The actress Angelina Jolie prompted droves of women to seek genetic testing after she revealed, in 2013, that a “faulty gene” called BRCA1 had given her an 87 percent chance of developing breast cancer.

In the face of those odds, Jolie had decided to have her breasts removed. “I chose not to keep my story private because there are many women who do not know they that they might be living under the shadow of cancer,” the Oscar winner said.

The subsequent surge in women asking for DNA tests was dubbed the “Angelina effect.” Yet most never found out what they wanted to know. That’s because only 10 percent of women with a family history of breast cancer are ever found to have an inherited cancer gene.

Now Myriad Genetics, the Utah firm that tested Jolie’s genes, says it has started offering a new type of DNA test that could eventually tell any woman her risk of breast cancer.

The new test works very differently from older ones. Instead of checking notorious genes like BRCA1 and BRCA2, another gene with variations tightly linked to breast cancer, it instead scavenges for small clues distributed throughout a woman’s genome. Adding these together creates what is called a “polygenic” risk score. In some cases, women are learning that their potential risk of breast cancer is 60 percent or more.

“It’s like we’ve discovered another BRCA, but it is not one gene,” says Peter Kraft, an epidemiologist at Harvard University who is involved in genetic studies of breast cancer.

Scientists are calling polygenic risk scores a potential crystal ball. In addition to breast cancer, tests to predict who will get Alzheimer’s or suffer a heart attack are in development. Myriad is the first large company to market one, several doctors said.

The new predictions are the payoff of billions spent by the U.S. and other governments over the last decade on giant population studies that searched for the genetic causes of disease. By comparing people’s DNA, scientists began zeroing in on individual genetic letters—among the billions in a genome—that, statistically, appeared more often in those who got specific diseases like breast cancer.

“A poly-gene is a gene that acts in concert with other genes. It has a small effect, but when you put them all together, we found it did predict the risk of breast cancer,” says Myriad’s chief scientist, Jerry S. Lanchbury.

In its new test, Myriad combines 86 DNA variants with a person’s history, including information on how old a woman was at puberty. The results can be as strongly indicative of breast cancer risk as a mutation in the BRCA gene, but those odds will apply to many more women.

For now, Myriad’s risk score, which it began offering in September as part of its standard cancer test, is available only for women of European background who have a family history of cancer.

Extra research will be needed to build genetic predictors for blacks or Hispanics. Myriad says it is planning that work. A small company called Phenogen Sciences says it has a test it sells for $199 that's valid for all races, although it is not yet widely used.

Ora Karp Gordon, a cancer doctor in Los Angeles, says the scores are helping patients she calls the “worried well” who don’t have a BRCA mutation but do have a frightening family history of cancer. For about one in five of these women, she says, the extra information determines whether they are really in a high-risk category or not. If they are, she can advise them to seek mammograms at a younger age and get MRI tests.

Gordon says the predictions aren’t yet certain enough to cause anyone to have her breasts removed, as Jolie did. She says one young patient, only 30, received an exceptionally high life risk score of 72 percent. “It would be terrible if she chose to get preventive surgery,” says Gordon. That’s because until more follow-up research is done, the new scores can't be taken at face value as someone's "absolute" risk, she says.

The big question going forward is whether every woman should get the test. “That is where technology is going to push us, but I don’t think we have the infrastructure in medical care [yet] to give everyone a personalized and accurate risk assessment,” says Sara Pirzadeh-Miller, assistant director for cancer genetics at the University of Texas Southwestern Medical Center.

Risk scores can easily be calculated for anyone whose genome has been analyzed. That means it might not be long before direct-to-consumer testing companies get involved in predicting serious common diseases. It’s also becoming more common for newborns and even IVF embryos to be sequenced. At least one company says it plans to use risk scores to predict disease risk even before people are born.