In 1936, the NFL created a draft. There were nine teams in the league at that time, so they held a nine round draft.
The league was not very popular at the time, taking a distant backseat to Major League Baseball and college football. Many of the players drafted eschewed the opportunity to play in the NFL, a practice that continued into the 1950's, because they could earn much more money working elsewhere.
This includes the first player ever drafted, who happened to also be the first winner of the Heisman Trophy.
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Article Source: Bleacher Report - Oakland Raiders