While there are distinct advantages to left-handed play in interactive man-against-man sports (like tennis, baseball, boxing, etc), there is, as might be expected, little or no difference in the performance of right- and left-handers in sports which involve man-against-clock (such as swimming, running, cycling, gymnastics, etc). A 1996 study by Michel Raymond and others found an average proportion of left-handers in interactive sports of about 32%, compared to just 11% (similar to that in the general population) in non-interactive sports. There is a perception that left-handers are over-represented in golf, just as they are in tennis, baseball, etc, but there is no reason why left-handed play should create an advantage in golf, and it seems likely that the percentage of left-handed golfers is not actually exceptional.
The most obvious advantage of a left-hander in sports is that opponents facing them are less used to dealing with their stances, moves, angles, etc, which can yield an element of surprise and unpredictability. One particularly famous anecdote tells of a 1947 boxing match in which natural left-hander Mike Collins emerged from his corner in a right-handed stance before suddenly shifting left and delivering the fight's first and last punch, knocking out his opponent, Pat Brownson, in a record-breaking four seconds. In baseball, there are even “left-handed specialists”, left-handed relief pitchers who specialize in pitching to left-handed batters, weak right-handed batters or switch hitters who bat poorly right-handed.
It should be noted, though, that this “infrequency advantage” only holds while left-handers remain in a relatively small minority, i.e. it is frequency dependent. When right-handers become sufficiently practised at facing left-handers, their advantage all but disappears. The tactical advantage of left-handed play, however, remains undisputable.
It has also been argued that the relatively close proximity of the visual-spatial processing areas in the right hemisphere of the brain to the dominant motor cortex of the left-hander gives them additional hand-eye coordination advantages, and that left-handers’ relatively well-developed non-dominant side, relative to right-handers, gives them better balance and overall strength and control. None of these claims have been satisfactorily proven, though, and other claims of superior attention capabilities or fine motor skills also appear to be largely spurious.
As becomes strikingly clear from the list of Famous Left-Handers, many left-handed or left-footed sportsmen are actually right-handed in other respects, and have presumably learned to employ their left side for it sports advantage, or for a variety of other reasons. For example, many baseball and cricket players bat left and throw/pitch/bowl right, or vice versa; left-swinging golf champions Phil Mickelson, Mike Weir and Steve Flesch all prefer their right hands for almost all other tasks; boxer Marvin Hagler is right-handed but adopted a left-handed southpaw stance; lefty tennis-players Martina Navratilova and Rafael Nadal are right-handed in other respects; etc. Interestingly, though, there are also counter-examples: right-handed golfer Arnold Palmer performs most non-golfing activities left-handed; Henry Cooper and Oscar de la Hoya box in the orthodox (right-handed) stance, but are left-handed in most other respects; etc.
Incidentally, the word “southpaw” used to describe a left-handed sportsman, particularly boxers, is usually deemed to have originated as a baseball term during the early days of American baseball (although, interestingly, the term was used in some parts of northern England until recent years). Baseball parks are usually aligned so that the batter faces east and so does not have the late afternoon or evening sun in his eyes; a left-handed pitcher is therefore throwing with the arm on the south side, hence southpaw. The "southpaw stance" in boxing, as opposed to the “orthodox” right-handed stance, is one where the boxer has his right hand and right foot forward, leading with right jabs and following up with a left hook. This, then, is the normal stance for a boxer with a dominant left-hand.