For the head of admissions at a medical school, Dr. Mark Henderson is pretty blunt when sizing up the profession.

“Mostly rich kids get to go to medical school,” he said.

In his role at the medical school at the University of California, Davis, Dr. Henderson has tried to change that, developing an unorthodox tool to evaluate applicants: the socioeconomic disadvantage scale, or S.E.D.

The scale rates every applicant from zero to 99, taking into account their life circumstances, such as family income and parental education. Admissions decisions are based on that score, combined with the usual portfolio of grades, test scores, recommendations, essays and interviews.

The disadvantage scale has helped turn U.C. Davis into one of the most diverse medical schools in the country — notable in a state that voted in 1996 to ban affirmative action.

With the Supreme Court’s ruling last week against race-conscious admissions, the medical school offers a glimpse of how selective schools across the country might overhaul their admissions policies, as they look for alternative ways to achieve diversity without running afoul of the new law.

Last week, President Biden called adversity scores a “new standard” for achieving diversity.

Word has gotten out about the U.C. Davis scale. Dr. Henderson said that about 20 schools had recently requested more information. And there are other socioeconomic measurements, including Landscape, released in 2019 from the College Board, the nonprofit that administers the SATs. That tool allows undergraduate admissions offices to assess the socioeconomic backgrounds of individual students.

But skeptics question whether such rankings — or any kind of socioeconomic affirmative action — will be enough to replace race-conscious affirmative action. And schools that use adversity scales may also find themselves wandering into legal quagmires, with conservative groups promising to fight programs that are simply stand-ins for race.

Over the years, medical schools have made some progress in diversifying their student bodies, with numbers ticking up. But just like undergraduate admissions, wealth and connections continue to play a determining role in who is accepted. More than half of medical students come from families in the top 20 percent of income, while only 4 percent come from those in the bottom 20 percent, according to data from the American Association of Medical Colleges.

There is also a family dynamic. Children of doctors are 24 times more likely to become doctors than their peers, according to the American Medical Association. It’s hard to know why the profession passes down from generation to generation, but the statistic drove the association to adopt a policy opposing legacy preferences in admissions.

“That’s a staggering economic gap between medical students and the general public,” said Dr. Henderson, who comes from a working-class upbringing and now serves as associate dean of admissions.

As a consequence, the number of Black doctors remains stubbornly low: About 6 percent of practicing doctors in the United States are Black, compared with 13.6 percent of the American population who identify as Black.

With the Supreme Court decision, “that number is likely to go down,” said Dr. James E.K. Hildreth, the president of Meharry Medical College, formed in 1876 in Nashville to train Black health care providers.

Leaders in medicine say training more Black and Hispanic doctors could help bridge the vast divides in American health care. Research shows that doctors from underrepresented racial and ethnic groups are more likely to work in primary care or in locales where doctors are scarce.

And patients have better outcomes when treated by doctors from similar backgrounds, said Dr. Jesse M. Ehrenfeld, president of the American Medical Association.

The U.C. Davis scale has drawn attention because of its ability to bring in diverse students using what the schools says are “race-neutral” socioeconomic models.

In its most recent entering class of 133 students, 14 percent were Black and 30 percent were Hispanic. Nationally, 10 percent of medical school students were Black and 12 percent were Hispanic. A vast majority of the U.C. Davis class — 84 percent — comes from disadvantaged backgrounds, and 42 percent are the first in their family to go to college.

The overall acceptance rate has been less than 2 percent.

In the Davis scale, first used in 2012, eight categories establish an adversity score for each candidate. Factors include family income, whether applicants come from an underserved area, whether they help support their nuclear families and whether their parents went to college.

The higher an applicant rates on the disadvantage scale, the bigger the boost.

There is no set formula on how to balance the scale with the academic record, Dr. Henderson said, but a simulation of the system revealed that students from underrepresented groups grew to 15.3 percent from 10.7 percent. And the share of economically disadvantaged students tripled, to 14.5 percent of the class from 4.6 percent.

At the same time, scores from the MCAT, the standardized test for medical school applications, dropped only marginally.

Still, it’s not easy to persuade medical schools to upend admissions standards, particularly anything that undermines the value of test scores and grades. Dr. Henderson said he had received pushback from his own colleagues.

“Doctors say their kids got into medical school elsewhere, and they didn’t get in here,” he said.

As the children of doctors, he said, those applicants earned an S.E.D. score of zero.

A number of scholars, including Richard D. Kahlenberg, have promoted using class-conscious preferences, which they say could address racial inequities in education without fostering the resentment often prompted by racially based diversity plans.

And President Biden said on Thursday that his administration would develop a “new standard for colleges taking into account the adversity a student has overcome.”

“The kid who faced tougher challenges has demonstrated more grit, more determination,” Mr. Biden told reporters at the White House, “and that should be a factor that colleges should take into account in admissions.”

He might be talking about someone like Eleanor Adams, a member of the Choctaw Nation, who said that she did not think medical school was an option for her.

“I didn’t grow up with a lot of money,” she said.

But she found mentors who encouraged her, and today she is in her third year of medical school at U.C. Davis, which is in Sacramento. She plans to become an Indian Health Service doctor in Oklahoma — fulfilling one of the school’s goals, Dr. Henderson said, which is to train doctors who will return to their communities.

At schools in other states without affirmative action, such as the University of Michigan, admissions officials have complained that enrolling more socioeconomically disadvantaged students has not significantly increased the share of Black, Hispanic and Native American students.

“Those tools certainly have utility, but they fall short of accomplishing what a race-conscious admission practice does,” said Dr. Ehrenfeld of the American Medical Association.

The socioeconomic rankings could also be legally challenged. Chief Justice John G. Roberts Jr., in his majority opinion on affirmative action, wrote that colleges could consider how race had affected an applicant’s life. But he also warned against using proxies for race.

The Pacific Legal Foundation, a libertarian activist group, has already sued a selective school, Thomas Jefferson High School for Science and Technology in Alexandria, Va., for using economic factors as stand-ins for race in admissions.

Joshua P. Thompson, a lawyer for the foundation, said the legal questions surrounding these disadvantage indexes were complex.

“I think the devil is going to be in the details,” Mr. Thompson said. “The Supreme Court was pretty clear that what can’t be done directly can’t be done indirectly.”

Should it come to that, Dr. Henderson said that his school’s disadvantage scale would be defensible in court.

“Am I worried about it? Yes,” Dr. Henderson said of a lawsuit. “Is it going to stop me? No.”