOs and (2) coverage dynamics will be path-dependent and thus potentially sensitive to small events early in organization histories. Using new methodology from statistical physics I show that media attention is indeed power-law distributed within three large datasets describing counts of media stories to SMOs spanning multiple movements, time periods and media outlets. I then explore the path dependent nature of media coverage with a comparative analysis of the Black Panther Party and the Revolutionary Action Movement. The two groups were initially very similar, the Black Panthers, however, were able to turn early media attention into further media attention, while the Revolutionary Action Movement was not, eventually resulting in a roughly eighty fold difference in levels of media attention between the two groups. Jointly, the quantitative and qualitative results provide broad support for the positive feedback model.