While at TCU Swaim was a part of five Southwest Conference Championships[1] as a player and coach and led his team to two NCAA Division I Men's Basketball tournaments.

[6] The teams on which Swaim played as point guard for TCU coach Buster Brannon won the Southwest Conference championship in 1951, 1952, and 1953.

In his senior year, he was invited to play in the Second Ararat Shrine Temple East-West All Star Basketball Game in Kansas City, Missouri.

[13] After graduation from TCU in 1953, Swaim entered the United States Marine Corps as a second lieutenant, having gone through the platoon leaders training program in college.

Swaim became a student and advocate of the "zone press" as a defensive strategy, and he had the personnel to make it work: Mickey McCarty, a 6-5 extraordinary athlete who played the forward position; James Cash Jr., a 6-6 center who was the first black basketball player in the SWC; Tom Swift at the other forward position; Rick Wittenbraker and Bill Swanson at the starting guard spots; and a solid bench for support.

TCU was behind 31-29 at halftime, but when Arkansas' 74-73 upset of Texas was announced with 5:39 left in the game, the Frogs were ahead 59-51, and the Purple supporters started the chant - all the way to the championship.