He was 19 then, and the accolades were already piling up, so this hardly seemed like the time for drastic measures or new tricks.
Jimmie Schaffer, the Asheville manager that season, watched Murray struggle for four months as a right-handed hitter before suggesting he experiment with switch-hitting. Other Orioles officials thought Schaffer was nuts.
They had seen Murray blister baseballs from the right side in previous years, so they flocked to Asheville to stop the experiment in its tracks. Murray looked at each of them with those steely eyes and told them he'd be fine.
He wanted to try this, too.
Reluctantly at first, the Orioles let it happen and watched Murray blossom into one of the greatest switch-hitters in baseball history. Yesterday, he became the 38th first-ballot player elected into the Hall of Fame.
If Schaffer felt any extra satisfaction upon hearing the news, it was knowing he played a big role at a pivotal moment in Murray's career. It was knowing he stuck to his gut feeling, even if it meant risking his own job.
"It was a tough fight for Eddie and myself, until everybody started believing it," Schaffer said. "It's quite rewarding to see a guy like that go into the Hall of Fame."
Murray was a lock to make it from the moment he retired after the 1997 season. He was on 85 percent of the ballots (423), and it takes just 75 percent to get elected.
Along with Hank Aaron and Willie Mays, he is one of only three players to reach two of baseball's most revered offensive plateaus -- 3,000 hits and 500 home runs. No other switch-hitter can claim that achievement, not even Mickey Mantle (2,415 hits, 536 home runs).
Showing remarkable consistency, Murray played 21 seasons in the big leagues, winning three Gold Glove Awards at first base and leading the Orioles to the World Series in 1979 and 1983.
For those who saw Murray before that fateful summer of 1975, there's little doubt he would have been a star had he continued batting strictly right-handed. But would he have made the Hall of Fame?
"That's a darn good question," said Dave Ritterpusch, the Orioles' scouting director from 1973 to 1975. "I think it was a brilliant move making him a switch-hitter."
Ritterpusch oversaw the Orioles' 1973 draft and picked Murray in the third round out of Locke High in Los Angeles. He said the Orioles were fortunate to get Murray so low, especially considering Murray was just 17 when he graduated from high school.
"It was apparent that the rest of the industry suspected he didn't have the drive," Ritterpusch said. "We used psychological profiles for everybody, and in Eddie's case we found that he had tremendous emotional control. He had a lot of drive, but it was masked by his emotional control."
Ritterpusch figures it was that ability to stay cool that helped make Murray one of the greatest clutch players in the game. With the bases loaded, Murray hit better than .400 for his career.
After winning Appalachian League MVP honors at Rookie-level Bluefield in 1973, Murray led the Florida State League in total bases the following year at Single-A Miami. But in 1975, his progress hit a snag at Asheville.
Like mothers with their chicken soup, Schaffer had a remedy for hitters who were struggling. He would pull them aside for early batting practice, and have them take a few swings from the other side of the plate.
Even if that was awkward, it helped them feel more comfortable once they returned to their natural side.
"So I asked Eddie to try it, and he just smiled a bit," Schaffer said. "He started hitting line drives all over the ballpark. In fact, he hit a couple in the seats. I asked him about it, and he said he tried it back in Little League, but in the pros and even in high school, they didn't want him to do it."
Schaffer had Murray hit left-handed every other day before home games for about three weeks. "It was just him and I," Schaffer said. "I never told anyone in Baltimore."
Then, one day late in the season, Murray struck out in his first at-bat against Knoxville starter Tim Stoddard, missing badly on a breaking ball that tailed away.
Schaffer decided it was time. He asked Murray if he'd like to try hitting left-handed -- in a game. Once again, Murray smiled.
Hitting left-handed for the first time in his professional career, Murray took two quick strikes from Stoddard, the future Oriole, before fighting off a pitch and dumping it into shallow left field for a base hit.
With that, Schaffer finally told the decision-makers back in Baltimore what he and Murray were up to, and this created quite a stir from the likes of minor-league director Jack Pastore and minor-league troubleshooter Cal Ripken Sr.
"Cal said, 'You can't do that; you'll get fired,' " Schaffer recalled. "I said, 'That's OK. It's something I believe in. And even more importantly, it's something Eddie believes in. too.' "
Said Ritterpusch: "I was concerned, so I went down to Asheville and talked to [Murray] on the field. He said, 'I see the ball better when I hit from both sides.' So I figured why not let him try it, if he's comfortable with it?"
Said Pastore: "Originally, I said, 'If he's struggling a little bit from one side, why should we move him to the other?' But after consulting with [Murray] a little bit, I figured why not? It can't hurt anything. For him, that might have been what turned him around."
The Orioles sent Murray to the instructional league and let him switch-hit. In 1976, he was back in Double-A with Schaffer, this time in Charlotte, and at midseason he had 12 home runs -- six left-handed, six right-handed.
By 1977, Murray was the American League Rookie of the Year. He hit home runs from both sides of the plate in the same game 11 times, a major-league record.
"I was with Kansas City for nine years, and every time we'd play the Orioles, Eddie would come over and talk to me," Schaffer said. "He'd say, 'I know what's going on. Everyone's jumping on the bandwagon, but you and I know.' "