I imagine 85's estimate is based upon experience attending the Academy and knowning the environment (just my guess... I am sure they will explain). I would say that number is about right in my experience. As a basketball player I was constantly hurt and injured at the Academy (broken bones, concussion, etc). The athletic training staff for the sports teams and the medical care provided by the Navy was really good at the Academy (way better than when I was in the fleet to be honest). In order to keep Division I athletes on the field, court, etc. the training staffs are very busy folks taking care of our broken bodies. I would probably say the varsity and club level athletes have more severe injuries on average than your intramural athletes (just read the papers about the injuries the football team sustains and are playing through... probably not as bad as a list of injuries of the intramural flag football team for a company - but not saying they don't sustain injuries, stuff happens all time). The goal of the Academy is to commission us, so therefore we need to be medically qualified. I think the medical staff does a great job getting us back on our feet and ready for commissioning. Being young and in shape really helps the recovery timeline and getting us going again.
Also it is key to understand if you are hurt (pulled muscle, sprain, etc where rest, ice and some Advil will help) vs. being injured (needs a doctor's care, possible rehab, etc). Learning to push through these is part of learning to push the limits, but being smart about it. This is key when you are a Detailer with Plebes - Identifying kids who are really injured and need care, but won't say a thing. Sometimes you have to make them see a Doc. Just like any dorm type environment sickness spreads quickly, the Academies are not immune to this. Just a part of life when you have 4000 people living that closely together. Eating right, being in shape, getting plenty of rest (the biggest challenge at the Academy) are the best ways to prevent this. Plebe hack is notorious during Plebe Summer... this is when the Plebes are pretty broken down after a week or two and they all get sick. Happens every year, most adjust to it and Parents Weekend with some rest, food and love from Mom and Dad helps.