“…in the past 10 years, visa overstays in the United States have outnumbered border crossings by a ratio of about 2 to 1, according to Robert Warren, who was for a decade the director of the statistics division at the agency that has since been renamed U.S. Citizenship and Immigration Services, and who is now a senior visiting fellow at the Center for Migration Studies, a New York–based organization.” (The Atlantic)
from the Department of Homeland Security’s report for FY 2018:
An overstay is a nonimmigrant who was lawfully admitted to the United States for an authorized period, but remained in the United States beyond his or her authorized period of admission. During FY 2018, there were 54.7 million non-immigrant entries non-citizen entries into the U.S. with expected departures in FY 2018. The overstay rate for this inflow was estimated at 1.2%. [this means about 700,000 persons.]
For visitors from countries not needing a visa, the rate was 1.9%. For those with student visas, 3.7%; for visitors from Mexico, 1.4%.
Note that this is just for FY2018 entrants with an expected departure in the same fiscal year.