I have been reading some papers on screen space directional ambient occlusion and the formula with which AO is formally described such as seen below. We all know this sum should be between 0 and 1 as to be compatible with the law of conservation of energy but if we calculated this sum in the case of no occluders the value we get is 1.28 which cannot be. The only way to fix this would be to put back the sin term that's required for integrating over the hemsiphere. Can anyone comment on why AO is formulated as such .

Thanks