Has Automated Essay Scoring Reached Sufficient Accuracy? Deriving Achievable QWK Ceilings from Classical Test Theory

Automated essay scoring (AES) is commonly evaluated on public benchmarks using quadratic weighted kappa (QWK). However, because benchmark labels are assigned by human raters and inevitably contain scoring errors, it remains unclear both what QWK is theoretically attainable and what level is practically sufficient for deployment. We therefore derive two dataset-specific QWK ceilings based on the reliability concept in classical test theory, which can be estimated from standard two-rater benchmarks without additional annotation. The first is the theoretical ceiling: the maximum QWK that an ideal AES model that perfectly predicts latent true scores can achieve under label noise. The second is the human-like ceiling: the QWK attainable by an AES model with human-level scoring error, providing a practical target when AES is intended to replace a single human rater. We further show that human--human QWK, often used as a ceiling reference, can underestimate the true ceiling. Simulation experiments validate the proposed ceilings, and experiments on real benchmarks illustrate how they clarify the current performance and remaining headroom of modern AES models.