The answer is NONE. In fact only 75 games since 1901 have been caught be left handers. Theories abound as to why this is the case but most likely it’s a simple as this. Left handers are a small minority of the population and as such have high value as hitters and pitchers. Therefore if you find one with a great swing you give him a relatively quiet life in the outfield and let him hit every day. If you find one with a great arm let him pitch.
Incidentally almost no left handed throwers ever ply at the four infield positions for the simple reason that lefties find it hard to make a throw to first base where much of the action happens.