The value of loyalty is on the decline if you are an airline passenger.

When United Airlines and Delta Air Lines announced plans recently to overhaul their loyalty rewards programs, industry experts assumed the changes would benefit airlines at the expense of passengers.

Now a new study calculates exactly how much fliers will lose.

Both airlines announced plans to switch from a loyalty rewards program that awards miles based on total distance flown to programs that dole out miles based on how much travelers spend on airfare.

Members of United’s MileagePlus program will collect an average of 11 percent fewer reward miles, flying on the most popular routes, under changes that take effect March 1, according to a study by Boston flight research site Hopper.com.

Meanwhile, members of Delta’s SkyMiles program will get an average of 22 percent fewer miles under changes starting Jan. 1, the study said.

“Overall, typical fliers earn fewer miles on both systems,” said Hopper’s chief data scientist, Patrick Surry.

The effect on individual fliers will vary, depending on the loyalty tier of the traveler and the fares they pay.

Among major air carriers, only American Airlines continues to offer a distance-based loyalty system. Brian Kelly, a loyalty rewards expert and founder of the website ThePointsGuy.com, said American may leave its program unchanged to differentiate itself from competitors.

“I don’t think it’s a slam dunk that American will follow,” he said.