Like other pro sports, the team finished last and with the worst record, or you trade for it.
The lowest MLB draft pick number for a player who made it to the majors is 1,165th overall.
Cincinatti
The Cincinnati Red Stockings were the first team in MLB history
Cincinnati red stocks
Alex Wimmers, a right-handed pitcher from The Ohio State University. He was selected in the first round, with the 21st overall pick, by the Minnesota Twins.
The present-day Cincinnati Reds.
Not the team that lost
bASeBALl was evented n 1789
50%
Braves-MLB
Baseball was evented n 1789
Alex Rodriguez, currently (2009) with the New York Yankees.