Buffalo School Superintendent James Williams picked a rotten time to oppose the growth of charter schools.

A new, multiyear study of New York City’s charter schools by Stanford University economist Caroline Hoxby shows that students who attended charter schools not only outperformed their counterparts in traditional, inner-city public schools, they also closed much of the “achievement gap” between inner-city and suburban schools.

The study finds that students in inner- city charter schools from kindergarten through eighth grade, who are predominantly African-American and disproportionately poor, achieved nearly the same scores on state math exams as their peers in more affluent suburban schools and made significant gains on state English exams.

For decades, opponents of school choice, namely the teachers’ unions, have dismissed any success of charter schools by suggesting that any increase in test scores was accomplished by stealing or “creaming” successful public school students.

The methodology used in this latest study exposes that argument as a red herring. According to the study, more than 90 percent of applicants to New York City charter schools are admitted through a random lottery, rendering it impossible for charter schools to “cream” the best students.

Furthermore, the Hoxby study compares only those scores of the charter school students who gained admission by virtue of the lottery with those students in traditional public schools who applied for admission, but did not win the lottery.

This leaves only one variable: the education the students received.

As a result of this study, no amount of explanation can excuse the fact that students in New York City charter schools are performing better than their traditional public school peers.

Hoxby identified features of charter schools that likely improve academic achievement: merit pay for teachers, an incentive-based disciplinary policy and a longer school year for students.

In Buffalo, the superintendent and the teachers’ union tentatively agreed to a longer school year for a few public schools. However that limited agreement was achieved only after Williams caved to union pressure by opposing the creation of any new charter schools.

Quid pro quos may help in future union negotiations, but providing the children of Buffalo with the best education should be non-negotiable.

Charter schools are no longer a novelty; they are a necessity for cities like Buffalo where less than 50 percent of high school students graduate.

Charter schools should have the support of Buffalo’s superintendent and now they have the evidence to prove it.

Katie Campos is director of development at Democrats for Education Reform. James Gardner, a Republican, worked for the Center on Children and Families at the University of Florida Levin College of Law.