We numerically investigate the relationship between the main parameters of thinned antenna arrays using a specifically designed evolutionary algorithm, the Multi-Objective Pareto Evolution for Thinning (MOPET). We provide some useful results that allow for the assessment of the achievable performance of antenna arrays and help researchers and practitioners design radar, 5G, and 6G systems. In particular, our approach allows us to quantify the advantage of thinned arrays with respect to traditional equispaced arrays (EA); as an example, using the same number of radiators, we can obtain the same directivity of an EA with a reduction in the side-lobe level (SLL) of more than 10dB, or increase the directivity of a couple of dB maintaining the same SLL of the EA, or get a combination of the two improvements. Moreover, the advantage of thinned architectures with respect to standard EA seems to improve with the increase in the dimension of the array.