By Clayton M. Christensen and Michael B. Horn

In New England, where we live, small private colleges have felt the chill of winter. Nearly every week brings the news of another college closing or looking to merge.

That’s brought renewed attention to the predictions we’ve made that a spate of colleges are likely to fail — meaning close, merge or be acquired, or declare bankruptcy — in the years ahead.

We’ve admittedly played with those predictions over time — from suggesting that 25 percent of colleges would fail in The New York Times in 2013 to one of us, Clay Christensen, making more casual predictions in front of audiences where he has said that 50 percent of colleges would fail. The predictions have predictably generated some animosity and rolling of eyes. But it’s also prompted some college and university presidents to tell us in public and private settings that they think the 50 percent failure prediction is conservative — that is, the number of failures will be far higher.

Either way, the varied responses bring to mind something Clay Christensen often tells his students: you might not like gravity, but gravity doesn’t care. Many colleges are in trouble. And they are not in trouble because we are saying so.

Nor are they in trouble primarily because of disruptive innovation. Many have mistaken our predictions for claims that online learning will be the most significant factor in sending colleges and universities to their ruin.