Ellison was nicknamed "Never Nervous Pervis" for his play with the University of Louisville. At 6 ft 9 in and 242 lb, he started all four years as the center under coach Denny Crum. In his freshman year he led Louisville to its second national championship and was named the Most Outstanding Player—the second time a freshman had ever been awarded that honor, after Arnie Ferrin in 1944 for Utah.

Ellison was made the first overall pick in the 1989 NBA draft by the Sacramento Kings. Teammate Danny Ainge gave Ellison the nickname Out of Service Pervis. An injury kept him on the sidelines for 48 of 82 games of his rookie year, after which he was traded to the Washington Bullets. Although he was assigned as a backup in 1990–1991, the following year he became a starter and earned Most Improved Player honors after averaging 20.0 points, 11.4 rebounds and 2.68 blocks per game.

Assorted injuries plagued his career, including two knee problems that kept him benched for 29 games in 1992–1993 and 30 games in 1993–1994. As a free agent, Ellison signed with the Boston Celtics in 1994 but did not play until midway through the season because he was still rehabilitating from knee problems. A broken toe suffered while moving furniture kept him out of most games between 1996 and 1998. After participating in 69 out of a possible 246 games over the final three seasons with the Celtics, he joined the Seattle SuperSonics in 2000 but retired after playing nine games. He now coaches basketball for Life Center Academy in Burlington, New Jersey and is a resident of Voorhees Township, New Jersey.

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