Deputy Attorney General Sally Yates has announced that the federal government will begin reducing its use of private prisons. Former presidential candidate Bernie Sanders, who campaigned for such a policy change, spoke for many liberal politicians when he praised the move as a major step toward reducing mass incarceration: "It is an international embarrassment that we put more people behind bars than any other country on earth. Due in large part to private prisons, incarceration has been a source of major profits to private corporations.” Yet despite the outsize attention they draw in some political quarters, private prisons are bit players in the sorry drama of mass incarceration.

That 19 percent of federal prisoners are in private facilities may seem to imply a massive presence of corporations within U.S. corrections, but the federal government houses only 12.7 percent of U.S. inmates. As a result, even if the Justice Department went beyond its announced plans and immediately transferred all privately housed inmates to federally operated facilities, only 40,000 of the more than 1.5 million U.S. prisoners would be affected.

The American prison system is overwhelmingly operated by states, and state data underscores that incarceration is firmly under public-sector control. The governors of 20 states are surely not going to heed calls to close private prisons, because to do so they’d have to open one first. Among those states that do house inmates in private facilities, many do so sparingly. For example, at the end of 2014, Alaska, Maryland, North Carolina, South Carolina and South Dakota each held no more than 30 prisoners in private facilities. (That’s a number, not a percent.)

A handful of states do house more than one-fifth of their inmates in private facilities.  New Mexico is the highest at 43.8 percent, followed by Montana (38.7 percent), Oklahoma (26.3 percent), Hawaii (24.3 percent), Mississippi (21.9 percent), Vermont (21.8 percent) and North Dakota (21.6 percent). But these states don’t collectively account for enough inmates to overturn the general conclusion that private facilities are a small part of the state prison system. Indeed, for every state prisoner in a private prison somewhere in the United States, more than 13 are in government-operated facilities.

The idea that private prisons are central to mass incarceration may appeal politically to people who are generally skeptical of corporations. But the reality is that more than 90 percent of U.S. prisoners are directly watched over by the government and 100 percent are serving sentences that were established by the government.

Humphreys is a professor of psychiatry at Stanford University.