Thompson played in Major League Baseball during the Whiz Kids era during a career which spanned 12 seasons (1940–1941, 1946–1955).

[1] Before his major league career, Thompson entered the military and participated in Operation Market Garden, where he led a platoon to secure a bridge over the Maas River.

[5] After the 1940 college season, Thompson was signed by Major League Baseball's Boston Red Sox as an amateur free agent.

[8] Under manager Heinie Manush, Thompson played for the Greensboro Red Sox in the Piedmont League during the 1941 season; he amassed an 8–13 record and a 3.56 ERA in 162 innings pitched.

[9] Thompson entered the Army of the United States in 1941 and was assigned to the 504th Parachute Infantry Regiment, a part of the 82nd Airborne Division.

[2] In 1944, as a first lieutenant, Thompson led his men during an air raid as part of Operation Market Garden in the German-occupied Netherlands.

The light in the jump bay of the platoon's C-47 Skytrain was later than expected, moving their landing zone from its intended location near Grave, Netherlands; the plane was passing over buildings when the paratroopers were signalled to leave the aircraft, and Thompson decided to wait until reaching several approaching fields.

[2] Thompson was wounded twice during the war, for which he received two Purple Hearts;[2] fellow pitcher Robin Roberts later wrote that his Phillies teammates "understood that Jocko still carried around a considerable amount of shrapnel in his body".

After he posted a 6–12 record—the team's worst mark among starters with 30 or more appearances[14]—the Red Sox did not retain Thompson's rights when their working agreement with the Maple Leafs ended.

[15] At the end of the season, manager Eddie Sawyer called Thompson and Jim Konstanty up to the major league level.

He pitched a complete game against the Cincinnati Reds, allowing one run on five hits, striking out five, and walking five batters to collect the first win of his major league career.

[20] Thompson finished 1949 with a 1–3 record at the major league level, with a career-high ERA of 6.89, 12 strikeouts and 11 walks in 31+1⁄3 innings.

[26] He also took a late-game loss in a doubleheader against the Baltimore Orioles, as they staged a five-run rally in the ninth inning to defeat Toronto.

[30] Thompson appeared in relief of Church after his return on September 15, but the Phillies lost, 5–0, due in part to a Bobby Thomson inside-the-park grand slam.

[6] 1951 was Thompson's only full season as a regular in the major leagues, when he beat out Leo Cristante in spring training to make the team.

[39] In August, Thompson entered in relief in the first inning of a game against the Pittsburgh Pirates after Russ Meyer was knocked out of the contest, staging a "respectable duel" with Mel Queen to the eighth inning in a 12–7 Phillies victory;[40] later in the month, he shut out the Reds on three hits to complete a series sweep by the Phillies.

[41] Thompson also defeated St. Louis late in the pennant race when the Cardinals were battling the Dodgers for the top position in the league.