Weighted student budgeting comes and goes in American school districts. I rarely write about it because it is difficult to describe without putting readers to sleep. It is also hard to make comparisons from one district to the next because everybody does this sort of portable student funding differently.

And yet it is important because the technique can significantly improve the educations of low-income students. If done right, weighted student formulas provide more money to teach children who need extra help and allow educators to address each child’s needs. That is why I grabbed with eagerness a study of a new weighted student formula at one of the Washington area’s biggest and most important districts, Prince George’s County.

The “Weighted Student Formula Yearbook 2013” by two experienced analysts at the Reason Foundation, Katie Furtick and Lisa Snell, compared Prince George’s with 13 otherbig U.S. districts with similar funding systems. Prince George’s ranks 10th on the yearbook’s list, with a grade of C. That’s better than Baltimore, with an F, and Milwaukee, with a D, but not nearly as good as Houston, which ranks first with an A-plus.

“In most school districts,” Furtick and Snell write, “even when extra funding is generated for the district by disadvantaged students, it does not necessarily reach the schools these students attend. Furthermore, in most school districts, individual school principals are held accountable for results, but principals have negligible autonomy since decisions about budgeting, expenditure, curriculum and hiring are largely made by district, state and other officials outside individual schools.”

However, when funding is tied to each student’s needs and follows them from school to school, whenwhen funding is in real dollars not distorted by staffing rules, and when principals can allocate the money as they see fit, achievement improves, the analysts said.

“Holding all else constant,” they write, an increase in “budget autonomy predicts that a given school district would have higher standing proficiency rates, and faster proficiency rate improvement relative to other districts within its state. These findings hold for disadvantaged groups.”

Houston principals, for instance, have discretion over 43 percent of their district’s budget, while Prince George’s principals have similar power over only 25 percent of the budget, despite their district’s switch to a weighted student formula.

Furtick and Snell gave Prince George’s good marks for improving principal training and providing useful data on achievement, with explicit accountability goals. But the district lost points for its failure to calculate teacher costs based on real salaries. Instead, like many districts, Prince George’s multiplies the average district teacher salary by the number of teachers to calculate teacher costs at each school.

“This means that a more-popular school with more-experienced teachers is often subsidized by less-popular schools with less-senior staff members,” Furtick and Snell said. Inexperienced teachers are usually less effective. Students are shortchanged.

The analysts rated the achievement success of all the districts on their list using proficiency rates, achievement gaps and graduation rates. Prince George’s got good marks for increases in proficiency in recent years, but bad marks for low achievement rates compared with other Maryland districts.

Furtick and Snell noted that the Prince George’s move toward more flexible budgeting and use of resources had been weakened by its failure to give principals power over staffing. The teacher contract demands that “hiring decisions and teacher placement are determined by seniority rather than by mutual consent between the principal and the employees,” they said.

Research has shown that public schools improve when principal hiring and training are strengthened, but only if those principals are given more power. Halfhearted stabs at weighted student formulas, as is happening in Prince George’s, don’t do the job.