Old Smoky, who inherited his name from his father, was a National League All-Star with three different teams. Built short and squat, he was a fine catcher and became of one of the best pinch hitters of his era. He retired with a record 507 pinch at-bats. Only Manny Mota has surpassed Burgess's 145 pinch hits.

Burgess batted .368 in 108 games for the Phillies in 1954. Always a strong, lefthanded hitter, he drove in nine runs for the Reds against Pittsburgh on July 29, 1955. Three of his four hits were home runs - one a grand slam off future batterymate Vern Law. He finished 1955 with a career-high 21 HR. He reported that his most satisfying pinch hit was his home run off Chicago's Sam Jones with two games left in the 1956 season. The Reds needed just one HR to equal the NL record of 221 set by the Giants. Manager Chuck Dressen ordered Burgess to hit for Roy McMillan, barking, "Make it a home run - or nothin'!" The ball landed on Sheffield Avenue. On May 26 of that season, he had caught a three-pitcher no-hitter when Johnny Klippstein, Hersh Freeman, and Joe Black combined to skunk the Braves. Exactly three years later, he was Harvey Haddix's batterymate when the Pirate hurler pitched his famous 12-inning perfect game against the Braves.

After almost six seasons in Pittsburgh, Burgess was sold to the contending White Sox late in 1964. In his first AL appearance he hit a pinch homer off Detroit's Dave Wickersham to tie a crucial stretch-drive game. Much heavier than in his NL prime, Burgess almost seemed to roll out of the dugout for his frequent pinch-hitting appearances. From 1965 through 1967, he appeared in 237 games, catching only seven. He led the AL in pinch at-bats all three seasons, and in pinch hits the first two. He retired as a .286 lifetime pinch hitter. During the 1980s he coached in Atlanta's farm system.