The Matthews correlation coefficient (MCC) is more reliable than balanced accuracy, bookmaker informedness, and markedness in two-class confusion matrix evaluation
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Abstract Evaluating binary classifications is a pivotal task in statistics and machine learning, because it can influence decisions in multiple areas, including for example prognosis or therapies of patients in critical conditions. The scientific community has not agreed on a general-purpose statistical indicator for evaluating two-class confusion matrices (having true positives, true negatives, false positives, and false negatives) yet, even if advantages of the Matthews correlation coefficient (MCC) over accuracy and F1 score have already been shown.In this manuscript, we reaffirm that MCC is a robust metric that summarizes the classifier performance in a single value, if positive and negative cases are of equal importance. We compare MCC to other metrics which value positive and negative cases equally: balanced accuracy (BA), bookmaker informedness (BM), and markedness (MK). We explain the mathematical relationships between MCC and these indicators, then show some use cases and a bioinformatics scenario where these metrics disagree and where MCC generates a more informative response.Additionally, we describe three exceptions where BM can be more appropriate: analyzing classifications where dataset prevalence is unrepresentative, comparing classifiers on different datasets, and assessing the random guessing level of a classifier. Except in these cases, we believe that MCC is the most informative among the single metrics discussed, and suggest it as standard measure for scientists of all fields. A Matthews correlation coefficient close to +1, in fact, means having high values for all the other confusion matrix metrics. The same cannot be said for balanced accuracy, markedness, bookmaker informedness, accuracy and F1 score.
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F1 and MCC were introduced to address the challenges caused by class imbalance, where classification accuracy can be inflated by classifying all patients as low risk when the event is rare.
“F1 and MCC were introduced to address the challenges caused by class imbalance, where classification accuracy can be inflated by classifying all patients as low risk when the event is rare.”
From Evaluation of performance measures in predictive artificial intelligence models to support medical decisions: overview and guidance (2025) · cites this paper as [80]
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- Authors
- Chicco, D., Tötsch, N., & Jurman, G.
- Affiliations
- Krembil Research Institute (CA)
- University of Duisburg-Essen (DE)
- Fondazione Bruno Kessler (IT)
- Corresponding author
- Chicco, Davide
- Venue
- BioData Mining
- Published
- 2021-02-04
- Volume
- 14
- Issue
- 1
- Pages
- 13-13
- ISSN
- 1756-0381 (ISSN-L)
- PMC
- PMC7863449
- OpenAlex
- W3126232929
- Cited by
- 893
- References
- 70
- Citations by year
- 2026: 119 · 2025: 188 · 2024: 172 · 2023: 198 · 2022: 153 · 2021: 62
- FWCI
- 51.49
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- BioData Mining (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, other-oa)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Iris (University of Trento) (submittedVersion, cc-by)
- BOA (University of Milano-Bicocca) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- Funders
- Deutsche Forschungsgemeinschaft (CRC 1093, CRC1093/A7)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Imbalanced Data Classification Techniques
- Physical Sciences › Computer Science › Artificial Intelligence › Machine Learning and Data Classification
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- Matthews correlation coefficient, balanced accuracy, markedness, prevalence bias, F1 score, accuracy
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