Some more statistics to threw on the pile:
http://www.army.mil/article/89263/Cadet_Command_exceeds_commissioning_mission/
Admittedly, this was from 2012, but I don't think things have changed too dramatically since then.
In 2012, US Army Cadet Command (ROTC) commissioned a total of just under 6,000 fresh 2nd lieutenants.
Of that number, the article cited above says that 1,500 were non-scholarship cadets. Which must mean that around 4,500 were on some form of ROTC scholarship.
The figures cited above in this thread (600/year in 4-year scholarships & 1900/year in 3-year scholarships) total 2,500. Which means, I guess, the remaining 2,000 cadets had 2-year scholarships?
Add another 1,000 new 2nd lieutenants coming out of West Point and you have 7,000 fresh officers per year. Bear in mind not all of these 2nd looeys will be active duty. From what I've read, probably 25% of so are US Army Reserves and US Army National Guard.
Assuming, therefore, that 1,750 new officers are reserves/guard, this brings us down to maybe 5,250 new officers on active duty.
Then there's OCS, which I have zero idea how many officers it produces annually. US Air Force OTS produced 550 officers in 2015 and their goal is double that in 2016, from what I've read in the Air Force Times, so the Army probably has at least 1,000 OCS grads planned for 2016 (again, not all active duty).
So we're probably looking at, what, 6,000 or so new 2nd lieutenants on active duty in 2016?
I believe the Army has a goal of 60,000 new enlisted recruits for active duty, so this would be a 10-to-1 ratio between new enlisted ranks and new officers.
Sound about right?