Putting together all the evidence, what they found is that U.S. authorities are catching somewhere between 40 percent and 55 percent of the people who try to cross the border illegally. That’s more than in the past, when the Border Patrol had less manpower, but it’s still just somewhere around half, or even less.

And nobody is quite sure if that is accurate; 40 to 55 percent of what? Knowing that answer requires knowing the total number of people who have tried to enter the U.S. illegally in any given year, including the ones who successfully evaded Border Patrol. The DHS estimate of that group, the so-called “gotaways,” is almost surely too low, and new information from drone-based surveillance suggests more illegal immigrants may be getting through than previously thought.

To that 40 percent to 55 percent who are apprehended, DHS adds another number referred to as “turnbacks.” Those are people who try to enter illegally, make some progress, and then retreat back into Mexico. There are estimates that the turnback rate across the whole border is about 23 percent.