Professional career
Cleveland Browns
Schum signed with the Cleveland Browns on March 28, 2013 but was later waived by the team on May 13, 2013.
Tampa Bay Buccaneers
On January 6, 2014, The Tampa Bay Buccaneers signed Schum to a reserves/futures contracts and was later waived on May 21, 2014.
New York Jets
Schum was signed by the New York Jets on June 19, 2014 to compete with incumbent Ryan Quigley in training camp. He was released on August 23, 2014.
Second stint with the Buccaneers
The Buccaneers signed Schum to their practice squad on November 14, 2014, but was waived four days later.
Second stint with the Jets
The Jets signed Schum to a reserve/future contract on December 30, 2014. He was released on August 18, 2015.
Third stint with the Buccaneers
On August 26, 2015, the Buccaneers signed Schum to compete with Karl Schmitz and Michael Koenen. By September 1, Schum was the last remaining punter on the Buccaneers roster after roster cuts. On August 28, 2016, Schum was waived by the Buccaneers.
Green Bay Packers
Schum was claimed off waivers by the Green Bay Packers on August 30, 2016.
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