Much of the misery could be prevented, the new C.D.C. research found. An analysis of 32,867 patient visits in nine states found that even as the Delta variant predominated, the vaccines had an overall effectiveness rate of 86 percent at preventing hospitalizations, though they were less protective for adults aged 75 and over.

Moderna vaccines had the highest efficacy rate, at 95 percent, compared with 80 percent for Pfizer-BioNTech and 60 percent for the Johnson & Johnson vaccine.

The shots’ effectiveness at preventing infection declined somewhat, from 91 percent to 78 percent, as the variant spread. The Moderna vaccine had an effectiveness rate of 92 percent against infection, compared with 77 percent for the Pfizer-BioNTech shot and 65 percent for Johnson & Johnson…

The new data show that vaccine mandates will protect millions more people, particularly against severe disease, and will relieve pressure on the health care system, Dr. Dean said. “It also sets a precedent for other organizations to make similar decisions” about mandates, she added.