We present a comprehensive, density functional theory based analysis of the direct synthesis of hydrogen peroxide, H2O2, on 12 transition metal surfaces. We determine the full thermodynamics and selected kinetics of the reaction network on these metals, and we analyze these energetics with simple, microkinetically motivated rate theories to assess the activity and selectivity of hydrogen peroxide production on the surfaces of interest. By further exploiting Bronsted-Evans-Polanyi relationships and scaling relationships between the binding energies of different adsorbates, we express the results in the form of a two-dimensional contour volcano plot, with the activity and selectivity being determined as functions of two independent descriptors: the atomic hydrogen and oxygen adsorption free energies. We identify both a region of maximum predicted catalytic activity, which is near Pt and Pd in descriptor space, and a region of selective hydrogen peroxide production, which includes Au. The optimal catalysts represent a compromise between activity and selectivity and are predicted to fall approximately between Au and Pd in descriptor space, providing a compact explanation for the experimentally known performance of Au-Pd alloys for hydrogen peroxide synthesis, and suggesting a target for future computational screening efforts to identify improved direct hydrogen peroxide synthesis catalysts. Related methods of combining activity and selectivity analysis into a single volcano plot may be applicable to, and useful for, other aqueous phase heterogeneous catalytic reactions where selectivity is a key catalytic criterion.