This question has been bugging me for awhile, and it mainly comes out of Rickson Gracie's arguments in regards to self defense BJJ vs Sport Bjj, and the age old Martial Art vs Martial Sport debate. When I think about what a martial sport can bring to a table vs a martial art, I simply have to give the edge to the sport. They develop speed, cardio, strength, and are applying their skills over and over again in a controlled environment. MMA is a sport that is currently giving traditional arts a run for their money. Their exponents just appear to be better fighters overall than their traditional peers. People constantly say that Boxing is great for self defense, and Boxing is definitely a sport at just about every level of practice.
Here is vid of a sport Bjj practitioner in a fight on a basketball court:
While he was consistently interrupted by bystanders, he still executed his moves well, and clearly controlled his opponent at every stage of the fight.
Anyway, I'd be interested to hear what others think about this.
As a starting point, if you look at my other posts I think you'll see I'm pretty positive about martial sports in general. With that out of the way I'm going to try to give you another perspective on this topic.
Just talking about self defense, as opposed to any of the other many reasons to practice a martial art or sport, I think a big part of the disconnect in these sport vs art conversations is what people mean by self defense. When I read these threads everyone throws around the term self defense but nobody clearly defines it and it's pretty obvious that very few people are talking about the same thing.
One big divide seems to be between those who think a semi-consensual street fight is a self defense situation (what I'm going to call Type 1 SD) and those who think that street fights are best avoided through non-physical means. If a street fight seems like the most common self defense situation for you then of course martial sports seem like the best thing for self defense because a street fight (like this video) is a lot like an MMA fight, except your opponent is frequently not as skilled.
If your definition of physical self defense (and by that I mean ignoring conflict avoidance, de-escalation, situational awareness, and other approaches to preventing violence altogether) ISN'T about street fights then things aren't as clear. Frequently, people seem to be talking about unexpected, completely non-consensual assaults and that the goal in this case is to minimize the risk of injury and legal complications (what I'm going to call Type 2 SD).
In a lot of Type 2 SD situations, what might be most helpful is enough stand up grappling and striking skills to avoid being taken out or down and to make space to run as early in the encounter as possible if it can't be avoided altogether. On top of that, enough strength and stamina to sprint for a couple of blocks at high speed would be really valuable. Could MMA and related sports arts provide those skills? Sure, and so could a number of appropriately taught traditional arts.
Either way, from my understanding of motor learning theory, these skills need to be taught specifically for this purpose if the students want to optimize their skills for self defense. Of course at that point you're starting to leave the realm of sports even if you're basing the training on MMA fundamentals. Also, please note that I didn't say I could point to anyone in particular who's providing better training for this than MMA sport training, just that there are better ways to approach this in theory and some people believe that their training is doing so and some few of them are probably right.
If you have a reasonable expectation that you're going to get mugged or assaulted by an armed and potentially murderous assailant (Type 3 SD?), you probably shouldn't be wasting your time on martial arts or sports at all and instead either make different lifestyle choices, or if that's not possible (and you live in the US), buy and carry a suitable handgun and get really good at using it. Also, don't forget to take some classes on weapon retention and really practice it.
The other thing that people don't talk about is the difference in practitioners themselves. If you're 19, working a job that doesn't care if you come in looking banged up and you're single, then spending hours at the MMA gym getting in prime shape for 5 - 5 minute rounds and to take and dish out a real beating might be the best thing for you. If you're 50, married with 2 kids and have to give regular client presentations it probably isn't even an option.
Even if it is theoretically an option at that point, how long will a standard MMA gym remain functional for you? And if the 50 year old is strictly interested in self defense (Type 2) and cares not a bit for the sport as a sport, there's an awful lot of time spent on skills and conditioning that is superfluous and to some degree likely detrimental to their goals. Now again, you could create an MMA based class tailored to this sort of person, but then you're starting to leave the realm of sports.
Now that I'm approaching 50, I can sympathize with the theoretical 50 year old above. I work a lot of evenings and I'm married which makes it tough to attend more than a couple of classes a week. I'm lucky enough to work a job where I could probably get away with black eyes and cauliflower ears but it wouldn't be the best career choice I could make. I work out, I'm in reasonable shape, but I've found that it takes longer to get in great cardiovascular shape and it goes away faster than it used to. I'm a lot more committed to strength training, where the gains are a little slower than in my youth but they still stick around, and a lot less interested in spending my limited time doing hours of road work and skipping rope.
At this point I have close to no interest in competing in boxing, Muay Thai, Judo, or MMA events, though I do have some interest in competing in BJJ. And while I think there's value in BJJ for (Type 2) self defense, I'd personally be far more interested in something primarily focused on stand up grappling for that purpose because I want to get away from an attacker, not role around with him. Even if they're hypothetically the best choice for self defense for someone, from what I've seen the MMA gyms around here aren't a very good self defense fit for me at this stage in my life.