It looks as though a Clean Sleeve at a military academy is a form of negative evidence.
See ARMED FORCES: The Quiet Ones (Time, Monday, Aug. 29, 1960)
At West Point, he was a "Clean Sleeve" —neither scholar, nor athlete, nor class leader. "No one." says a classmate, "would have expected him to become the first general in his class, or any general at all, as far as that goes."
Read more: http://www.time.com/time/magazine/article/0,9171,939168,00.html
The number of Stripes would indicate rank (or within Annapolis, the class for that year).
Two stripes would indicate he was a MIDN 2/C. (This would not equate to years of college as originally suggested {In civilian college terms, a Junior?} because officer cadets had rank within their year class as well as within the broader structure of the Navy.)
See the badges of rank illustrated at http://en.wikipedia.org/wiki/File:USN_Midshipman_Insignia.png
In academic life ashore Numerals would have been called "Letters" and won for sports
Close attention is paid to athletic instruction and physical
training, all kinds of indoor and outdoor sports being indulged in.
To those who excel in the various events the traditional yellow
"N" and class numerals are awarded. The baseball and football schedules include a series of games with all nearby colleges, the culminating games being with the Military Academy.
from Military and Naval America Harrison Summers Kerrick, Doubleday, Page & Company (n.d.)