Finley played both baseball and football at Southern Methodist University from which he graduated in 1937. He was a member of the SMU 1935 national champions and 1936 Rose Bowl team. At SMU, Finley is most famous for his play on November 30, 1935, in which No. 1 SMU played No. 2 TCU and Sammy Baugh in Ft. Worth. SMU scored the first 14 points of the game. But TCU came back and with the Horned Frogs leading late, 14–13, the Mustangs had fourth-and-four at the TCU 37. Out of punt formation, Finley threw a 37-yard touchdown to Bobby Wilson. SMU won, 20–14, and went to the Rose Bowl.[1]
Finley was the varsity baseball coach at SMU from 1965 to 1976.[2]
Finley wore uniform number 14 in 1970, which was claimed by line judge and future referee Gene Barth in 1971. Bob Frederic, a back judge on the crew of Jack Vest in 1970, was promoted to referee in 1971 to succeed Finley as crew chief. The other five members of Finley's 1970 crew remained with Frederic through the 1973 season, prior to Lepore's promotion to referee for 1974.