Objective: To examine the limitations of peer grouping and associated challenges measuring social risk in Medicare's Hospital Readmission Reduction Program (HRRP). Under peer grouping, hospitals are divided into quintiles based on the proportion of a hospital's Medicare inpatients with Medicaid (“dual share”). This approach was implemented to address concerns that the HRRP unfairly penalized hospitals that disproportionately serve disadvantaged patients. Data: Public data on hospitals in the HRRP. Design: We examined the relationship between hospital dual share and readmission rates within peer groups; changes in hospitals' peer group assignments, readmission rates, and penalties; and the relationship between state Medicaid eligibility rules and peer groups. Data Collection: Public data on hospital characteristics and readmission rates for 3119 hospitals from 2019 to 2020. Principal Findings: The proportion of dual inpatients among hospitals of the same peer group varied by as much as 69 percentage points (ppt). Within peer groups, a one ppt increase in dual share was associated with a 0.01 ppt increase in the difference from the median readmission rate (p < 0.001). From 2019 to 2020, 8.8% of hospitals switched peer groups. Compared to hospitals that did not switch, those moving to a lower peer group had a higher mean penalty in 2020 (0.096 ppt; p = 0.006); those moving to a higher group had a lower mean penalty (−0.06 ppt; p = 0.079). However, changes in penalties did not correspond to changes in readmission rates. Hospitals in states with higher Medicaid income eligibility limits were more likely to be in higher peer groups. Conclusions: Peer grouping is limited in the extent to which it accounts for differences in hospitals' patient populations, and it may not fully insulate hospitals from penalties linked to changes in patient mix. These problems arise from the construction of peer groups and the measure of social risk used to define them.