# Receiver operating characteristic (ROC) movies, universal ROC (UROC) curves, and coefficient of predictive ability (CPA)

arXiv: https://arxiv.org/abs/1912.01956 · HTML: https://mlsanity.com/paper/1912.01956/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2019.

## Built on by (most cited first, 4 of 4)

- [WeatherBench Probability: A benchmark dataset for probabilistic medium-range weather forecasting along with deep learning baseline models](https://mlsanity.com/paper/2205.00865/) (2022)
- [Evaluating Probabilistic Classifiers: The Triptych](https://mlsanity.com/paper/2301.10803/) (2023)
- [A Comparative Study of Hybrid Models in Health Misinformation Text Classification](https://mlsanity.com/paper/2410.06311/) (2024)
- [Probabilistic measures afford fair comparisons of AIWP and NWP model output](https://mlsanity.com/paper/2506.03744/) (2025)

## Abstract (arXiv)

Throughout science and technology, receiver operating characteristic (ROC) curves and associated area under the curve (AUC) measures constitute powerful tools for assessing the predictive abilities of features, markers and tests in binary classification problems. Despite its immense popularity, ROC analysis has been subject to a fundamental restriction, in that it applies to dichotomous (yes or no) outcomes only. Here we introduce ROC movies and universal ROC (UROC) curves that apply to just any linearly ordered outcome, along with an associated coefficient of predictive ability (CPA) measure. CPA equals the area under the UROC curve, and admits appealing interpretations in terms of probabilities and rank based covariances. For binary outcomes CPA equals AUC, and for pairwise distinct outcomes CPA relates linearly to Spearman's coefficient, in the same way that the C index relates linearly to Kendall's coefficient. ROC movies, UROC curves, and CPA nest and generalize the tools of classical ROC analysis, and are bound to supersede them in a wealth of applications. Their usage is illustrated in data examples from biomedicine and meteorology, where rank based measures yield new insights in the WeatherBench comparison of the predictive performance of convolutional neural networks and physical-numerical models for weather prediction.