Question: In which years did the great-grandfather of the 23rd pick of the 2010 MLB draft play professional football?
Context: Joc Russell Pederson ( ; born April 21, 1992) is an American professional baseball center fielder for the Los Angeles Dodgers of Major League Baseball (MLB).  His father, Stu Pederson, played for the Dodgers in 1985.  Pederson was drafted by the Dodgers in the 11th round of the 2010 MLB Draft, out of Palo Alto High School. Christopher Tyler Austin (born September 6, 1991) is an American professional baseball first baseman and outfielder for the New York Yankees of Major League Baseball (MLB).  He played baseball for Heritage High School in Conyers, Georgia, before the Yankees selected him in the 2010 MLB draft.  He became a highly regarded prospect, but missed playing time due to injuries.  Austin made his MLB debut in 2016. Rocky Gale (born February 22, 1988) is an American professional baseball catcher for the San Diego Padres of Major League Baseball (MLB).  He attended the University of Portland where he was named the West Coast Conference defensive player of the year before being drafted by the Padres in the 2010 MLB draft.  He made his MLB debut in 2015. Delino Diaab DeShields Jr. (born August 16, 1992) is an American professional baseball center fielder for the Texas Rangers of Major League Baseball (MLB).  He was drafted with the 8th pick overall by the Houston Astros in the 2010 MLB Draft, and is the son of former MLB player Delino DeShields. Clarence Fred Gehrke (April 24, 1918 – February 9, 2002) was an American football player and executive.  He played in the National Football League (NFL) for the Cleveland / Los Angeles Rams, San Francisco 49ers and Chicago Cardinals from 1940 through 1950.  To boost team morale, Gehrke designed and painted the Los Angeles Rams logo in 1948, which was the first painted on the helmets of an NFL team.  He later served as the general manager of the Denver Broncos from 1977 through 1981.  He is the great-grandfather of Miami Marlin Christian Yelich Mario Eduardo Lemus Hollands (born August 26, 1988) is an American professional baseball pitcher who is currently a free agent.  He played college baseball for the UC Santa Barbara Gauchos, where he earned a degree in sociology.  The Phillies drafted him in the 2010 MLB Draft, and after a few seasons in the farm system, they invited him to spring training in 2014.  After performing well in those exhibition games, he made the Phillies' 2014 Opening Day roster, and although he walked too many hitters, showed some potential to emerge as a decent relief pitcher.  His teammates described him as a good personality to have in the bullpen, and his coaches approved of his development.  Meanwhile, he is pursuing another college degree; he is studying merchandise marketing at the Fashion Institute of Design & Merchandising. Greg Joseph Garcia (born August 8, 1989) is an American professional baseball infielder for the St. Louis Cardinals of Major League Baseball (MLB).  The Cardinals selected him in the seventh round of the 2010 MLB Draft from the University of Hawaii.  He made his major league debut April 28, 2014. The 2010 Southern Nevada Coyotes baseball team represented the College of Southern Nevada in the 2010 NJCAA baseball season.  This season is most notable for their team leader, seventeen-year-old outfielder (who also got plenty of playing time as a catcher and pitcher) Bryce Harper.  Harper got national attention during his only season at CSN, winning the prestigious Golden Spikes Award and becoming only the second player not from a Division I university to win the award (the other being Alex Fernandez in 1990).  Behind the hitting of Harper, and the leadership of coach Tim Chambers, the Coyotes had their best season to date, with a record of 52–16, and a playoff finish as semifinalists of the JUCO World Series at Suplizio Field in Grand Junction, Colorado.  Following this season, Harper would be the first overall selection in the 2010 MLB Draft.  In his MLB Career with the Washington Nationals, Harper has been a multiple time All-Star the National League Rookie of the year, and the National League MVP. Christian Stephen Yelich (born December 5, 1991) is an American professional baseball left fielder for the Miami Marlins of Major League Baseball (MLB).  Yelich was drafted out of high school by the Marlins in the 1st round (23rd overall) of the 2010 Major League Baseball Draft.  He stands 6 feet 3 inches and weighs 195 pounds. The Major League Baseball Draft is the process by which Major League Baseball (MLB) teams select athletes to play for their organization.  High school seniors, college juniors and seniors, and anyone who had never played under a professional contract were considered eligible for the draft.  The 1987 MLB Draft took place as a conference call to the Commissioner of Baseball's office in New York from June 2–4.  As opposed to the National Football League Draft which appeared on ESPN, no network aired the MLB Draft.
Answer: 1940 through 1950