Energy-energy correlations (EEC) measure the energy that go into two detectors as a function of the angle between them. It is one of the earliest QCD observables, designed to characterize the shape of hadronic energy flow in e+e- annihilation. Recently, there is renewed interest in this observable from different perspectives. We developed a new approach to compute EEC directly from finite correlation functions. In this way, one completely avoids infrared divergences. In maximally supersymmetric Yang-Mills theory (N = 4 sYM), we derive a simple formula relating the EEC to a triple discontinuity of a four-point correlation function. We use the new formula to predict the asymptotic behavior of the EEC in the back-to-back and collinear limits. In particular, we obtained the sub-leading power expansion in the back-to-back limit and provide useful data to sub-leading power rapidity resummation.