What I managed to find easily just now in https://www.justice.gov/usao/reading_room/reports/asr2012/12... page 9 has: "Of the 87,709 defendants terminated during Fiscal Year 2012, 80,963, or 93 percent, either pled guilty or were found guilty."
So quite high, but not anything like over 99%.
This is federal cases, though, so maybe state cases have higher enough volume and conviction rates to make the overall number over 99%? Again, I would love to see hard data.