College football players are initially assigned to teams in the National Football League (NFL) through the league's draft selection process. At each team's turn to pick, the team has the option of exercising the pick itself or trading it to another team. If gains from trade are exhausted, draft picks should be exercised by the team with the highest expected value. That is, the expected player contribution garnered from a given pick should not be dependent on whether the pick was traded or retained. Regression results, however, indicate that controlling for a player's draft position, when a team trades up to acquire a player, that player is more likely to have greater on-field success. This suggests that there are too few draft day trades. Plausible reasons are high transaction costs or the fear of media scrutiny that draft trades can engender.