Rationale: Crisis standards of care (CSCs) guide critical care resource allocation during crises. Most recommend ranking patients on the basis of their expected in-hospital mortality using the Sequential Organ Failure Assessment (SOFA) score, but it is unknown how SOFA or other acuity scores perform among patients of different races. Objectives: To test the prognostic accuracy of the SOFA score and version 2 of the Laboratory-based Acute Physiology Score (LAPS2) among Black and white patients. Methods: We included Black and white patients admitted for sepsis or acute respiratory failure at 27 hospitals. We calculated the discrimination and calibration for in-hospital mortality of SOFA, LAPS2, and modified versions of each, including categorical SOFA groups recommended in a popular CSC and a SOFA score without creatinine to reduce the influence of race. Measurements and Main Results: Of 113,158 patients, 27,644 (24.4%) identified as Black. The LAPS2 demonstrated higher discrimination (area under the receiver operating characteristic curve [AUC], 0.76; 95% confidence interval [CI], 0.76-0.77) than the SOFA score (AUC, 0.68; 95% CI, 0.68-0.69). The LAPS2 was also better calibrated than the SOFA score, but both underestimated in-hospital mortality for white patients and overestimated in-hospital mortality for Black patients. Thus, in a simulation using observed mortality, 81.6% of Black patients were included in lower-priority CSC categories, and 9.4% of all Black patients were erroneously excluded from receiving the highest prioritization. The SOFA score without creatinine reduced racial miscalibration. Conclusions: Using SOFA in CSCs may lead to racial disparities in resource allocation. More equitable mortality prediction scores are needed.