The right-hander began his pro baseball career with the Appalachian League’s Cleveland Counts (and then the Morristown Jobbers when the team moved mid-season), hitting .370. He was released by Morristown to the Roanoke Tigers of the Virginia League in 1914 where he hit for a .295 average.
A first baseman, Graham was sold to the Cincinnati Reds by the Roanoke club on July 1, 1914. He was released by the Reds late in the season after playing in 25 games and batting .230 on only 14 hits in 61 plate appearances.
By April of 1915 Tiny was competing with Toronto veteran Tim Jordan for the Maple Leafs’ first base job. Under manager Bill Clymer Graham had 146 hits in 506 plate appearances for a .289 average. The next season the Leafs made a managerial change, naming Joe Birmingham to lead the club and Graham increased his hit production to 164 and his batting average to .294.
Graham played for Toronto again in 1917, this time under the tutelage of future Hall of Famer Nap Lajoie, reporting from his home in Nashville “in excellent shape”. However, Graham’s average slipped to .267 and in the spring of 1918 he was released to Chattanooga of the Southern Association.
Hitting at a .275 clip did not please Chattanooga president Sammy “Strang” Nicklin, although Graham had enlisted in the Army on July 31st. He was discharged on December 3 soon after World War I ended. Reporting in 1919, Graham sat out the beginning of spring training while Nicklin offered him to Texas League and International League teams. However, Graham was allowed to umpire the Lookouts’ first intra-squad game.
Eventually signing with Chattanooga he was unconditionally released mid-season, but was signed on July 12 by the Vols during a July series between Nashville and the Lookouts. First baseman Dick Kauffman had suddenly left the team, deciding he could make more money by playing with a semi-pro team in his home state of Pennsylvania. Manager Roy Ellam immediately filled the void in the Vols’ infield by signing Graham.
His season average was .248 on 86 hits between the two Southern Association clubs.
In his nine seasons in the minors, Graham never hit for a higher average than he achieved during his first season, although in his last year he hit .316 for Oklahoma City. Graham retired from baseball after the 1921 season with a career .291 average.
Upon his death on December 29, 1962 he was buried in Calvary Cemetery in his hometown.
(c) 2014 Skip Nipper. All Rights Reserved.
Baseball-Reference.com. Retrieved June 15, 2013
 Sporting Life, January 24, 914
 Sporting Life, April 24, 1915
 Sporting Life, April 21, 1917
 The Sporting News, March 7, 1918
 Nashville Banner July 13, 1919
 Ancestry.com. Retrieved December 22, 2014