The 1965 draft had a major league and AAA section (rounds 1-3), a AA section (4-7) and A-ball sections (8+). Each team had one pick in rounds 1-7 (MLB, AAA, and AA picks). Starting with the 8th round teams received a pick for each A-ball team in their system in the reverse order of the affiliate finishes. Franchises that shared affiliates, alternated the picks round-by-round. This means that a franchise will have multiple picks in a "round". For presentation reasons here, we have re-labeled the rounds to be the number of the selection made by this franchise. This means that the Twins' 10th round pick could come after the Mets' 12th round pick.
In the 53 drafts that have taken place through 2017, 22 of the 30 MLB franchises have had the first pick at least once. The Toronto Blue Jays , St. Louis Cardinals , Los Angeles Dodgers , San Francisco Giants , Cleveland Indians , Cincinnati Reds , Boston Red Sox , and Colorado Rockies have never had the first pick. The Montreal Expos never had the first pick, but the Nationals have had it twice. The Oakland Athletics have never had the first pick, but the Kansas City Athletics had the very first pick in MLB Draft history. The New York Mets , San Diego Padres , and Houston Astros have each had the first pick 5 times, and the Seattle Mariners , Pittsburgh Pirates , and Tampa Bay Rays have each had the first pick four times.