It seems obvious that there would be more injuries, and more serious ones, among high school and college athletes in football or soccer or lacrosse than, say, in running or tennis. But, how many more, and at what economic cost?

Those figures turned out to be hard to come by, researchers at Yale discovered, but, using the best data available, they calculated that if contact sports could be made noncontact — like flag football, for example — there would be 49,600 fewer injuries among male college athletes per year and 601,900 fewer among male high school athletes.

The savings — which include estimates of medical costs and time lost — could be as much as $1.5 billion per year for colleges and $19.2 billion per year for high schools. And that takes into account only the immediate consequences of an injury, a paper by the researchers says, not the long-term effects of concussions or repeated jarring of the brain in collisions. Or the repercussions of ligament tears, which can lead to a greater than 50 percent risk of arthritis a decade later, said Dr. Mininder Kocher, a professor of orthopedics at Harvard Medical School.

“The issue really is that contact is the driving force in all these major injuries,” said Ray Fair, an economics professor at Yale and the senior author of the paper. “Any sport that does not have contact, the injuries are not that great.”