Fighting/Self-Defense is the epitome of Interval Training combining cardiovascular endurance as well as anaerobic endurance. When coupled with the added psychological stress and associated adrenal dump of an unprovoked and unexpected attack, fighting is one of the most physically demanding venues the human body might be forced to endure.
Conditioning specificity for self-defense is a must for your overall martial art training. In the past, traditional martial arts used traditional training methods to strengthen and develop the body. Many of these practices while functional left a lot to be desired when it came to time involved and the return on that time investment. Today's methods incorporate modern science and equipment that allow the student to strengthen specific attributes in the limited time that students allot to training while still holding down a job, raising a family, etc.... Swimmers train to swim, runners train to run, and fighters train to fight. There will always be crossover skills when it comes to conditioning just as there are crossover skills when training in various martial activities. but being a good tournament fighter or forms competitor will not guarantee success in an ally. You must train and develop the specific skill sets required to specifically deal with violence.
A street fight or assault for the average person uses a significant amount of physical strength in a very short period of time. One-punch knockouts are rare, even for trained practitioners. Whether you choose to fight or run, your overall conditioning has a high probability of being the determining factor of whether you win or get away. You do not necessarily have to be stronger than your opponent but you should be able to last longer than he does.
Your ability to take damage and survive is also relative to your fitness level. Most people when faced with violence tend to "give up" or go defensive once they start taking damage. Physical conditioning goes hand and hand with mental toughness. A strong, trained body usually equates to a strong mind and a strong mind does not give up no matter how much pain or damage has been inflicted.
There are no rounds or time-outs in a violent encounter. You must be able to exert high-intensity effort for as long as it takes to survive or end the assault. You must also have enough physical strength to push, pull, and strike with damaging force. Last, you must have the *Mental Toughness* to never quit.