The Matthews Correlation Coefficient: Fifty years

Jesus S. Aguilar-Ruiz

Fifty years after its introduction, the Matthews Correlation Coefficient (MCC) remains central -and debated- in binary classification. This survey offers a comprehensive retrospective and an in-depth analysis of MCC, covering its historical development, mathematical foundations, and implications for practice. We clarify long-standing misconceptions, formalize its equivalences (to Pearson's correlation and to Chi2 in 2x2 tables), and examine its behavior under class imbalance. Beyond MCC, we develop analytical (derivatives) and graphical (contour plots) frameworks that generalize to any confusion-matrix-based metric. These frameworks expose structural properties -bias, robustness, sensitivity- that scalar summaries conceal, and they provide actionable guidance for selecting and interpreting performance measures in applications where reliability and fairness matter. Together, our results position MCC within a broader toolkit while clarifying when it is informative -and when alternatives may be preferable.