I have the following hypothesis:
A trained martial artist has no advantage over any other athlete in a barehanded street fight, provided the two have identical strength and weight. The third factor is speed, its limit is genetically determined and, speaking from experience, can be quickly reached by systematic athletic training to the highest level of ones athletic potential. Hence, to make this hypothesis more precise, we should assume that the martial artist and the other athlete are identical twins trained to the highest level of their athletic potential. The overall athletic potential is genetically determined and hence would be identical for identical twins.
Martial arts techniques, by and large, are too weak because they use isolated muscle groups (e.g. straight punch in karate), too slow because they involve accelerating a large mass through a large distance with muscles to weak for that purpose (e.g. round house kick), it is too easy to see them coming because the starting position is many moves away from the final position when the actual strike occurs, just plain useless in a street fight (e.g. ground fighting and submission techniques of UFC -- it is much easier and more effective to kick or stomp a downed opponent), or way too restrictive (e.g. in addition to the last example, striking the back of the head, neck, back, or kidneys is not allowed in any martial arts competitions). Also, a trained martial artist, in virtue of his training, will tend to stick to the techniques he constantly practices, and will show little flexibility/inventiveness in a street fight, compared to a non martial artist. This is an example of simple psychological conditioning.
The corollary of the above hypothesis, provided the hypothesis is correct, would be that in order to increase ones chances in a street fight, one should focus on developing ones strength and weight. Ones top speed will quickly come along from training. This can also be illustrated by the example of two identical twins. Suppose one took up martial arts and the other bodybuilding/strength training. Both systematically trained to the limit of their athletic potential for several years. It would seem that the one that took up bodybuilding would end up with superior strength and weight and the same if not superior speed (speed may be dependent on the power of muscular contractions) and hence would easily defeat his twin in a barehanded street fight.