In 1904, he earned All-American honors from Walter Camp, after leading his team to a 12–0 record, in which the Quakers outscored their opponents 222–4.

However, he was injured his knee in the third game of the season and was replaced at quarterback by Twister Steinberg – until he was relieved by Jack Hayden.

Stevenson tried to recover and rejoin the team, however the medical consensus was for him to sit out the remainder of the season, so that the bone could heal properly.

The injury prevented Stevenson from taking part in Canton's two-game series, against the rival Massillon Tigers, that would result in a scandal.

In 1949, while watching a game between Penn and Cornell, Stevenson proclaimed: "I don't like this two-platoon business," showing his favor having players play on both offense and defense.