In an editorial accompanying the C.D.C. researchers’ study, Harold Pollack, co-director of the University of Chicago Crime Lab, wrote that opioid-associated crime, like all crime, extracts an even larger toll when you consider its impact on families and communities.

“The most important reason to support treatment is to improve the well-being and social function of people with addiction disorders,” Mr. Pollack said. But there are other social benefits. When the criminally active get help for this, “the economic value of crime reduction largely or totally offsets the costs of treatment,” he added.

Relative to the costs of crime alone, treatment for substance use disorders is a good deal. Even though a typical burglary may result in a few thousand dollars of tangible losses, researchers have estimated that people are willing to pay 10 times that amount to avoid that loss and 100 times more to avoid armed robbery. This reflects the fact that crime exacts a large psychological toll — the threat or climate of it is far more costly than the crimes themselves.

The most cost-effective treatment for opioid use disorders includes counseling along with a craving-relieving prescription drug, like methadone or buprenorphine, sometimes combined with other medications. According to an economic analysis by the New England Comparative Effectiveness Public Advisory Council, this kind of treatment actually saves society money. For instance, New England states could save $1.3 billion by expanding treatment of opioid-dependent persons by 25 percent.

Though the war on drugs has not had a tangible impact on crime, treatment for substance use disorders has. A study by Emory University scholars found that a 10 percent increase in the treatment rate reduces the robbery and larceny theft rates by about 3 percent and the aggravated assault rate by 4 to 9 percent.