Bob Ross
Your god hates me
My understanding is that Billy Cobham is a left handed guy playing a right handed set... he rides with his left hand and kicks with his right.
If he were a left handed drummer he'd ride with his left hand and kick with his left foot.
I never heard that Cobham was left handed per se, simply that he recognized the value of not keeping your "time-keeping hand" (i.e., the hand normally whack-a-doodling on the hi-hat or ride) anywhere that it can get in the way of the other hand.
iow, by "riding" with your left hand on the hats (if you're sitting behind a typical right handed kit) & putting your ride cymbal over on the left side next to the hats, your right hand is now free to easily access the entire kit rather than just the snare drum for accents, backbeats, etc.
Lenny White plays this way also. Like a motherfucker I might add.