Scarce, who batted and threw left-handed, was initially drafted by the Cincinnati Reds in the twenty-sixth round of the 1969 amateur draft, but elected not to sign. In 1971, Scarce was the Phillies’ eighth round selection, subsequently signing on June 11, 1971.
Scarce first played college baseball for Manatee Junior College, in 1968 and 1969. He then transferred to FSU, pitching for the Seminoles in 1970 and 1971. Scarce was used as a relief pitcher, enjoying considerable success at the collegiate level, while racking up 30 saves over the two seasons. In 1970, he allowed only 13 hits in 33 innings, a school record. These achievements contributed significantly to the team’s being able to advance to the national title game of the National Collegiate Athletic AssociationCollege World Series, where they were defeated by USC, 2–1. In 1971, the lanky lefty was the squad’s co-captain, recording 18 saves — which stood as the NCAA single-season record for some time. Scarce advanced very rapidly and successfully through Minor League Baseball. He spent part of the 1971 season with the Peninsula Phillies, in the A+Carolina League, where he appeared in 20 games, compiling a 3–0 win–loss record, and a 1.29 earned run average. In 1972, Scarce pitched for the Reading Phillies in the AAEastern League, going 4–0 with a 0.46 ERA in 23 games. That same year, following a brief stint with the AAAEugene Emeralds, the parent-club Phillies sent for him.
On July 10, 1972, at the age of 23, Scarce made his major league debut. He entered the game in Philadelphia in the eighth inning against the Los Angeles Dodgers and pitched 3-plus innings. He gave up a run in the ninth inning, allowing the Dodgers to tie the score 3–3. Then in the eleventh inning, he allowed hits to the first two batters and was lifted. Both Davis and Mota went on to score leading to the Dodgers 5–3 win. Scarce was given the loss. Overall, Scarce appeared in 159 Major League baseball games and recorded 21 saves and a 6–19 record. Arm problems curtailed his career; they began in 1974 and worsened that fall, when Scarce believes he tore his rotator cuff. Scarce never started a game and in his 17 major league at bats, he never got a hit. Scarce played his last game on June 25, 1978.
