The direct detection of gravitational waves1,2,3,4from merging binary black holes opens up a window into the environments in which binary black holes form. One signature of such environments is the angular distribution of the black hole spins. Binary systems that formed through dynamical interactions between already-compact objects are expected to have isotropic spin orientations5,6,7,8,9(that is, the spins of the black holes are randomly oriented with respect to the orbit of the binary system), whereas those that formed from pairs of stars born together are more likely to have spins that are preferentially aligned with the orbit10,11,12,13,14. The best-measured combination of spin parameters3,4for each of the four likely binary black hole detections GW150914, LVT151012, GW151226 and GW170104 is the ‘effective’ spin. Here we report that, if the magnitudes of the black hole spins are allowed to extend to high values, the effective spins for these systems indicate a 0.015 odds ratio against an aligned angular distribution compared to an isotropic one. When considering the effect of ten additional detections15, this odds ratio decreases to 2.9 × 10−7 against alignment. The existing preference for either an isotropic spin distribution or low spin magnitudes for the observed systems will be confirmed (or overturned) confidently in the near future.