Murphy's squeaky-clean habits off the diamond were conspicuous in a league racked by drug and salary controversies. A devout Latter-day Saint (LDS; see also Mormon), Murphy did not drink alcohol, would not allow women to be photographed embracing him, and paid his teammates' dinner checks (as long as alcohol was not on the tab). In a scene reminiscent of The Babe Ruth Story, Murphy once promised a disabled girl in the stands he'd hit a home run for her -- and actually knocked out two.
Despite his career accomplishments, Murphy is typically not considered a viable candidate for the Baseball Hall of Fame. The reasons given for this are the lack of success of the teams Murphy played on and Murphy's decidedly mediocre performance at the very beginning and towards the end of his career, not to mention his high strikeout totals.
After his baseball career ended, Murphy became more active in the Church of Jesus Christ of Latter-day Saints (LDS Church). He served three years as president of the LDS Church's Boston mission. Murphy is a potential candidate for Governor of Utah in the 2004 election.