Edward Stack, who as the president of the National Baseball Hall of Fame conceived the eligibility rule that continues to prevent the election of Pete Rose, the prolific hitter who had been banned from Major League Baseball for gambling, died on Sunday in Port Washington, N.Y., on Long Island. He was 88.

His daughter Amy Stack said his death, at a senior living facility, was caused by complications of an injury in January that led to the amputation of his left leg.

In 1991, Mr. Stack, who held various positions at the Hall from 1961 to 2000 and presided over its annual induction ceremony in Cooperstown, N.Y., faced a challenge: what to do about Rose, a star player across three decades, whose 4,256 career hits, the most in baseball history, made him clearly worthy of enshrinement.

Two years earlier, the baseball commissioner, A. Bartlett Giamatti, had permanently banned Rose from the sport after an investigation found that he had bet on baseball games, including those of his own team, as a player and manager for the Cincinnati Reds in the 1980s.

Despite the ban, Rose would have been a first-time candidate for election to the Hall in voting by the Baseball Writers’ Association of America announced in early 1992.

Early that year, Mr. Stack told Fay Vincent, who had been Mr. Giamatti’s deputy before succeeding him as commissioner after Mr. Giamatti’s death in 1989, that the Hall’s board of directors should disqualify anyone on baseball’s permanently-ineligible list from being considered for the Hall.

“Stack said, ‘We should change the rule because there should be a moral dimension to being elected to the Hall,’” Mr. Vincent said by phone. “Stack had it right, and I didn’t have to encourage him.”

The rule change was unanimously approved by the Hall’s board. It did not specifically name either Rose or the most prominent other player on the ineligible list, Shoeless Joe Jackson, who had been banned after he was suspended for life with seven other members of the 1919 Chicago White Sox for a conspiracy to fix games in that year’s World Series.

“We’re cleaning up our rules of election,” Mr. Stack said in a news conference after the vote. “This is probably something that should have been done years ago. This is the way it should be.”

In 2022, Mr. Stack reiterated his opposition to letting Rose into the Hall.

“Never,” he told Newsday. “He broke baseball’s rules.”

Edward William Stack was born on Feb. 1, 1935, in Rockville Centre, N.Y., and grew up in nearby Sea Cliff. His father, also named Edward, was a carpenter and home builder, and his mother, Helen (Leitner) Stack, was a homemaker.

At 14, Ed, as he was known, was stricken with polio. He spent a year recovering in a children’s hospital and the rest of his life walking on weakened legs.

After majoring in accounting and graduating from Pace College (now Pace University) with a bachelor’s degree in business administration in 1956, he began working in Manhattan as an accountant for Clark Estates, a firm that handles financial management for the organizations affiliated with the influential Clark family of Cooperstown, including the Baseball Hall of Fame.

“I graduated Friday night,” he told a Pace publication, “and reported to work Monday morning.”

Mr. Stack never stopped working for the Clark family’s interests in Cooperstown, although he worked there part time while keeping a full-time office in Manhattan.

He became the Hall of Fame’s secretary in 1961, president in 1977 and chairman in 1979.

He also served on several other boards, including that of the Fenimore Art Museum, housed in a mansion donated by the Clark family. He oversaw renovations there and at Bassett Healthcare Network, which the Clark family funded at its inception, and construction of the Clark Sports Center, a fitness and recreation facility, where the Hall’s induction ceremony is held.

“I can honestly say that Ed deeply understood my family’s vision for Cooperstown and for the Clark-affiliated organizations,” Jane Forbes Clark, who became chairwoman of the Hall after Mr. Stack stepped down in 2000 and is the president of the Clark Foundation, said in an interview. “Ed instinctively knew how to honor that vision and bring it forward.”

Mr. Stack also oversaw construction at the Hall, including the addition of a three-story west wing in 1980 that created new exhibition space and a subterranean level to house vast collections of artifacts, as well as a $7.5 million expansion in 1989 timed to the Hall’s 50th anniversary, which replaced a former gymnasium with office space, more room for exhibits and a theater.

In addition to his daughter Amy, Mr. Stack is survived by his wife, Christina (Hunt) Stack, whom he met while she was a summer waitress at the Otesaga Resort Hotel in Cooperstown, owned by the Clark family; two other daughters, Suzanne and Kimberly Ann Stack; three grandchildren; and a sister, Barbara Aasheim.

Mr. Stack figured in a dream of Leon Day, a star Negro National League pitcher who, on the day he was elected to the Hall by the veterans committee in 1995, telephoned his wife, Geraldine, from his hospital room in Baltimore, where he was being treated for a heart ailment.

“I dreamt that Ed Stack came into my hospital room with this box and told me to open it,” she recalled him saying when she spoke at his Hall of Fame induction months later. “And when I did, baby, inside was the prettiest ring I ever seen”— emblematic of his election — “and I’ve got to get out of here and get up to the Hall of Fame and get my ring.”

He died six days later. He never got his ring.

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