Turn-taking is a cornerstone of coordination in multi-agent systems, ensuring fairness, efficiency, and conflict avoidance. While detailed metrics like ALT measures offer precise turn-taking analysis, their computational complexity limits scalability. We introduce Rotational Periodicity (RP), a lightweight metric combining Average Waiting Episodes (AWE) and Waiting Periods Evaluation (WPE), and propose a comprehensive framework for evaluating turn-taking against ideal patterns such as Perfect Alternation (PA). Evaluated in scenarios like the multi-agent Battle of the Exes (MBoE), RP integrates with Reward Fairness (RF) and Efficiency (E) to form a versatile framework for assessing and inducing coordination. This paper outlines this toolkit, emphasizing its adaptability for various turn-taking contexts and its computational efficiency for large-scale multi-agent simulations.