The federal government paid bonuses to 231 hospitals with subpar quality because their patients tend to be less expensive for Medicare, new research shows.

The bonuses are small, generally a fraction of a percent of their Medicare payments. Nonetheless, rewarding hospitals of mediocre quality was hardly the stated goal when the Affordable Care Act created incentives to encourage better medical care from hospitals, doctors and other health care providers.

A study published in the journal Health Affairs looked at the more than $1 billion in payments made last year in the Hospital Value-Based Purchasing program, which raises or lowers Medicare payments to hospitals based on the government’s assessment of their quality. Medicare primarily uses death and infection rates and patient surveys to judge hospitals, but it also evaluates how much each hospitals’ patients cost, both in treatment and recovery.

The 231 hospitals the study identified had below average scores on quality measures but were awarded the bonuses because caring for their patients during their stays and in the 30 days following their discharge cost Medicare less than what it cost at half of the hospitals evaluated in the program.

The Centers for Medicare & Medicaid Services began measuring cost to encourage hospitals to provide care in the most efficient way. In the period examined — the federal fiscal year that ended in September 2015 — spending counted for 20 percent of a hospital’s score in determining whether a hospital would get a bonus, penalty or regular payment.

The average bonus for those lower quality hospitals was an 0.18 percent increase in Medicare payments for each patient stay in a year.