Sutter, who hadn't told the club he had undergone elbow surgery during the offseason, even paid for it on his own, arrived in camp with a short-sleeve shirt that revealed a scar on his arm. Between that and his disappearing fastball, he immediately caught the eye of the Cubs' roving Minor League instructor.
That man was Fred Martin, a former big leaguer who was also the ace on one of the greatest Minor League teams of all-time -- the 1941 Houston Buffaloes -- and is sometimes referred to as the "father of the split-fingered fastball."
Martin took the 20-year-old Sutter -- who originally was drafted in the 21st round by the Washington Senators in 1970 but signed with the Cubs a year later for a $500 bonus -- under his wing. He taught the young hurler how to throw the derivation of the forkball that he'd mastered back in the Texas League while pitching for the Buffs.
"It was a pretty easy pitch for me to throw, actually," said Sutter, who was introduced to the New York media on Wednesday as the first pure reliever ever elected to the National Baseball Hall of Fame.
Sutter, who grew up in Lancaster, Pa., showed immediate improvement as he worked his way up the Cubs' Minor League system. In 1973, he made 40 relief appearances for Quincy, going 3-3 with five saves, a 4.13 ERA and 76 strikeouts in 85 innings.
Sutter was even better the following season as a member of the Key West Conchs of the Florida State League. Although the Conchs were a dreadful team, finishing with a 34-97 record, Sutter began to dominate hitters with a 1.35 ERA in 40 innings, allowing only 26 hits while fanning 50.
"We'd go two weeks without winning," recalled former Major Leaguer Dennis Lamp, who pitched with Sutter at each stop in the Minors and ultimately with the Cubs as well, "but once Bruce started throwing that split-fingered fastball, it was like, 'Oh my God.' No one had ever seen a pitch like that.
"It looked like it was over your head, and then it landed in the strike zone. He'd strike guys out and the ball would get by the catcher and roll all the way to the backstop."
Sutter finished the '74 season at Double-A Midland, where he saw action in eight games and posted a 1.44 ERA, allowing 22 hits in 25 innings with 14 strikeouts.
Of the 26 games in which Sutter appeared during that breakout season of '74, two were starts. Fans who attended those games were witness to a historical anomaly -- they were the only starts of his baseball career.
Indeed, from the time he started his professional career, Sutter was always a reliever.
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"When I was in the Minor Leagues, the higher draft picks who signed for the big money were the starting pitchers," he said. "But I had signed for $500, and I was the relief pitcher."
Lamp, who lives in Rancho Santa Margarita, Calif., remembered Sutter as a modest, low-key teammate, but said he also possessed the fierce competitiveness common to most great athletes. He likened him to former Dodgers ace Don Drysdale -- nicest guy in the world off the field, but a pit bull between the lines.
"Bruce had a big heart," Lamp said, "and hands like Dr. J, with huge fingers."
Those extra-large digits certainly helped Sutter perfect his new pitch, which is thrown from between his widespread fingers, imparting a wicked forward spin on the ball.
"When I used to throw hard, I would split my fingers when I threw my change-up," Sutter said. "But I never used my thumb, the way I do with the split-fingered fastball. The pitch has a spin on it, so it's harder for the hitter to tell whether it's a fastball or a split-finger.
"They say that if the hitters just laid off of it, it'd fall out of the strike zone. But it's hard to lay off because they have to make that decision in a split second."
Sutter's devastating new pitch was a big reason why Midland, which played its home games at Christensen Stadium back in those days, won the 1975 Texas League co-championship. Sutter was a key player, leading the league with 13 saves while recording a 2.15 ERA in 41 games.
"Bruce was a real catalyst of that team," said Lamp. "He'd come in with the bases loaded and none out, and we knew we'd get out of it with Bruce on the mound."
Sutter started the 1976 season with the Triple-A Wichita Aeros of the American Association, the highest rung in the Cubs' Minor League system. After a fast start -- he won two games, saved one and struck out 16 in 12 innings -- he was called up to the Majors for the first time.
"In those days, you had to get guys out at rookie ball to make it to A-ball. And you had to get guys out at A-ball to make it to Double-A," said Sutter. "I think the competition of fighting through each level of the Minors until I eventually made it to the Majors was a big help for me."
Though he made his Major League debut in a mop-up role against the Reds on May 9, the 23-year-old Sutter quickly found himself closing games, finishing the 1976 season with a 6-3 record, 10 saves and a 2.70 ERA in 52 appearances.
Over the next 11 seasons with the Cubs, Cardinals and Braves, Sutter totaled 300 saves, was named to six All-Star teams, won the 1979 National League Cy Young Award, led the NL in saves five times and nailed down Game 7 of the 1982 World Series for St. Louis.
"Sutter defined the term that is now common in baseball, that is the closer," said Jack O'Connell of the Baseball Writers Association of America, which conducted the Hall of Fame vote on Tuesday.
In Sutter's 13th year on the ballot, he was named on 76.9 percent of the ballots and was the only player inducted by the BBWAA. Fellow relievers Rich "Goose" Gossage (64.6) and Lee Smith (45) failed to receive the necessary 75 percent, placing third and sixth, respectively.
"It would have been nice if all three of us went," said Sutter, who still has the distinctive beard, albeit less shaggy than it was during his playing days and a lot grayer.
Sadly, his old pitching coach, Fred Martin, won't be around to see Sutter's induction ceremony on July 30 in Cooperstown, having passed away in 1979. Following Martin's death, Sutter came under the tutelage of Mike Roarke, another pitching instructor in the Cubs' system.
"I owe an awful lot to those two men," Sutter said. "Without their help, my stuff was just average."
With their help, however, Sutter became the stuff of legends.
Andrew Tarica is a staff writer for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.