An academic study that predicted Bernie Sanders’s economic platform would cause an enormous economic boom turns out to have been based on faulty math, or bad economic logic.

The analysis produced by Professor Gerald Friedman, an economist at the University of Massachusetts at Amherst, got a lot of attention when it argued that fully implementing the Sanders program would lead per capita gross domestic product — a measure of average income — to grow one-third higher in 10 years’ time than it otherwise would be. In this economic nirvana, jobs would be plentiful, unemployment rare, poverty low, inequality less severe and the budget in surplus. The study is not an official campaign document, but it has been lavishly praised by Mr. Sanders’s campaign.

It’s such an eye-popping claim that four leading Democratic economists, all former chairs of the Council of Economic Advisers, countered that it “cannot be supported by the economic evidence,” scolding Mr. Friedman that it makes “it that much more difficult to challenge the unrealistic claims made by Republican candidates.” And that in turn led to a thousand think pieces, accusations (and denials) of bad faith and an ugly public spat.

The problem is that for all the name-calling, none of Mr. Friedman’s critics had figured out what he had gotten wrong.