Oklahoma incarcerates more people per capita than most states yet still has some of the worst crime rates. Experts told lawmakers they can drive down both statistics by, in part, increasing the number of police on the street and boosting the use of diversion programs for lower-tier offenders.

“The severity of the sentence is not what matters,” said Jeremiah Mosteller, a senior policy analyst with Americans for Prosperity. “It’s the certainty of actually being punished.”

He said Americans for Prosperity believes greater police presence is part of the solution.

“We want to see more officers on t...