A new study evaluating 67 frontier AI models from 21 providers has identified a “co-failure ceiling,” showing that combining multiple AI models does not reduce failure rates as much as enterprises assume. The gap between expected and actual failure rates runs roughly 2.25 to 2.5 times on standard benchmarks. The paper, titled “When Does Combining Language Models Help? A Co-Failure Ceiling on Routing, Voting, and Mixture-of-Agents Across 67 Frontier Models,” submitted to arXiv on June 25, 2026, demonstrates that models tend to fail on the same questions more often than statistical independence would predict. The key metric, beta, measures the rate at which all models in an ensemble fail simultaneously. On the MATH-500 benchmark, the observed beta was 5.2%, compared to a modeled estimate of just 2.3%. Execution-graded code benchmarks showed a beta of 7.9%, and free-response questions hit 12.7%. The gains from combining models come primarily from models failing on different questions; when they all fail on the same problem, adding more models provides no benefit. Chen provides a method using the Clopper-Pearson bound that allows organizations to compute their actual beta from a held-out graded dataset at zero extra inference cost.