More and more towns in the states have installed central traffic managing software (ATMS). ATMS can not only enable traffic engineers to remotely access controllers but also enable them to collect more data than ever. How to better utilize these data to improve the performance of traffic signals has been a topic receiving wide interest in the signal community. In actuated coordination, the main-line greens may start earlier than what are programmed because uncoordinated phases could gap out and return unused green back to the main-line. In this paper, the authors considered the main-line greens random variants ranging from the programmed maximum greens to the whole cycle length. The authors first defined this new concept as Most-likely Optimal Offsets, then used cycle-by-cycle green usage reports and a Monte Carlo simulation model to determine the most-likely optimal offsets. The cycle-by-cycle green usage report is a typical function of major ATMS systems to provide the distributions of random main-line greens. It serves as the basis to infer the optimal offset distributions and thus allow for identifying the most likely optimal offsets. The case study revealed that the new offsets could significantly reduce the travel times on arterials with 95% confidence level compared to SYNCHRO 7 when the early-return-to-green frequently occurs. The implementation in the field also supported the speculations from simulation.