That's Muhammad Ali in his prime. He was the best. For his career, he spent all day learning how to do things like that. He had no fear of the incoming flurry. He also only had to worry about punches.
You, most likely, lack the amount of time it takes to do that as well as Muhammad Ali. You also have to worry about this happening by surprise, nowhere near a boxing ring, and with potential multiple attackers that can also use their knees, feet, and anything that an be held. The point is, there is a very small chance of you parrying or dodging anything other than an obvious haymaker from someone that was already in your face, building up to a fight. This is where the Elbow Cage comes in.
The cage is formed by pressing the palms flat to the head or with support at the wrist as I show in the image above. Though I'm using it to attack in the picture, this creates a solid structure and plane that can be used to great effect to deflect incoming attacks. What's even better, is that it is useful the first day it's learned and becomes an automatic response much faster than parrying and dodging. This is because it mimics one of our instinctual responses to something flying at us, balling up (covering). When that "Oh, crap!" moment happens, you just get your hands to your head. No having to focus on the punch or whatever and move or parry at just the right time. Even the MMA world has all but ditched parries and the bob & weave type dodging for a type of elbow cage they generally call the crazy monkey defense. We get more use out of it than the sporting arena, but the concept holds true throughout.
In the end, you have to ask yourself if what you're doing is the thing that has the best chance of success or if your pride is making you want to be good enough to pull it off.
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