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Twice Allgood was named the NAIA District 30 Coach of the Year in basketball. In 1986, he was named "Mr. Louisiana Basketball" by the Louisiana Association of Basketball Coaches. The LABC inducted Allgood into its Hall of Fame in 1990. He was inducted in 1991 into the Louisiana College Sports Hall of Fame.<ref name=naia>{{cite web|url=https://www.shreveporttimes.com/story/sports/2018/09/19/louisiana-sports-hall-fame-coach-billy-allgood-dies-87/1363182002/|title=Louisiana Sports Hall of Fame coach Billy Allgood dies at 87|author=John Marcase|publisher=''The Shreveport Times'' in [[Shreveport]], Louisiana|accessdate=December 26, 2018}}</ref>

Twice Allgood was named the NAIA District 30 Coach of the Year in basketball. In 1986, he was named "Mr. Louisiana Basketball" by the Louisiana Association of Basketball Coaches. The LABC inducted Allgood into its Hall of Fame in 1990. He was inducted in 1991 into the Louisiana College Sports Hall of Fame.<ref name=naia>{{cite web|url=https://www.shreveporttimes.com/story/sports/2018/09/19/louisiana-sports-hall-fame-coach-billy-allgood-dies-87/1363182002/|title=Louisiana Sports Hall of Fame coach Billy Allgood dies at 87|author=John Marcase|publisher=''The Shreveport Times'' in [[Shreveport]], Louisiana|accessdate=December 26, 2018}}</ref>

When he was inducted in 1999 into the Louisiana Sports Hall of Fame in [[Natchitoches, Louisiana|Natchitoches]], Allgood said in an interview that he did not want to coach blue-chip athletes. I'd rather coach blue-chip people."<ref name=ttt>{{cite web|url=https://www.thetowntalk.com/get-access/?return=https%3A%2F%2Fwww.thetowntalk.com%2Fstory%2Fnews%2Flocal%2F2018%2F09%2F19%2Flc-coach-billy-allgood-passes-away%2F1359447002%2F|title=Coach Billy Allgood passes away|publisher=''The Alexandria Town Talk''|date=September 18, 2018|accessdate= December 26, 2018}}</ref>Billy Jones, one of Allgood's players and a pallbearer at the coach's funeral, said that Allgood "made men out of boys. He was someone who truly was a legend, and he's going to be so sorely missed."<ref name=ttt/>

When he was inducted in 1999 into the Louisiana Sports Hall of Fame in [[Natchitoches, Louisiana|Natchitoches]], Allgood said in an interview that he did not want to coach blue-chip athletes. I'd rather coach blue-chip people."<ref name=ttt>{{cite web|url=https://www.thetowntalk.com/get-access/?return=https%3A%2F%2Fwww.thetowntalk.com%2Fstory%2Fnews%2Flocal%2F2018%2F09%2F19%2Flc-coach-billy-allgood-passes-away%2F1359447002%2F|title=Coach Billy Allgood passes away|publisher=''[[Alexandria Town Talk]]''|date=September 18, 2018|accessdate= December 26, 2018}}</ref>Billy Jones, one of Allgood's players and a pallbearer at the coach's funeral, said that Allgood "made men out of boys. He was someone who truly was a legend, and he's going to be so sorely missed."<ref name=ttt/>

Allgood died at his Pineville residence at the age of eighty-seven. Services were held in downtown [[Alexandria, Louisiana|Alexandria]], Louisiana, on September 22, 2018, at the Emmanuel Baptist Church, of which he was an active member. Dr. Chris Thacker, his pastor, officiated, assisted by former LC basketball players Drexel Robinson and Michael Talbert and manager Butch Morrison. Burial is at Forest Lawn Memorial Park in nearby Ball, Louisiana.<ref name=obit>{{cite web|url=https://www.legacy.com/obituaries/thetowntalk/obituary.aspx?pid=190276258|title=Billy Allgood obituary|publisher=''The Alexandria Town Talk''|date=September 21, 2018|accessdate=December 26, 2018}}</ref>

Allgood died at his Pineville residence at the age of eighty-seven. Services were held in downtown [[Alexandria, Louisiana|Alexandria]], Louisiana, on September 22, 2018, at the Emmanuel Baptist Church, of which he was an active member. Dr. Chris Thacker, his pastor, officiated, assisted by former LC basketball players Drexel Robinson and Michael Talbert and manager Butch Morrison. Burial is at Forest Lawn Memorial Park in nearby Ball, Louisiana.<ref name=obit>{{cite web|url=https://www.legacy.com/obituaries/thetowntalk/obituary.aspx?pid=190276258|title=Billy Allgood obituary|publisher=''The Alexandria Town Talk''|date=September 21, 2018|accessdate=December 26, 2018}}</ref>