Career
Ottawa
Brummage was the second head football at Ottawa University in Ottawa, Kansas and he held that position for four seasons, from 1904 until 1907. His coaching record at Ottawa was 14 wins, 16 losses, and 1 tie. This ranks him 11th at Ottawa in total wins and 12th at Ottawa in winning percentage (500).
Brummage took over the team after a one-year hiatus because the school was attempting to purge professionalism from their college sports teams.
Virginia Military Institute
After completing his tenure at Ottawa, Brummage moved to Lexington, Virginia to become the tenth head football coach at the Virginia Military Institute. He held that position for two seasons, from 1911 until 1912.
His career coaching record at Virginia Military Institute was 13 wins, 2 losses, and 0 ties. This ranks him eighth at Virginia Military Institute in total wins and first at Virginia Military Institute in winning percentage.
Kentucky
Brummage then went to Kentucky where he was football coach from 1913 to 1914, compiling an 11–5 record, and basketball coach from 1913 to 1915, compiling a 19–7 record.