Robert William Broome (September 14, 1916 â June 20, 1959) was an American football player and coach of football and baseball. He served as the head football coach at Appalachian State Teachers CollegeâÂÂnow known as Appalachian State UniversityâÂÂfrom 1956 to 1958, compiling a record of 13âÂÂ16. Broome was also the head baseball coach at Appalachian State from 1959 to 1957.