My colleague Reid Wilson explained in Outlook recently that Massachusetts appears to be our nation’s best state for education. Its preschool and kindergarten enrollment, testing standards, high school graduation rates, family income and parental employment put it at the top.

But in one important respect, the Bay State lags behind, particularly when compared with Washington-area schools. Its most affluent public high schools do a poor job giving average students a chance to prepare for college, a fact school evaluators usually ignore. Few people in Massachusetts know how little their schools challenge average kids, just as few people in the Washington area know how well their schools do on that front.

This is in part because the relevant statistics are obscure. Affluent Massachusetts high schools show very high passing rates on college-level Advanced Placement exams. In 2013, Dover-Sherborn High School had a 99 percent AP passing rate. Other top performers included Wellesley High, at 93 percent, Lexington High, at 92 percent, Lynnfield High, at 88 percent, and Foxborough High, at 87 percent. Those numbers far exceed the national average pass rate of 57 percent.

That’s good, right? Wrong. Those big numbers stem not from great teaching but from severe limits on who is allowed to take AP courses in those schools. Average students have to fight for the right to be challenged, something teenagers are reluctant to do. Who wants to take a course that your school, looking at your grades, says isn’t for you?

In the D.C. area, on the other hand, the doors to AP as well as International Baccalaureate and Advanced International Certificate of Education courses are wide open. Teachers and counselors, who have seen good results from challenging everybody, urge students to take those courses even when they haven’t asked for them.

The consequences are evident in AP data. Compare Dover-Sherborn High and a similar Washington-area school, Virginia’s Langley High in McLean. Both are highly regarded, with great teachers. Their low-income student populations are small, just 2 percent in each case.

In 2013, Dover-Sherborn’s 99 percent AP test passing rate was much higher than Langley’s 87 percent. But because the Massachusetts school kept average students out of AP classes, only 26 percent of its students took an AP exam, compared with Langley’s 43 percent. Because Langley, like most other D.C.-area schools, let anyone who wanted to work hard take AP, it had a higher percentage of total students who were successful. About 38 percent of students passed an AP exam at Langley compared with about 26 percent at Dover-Sherborn. That suggests about 80 Dover-Sherborn students — three classrooms full — would have done well on an AP exam but weren’t allowed to enroll in the course. One study indicates that even students who don’t pass do better in college than similar students who don’t take AP.

Here are some other comparisons. Foxborough High School, 15 percent low-income, had an 87 percent AP passing rate, much higher than the 57 percent passing rate at Quince Orchard High School in Gaithersburg, Md., which has a student population that is 22 percent low income. But only about 14 percent of all Foxborough students were successful on AP tests compared with 26 percent at Quince Orchard. Wellesley High, 5 percent low-income, had only a 19 percent AP success rate for all students, while 15 percent low-income Yorktown High in Arlington, Va., had a 37 percent success rate.

About 300,000 students with PSAT scores showing them ready for AP in 2013 did not take the courses. Massachusetts’s blindness to the potential of average students is common nationally, but some principals in the state tell me they’d like to change that. Their AP teachers are as good as those in this region. Why not give them a chance to challenge every student who wants to experience what college academics are like?