As a layman in martial arts, I've been curious about this question: In a real life situation, is it easy/difficult/impossible for a seasoned professional fighting expert (in whatever discipline of martial arts you name) to beat a much stronger man, without fighting training but superor both in size and strength to him? For the latter think of those husky men pulling trucks or hurling ironballs in world-strong-man competitions.
"Real Life Situations"
There are too many variables encoded in this term for it to have any meaning. Is the big man stealing your car? Running you over with a car? Picking a fight at the bar because his wife left him and he's sad and drunk? Throwing one ill-conceived haymaker? The problem with such questions is that the premise of "highly trained and conditioned fighter versus individual of enormous physical capabilities" is inherently chaotic even before one adds situational concerns such as who decides it's a fight first.
It sounds like what you're trying to ask is, "without odd sport-specific restrictions, how much better at fighting bigger, stronger opponents does learning how to fight make a person?" We can find suggestive parts of the answer in a few areas.
Areas of Evidence
In these combative arenas, smaller and weaker fighters frequently best stronger, bigger opponents. They frequently lose, too. Technique matters, but if technique is equal then physical attributes (size, strength, agility, power, reach, speed and so on) matter a lot. The standard advice for beating a physically superior opponent is to have superior tactics, technique, conditioning, and speed. In comparing combat sports to unscheduled street fights, some of those areas may be tougher to bring to bear.
It really comes down to whoever is better able to apply their strategy in the fight. If a champion can tire out their opponent, getting kneed in the face by the champ will not help their ability to fight back.
However no matter how skilled you are, in a fight you will get hit. Over a series of fights these add up. So at some point a champ might get knocked out relatively easily.
The fact fighters cut weight to get into lower weight classes implies it's worth having the size advantage.
In a self-defense scenario, between intelligence and physical skills, the latter gives you advantages over a untrained person, whereas the former gives you more chances of 'surviving' a less-smart person than you. If an untrained person is smarter than you, no matter how much you have trained, you will end up with a bottle on your head before you realize it, and thus all your physical training will be wasted.
I love MA, and I train it for many different reasons, but if I had to choose between being really fit and well trained, vs being really smart, if we are talking about self-defense, I would choose the latter. MA training will give you the confidence, and the speed, performance, etc. But in many cases it will not directly address matters such as your emotional state (before, during and after the fight) or train you to 'cheat', or to use other techniques in order to be 'smarter' than your aggressor.
In some types of aggression, you can often spot the Point of No Return, that is, you know that this guy is going for you and there is nothing you can do to convince him not to crush your skull. His body language will tell you that: his upper lip will be curled up, his chest will be forward, his breathing pattern will be more accelerated, fists clenched up. At this point, you need to acknowledge that you will 'die', unless you do something about it. So you hit first, you use a weapon, you distract him and run, you offer money to someone to help, whatever, as long as you get him by surprise. The goal on the streets is not to compare skill vs strength, but to survive by whatever means you have: usually intelligence will get you further.
To sum up, you don't need to necessarily train MA in order to really gain advantages against an aggressor on the streets: you just need to be smarter than him (and that also means, realizing that someone is starring at you and that you should leave the scene before things escalate further). If contemporary MA schools started to adopt this 'Urban Survival Combat' kind of thing and started getting people to realize the importance of outwitting an aggressor, then I would change my answer to say that: 'Yes, MA really train you for the streets'. Unfortunately most of MA disciplines have moved from a discipline that was to teach the individual to fight as part of an army to a system that train people for sports. Neither are suitable for a street self-defense where it is not very likely that you will be accompanied by a small army with you or that the aggressor will say: 'I will crush your skull using Karate rules only'.
If, however, you are a good MA student, smart and capable of not letting your testosterone mess up with your brain, you learn how to avoid this situations and should you ever get into them, you will know how to defend yourself before you attacker has even the chance to blink. So my answer is: 'Yes, MA will help you a lot, but what is covered in a MA school is only a tip of the iceberg on your self-defense study, and you will need to learn a lot about the psychology of different types of attacks/fights and tame your emotions'.
Some Reading on the subject: