Born in Nelson County, Virginia, Allen was the son of Loretta M. and Earl Raymond Allen, who was recorded in the 1920 and 1930 U.S. census records for Wayne County, Michigan as working as a chauffeur to a private family. He earned varsity letters in football, track and basketball at Lake Shore High School in St. Clair Shores, Michigan; having graduated in 1940. Allen went to Alma College in Michigan and later at Marquette University in Milwaukee, Wisconsin, where he was sent as an officer trainee in the U. S. Navy's World War II V-12 program. He graduated with a B.S. in education from Michigan State Normal College (now Eastern Michigan University) in Ypsilanti, and then attended the University of Michigan in Ann Arbor, where he earned his master's degree in physical education in 1947.

Allen's death may have been indirectly caused by a Gatorade shower. He died on December 31, 1990, from ventricular fibrillation in his home in Palos Verdes Estates, California, at the age of 72. Shortly before his death, Allen noted that he had not been feeling well since some of his Long Beach State players dumped a Gatorade bucket filled with ice water on him following a season-ending victory over the University of Nevada, Las Vegas on November 17, 1990 (he remarked that the university couldn't afford actual Gatorade).  The sports editor of the Long Beach State newspaper, the Daily Forty-Niner, was on the field that day and recalled that the temperature was in the 50s with a biting wind. Allen stayed on the field for media interviews for a considerable length of time in his drenched clothing, and boarded the bus back to Long Beach State soaking wet. Having promised a winning season to a football program on the verge of collapse, in his final game Allen delivered on his promise. His players hoisted him on their shoulders as photographers snapped away, and Allen's team ended the season with a winning record. Allen said his season at Long Beach State was the most rewarding of his entire career.  Allen's son George denied that the Gatorade shower caused the death, attributing it to an existing heart arrythmia. He stated that seeing Gatorade showers on television was a reminder that his father "went out a winner". After Allen's death, the soccer and multipurpose field area on the lower end of campus was dedicated in his honor as George Allen Field. A youth baseball field in Palos Verdes Estates is also named after him.

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