The majority of players never improve that noticeably because they tend to focus on the wrong aspects of the game. They focus on their particular character and what moves they feel are good for their character, while ignoring the biggest hurdle that is preventing them from making giant leaps of improvement: the basics. These are the fundamentals that can be applied to every character in any smash brothers game.
When playing with various people I frequently hear someone say after just losing a stock, "****, I should have done ______" and they ponder what they should have done differently in that particular situation. What they SHOULD be thinking is, "how did I let myself get up to 150% before that last hit removed a stock"
When people ask Isai (undisputed best ssb and great ssbm player) what they should be doing differently he replies, "don't get hit". Because Isai is known for his eccentricity, most players laugh and shrug this invaluable piece of advice off. Azen is also noted for saying "don't jump into the ****" which is essentially the same piece of advice.
Friends, do not make the mistake of taking these words lightly. Think about them carefully. That being said, I believe these are the two most important aspects of any smash brothers game:
1) Spacing
2) Minimizing Risks
Spacing - One of the most common mistakes I see is that players will focus most of their attention on their own character, while looking at their opponent with their peripheral vision. This should be the opposite...why do you need to look at your own character that intently? You know what you are going to do...what you don't know is what your opponent is going to do. You can't space yourself properly if you aren't looking at your opponent.
The biggest hurdle to proper spacing is movement. Try watching a random youtube brawl video and notice the use of only THREE types of movement.
a)rolling
b)jumping towards the opponent
c)dashing
Let's say characters (A) and (B) are facing each other with a space in between them: (A)_______________(B) . Character (A) decides to perform a short hop aerial that has little lag towards (B). Most players will either roll or dash away. You can block as well, but let's say (A) is Marth who is spacing himself at a distance that you can't shield grab afterwards. What many people fail to consider is simply WALKING a half an inch away. Now you are in a position to execute any command at your disposal. By rolling, or dashing away...you cannot immediately execute another command until the rolling/dashing animation has finished. You have to realize this isn't a demonstration on what you should do in a particular situation, but it is only meant to illustrate the benefits of walking to properly space yourself. Walking can also be used to avoid dash attacks. Smash brothers registers such fine movements on the analog stick that many times it is hard to notice any change in movement and your opponent may just interpret that situation as a missed dash attack when in reality you spaced yourself by moving slightly out of its range. This also applies to jumping. When you do an aerial attack toward an opponent, you don't need to jam your analog stick all the way towards them. Brawl allows you to have a lot of aerial control so that you can allow yourself to hit them with the very tip of your attack, thus protecting your body as much as you can.
Now that you are no longer harnessed by the movement constraints of the predictable scrub, let's look at two common glaring instances of poor spacing. When an opponent has either fallen on the ground, or is hanging on the edge in a position that they are able to do a "get up-attack" , you constantly see people getting hit by their opponent attacking out of those defensive positions. People tend to face the dilemma of not wanting to get hit, but also wanting to be close enough to punish their attack. All this requires is carefully walking to the safest distance. Unfortunately, most people get hit...take the 7% (i don't know how much it really is) damage and shrug it off. Who cares it's only 7%. But it is these small attacks that add up to the final blow that takes your stock off.
Poor spacing leads to another big problem I see: spamming/committing to attacks. When players poorly space themselves and find themselves close to their opponent in a position they had not predicted, the mashing of buttons ensues. Avoid this at ALL costs, every command should be carefully executed and intentional. Furthermore, if you properly spaced yourself there is no need to panic and hit random buttons since you are at a safe distance from them (you ARE at a safe distance right?).
Also, you should never fully commit to an attack if your opponent has reacted differently than you intended. What I mean is you should never have a preconceived notion of what you are going to do, regardless of what your opponent is doing. You are probably thinking that you don't do this...but we are all of guilty of doing it one time or another. Let's go back to that first example of the two characters facing each other. Let's say as Marth you intend to do a f-air toward character (B) but at the last second you see (B)'s shield go up. Many players are unable to quickly make another decision so they decide to commit to their first intention of doing a fair, in which they will most likely get shield grabbed. Now let's turn the tables and say I am player (B) who is holding the block. Let's say that the Marth notices the shield go up and adjusts his attack so that the fair goes through the block and ends up on the opposite side of character (B). I don't know how many players I've done this to who still tries to shield grab despite me being on the opposite side of them. This is because they had the notion that they were going to shield grab and were unable to adjust when Marth ended up on the other side of them. Do not fall into this trap of committing to attacks too often. You should constantly be adjusting what you are doing in reaction to what your opponent is doing.
Minimizing Risks can probably be best illustrated with an example. Let's say Marth and Sheik are facing each other and Sheik is blocking. Bad Marth players are notorious for spamming his forward smash, but in this situation, it is the most risky command you can perform. The Sheik has 5 options while holding block. She can:
1) continue holding block
2) roll left
3) roll right
4) spot dodge
5) jump
Assuming that Sheik chooses at random what move to do, the only way you are going to connect is if she jumps. That means at random, you have an 80% chance of being punished for this decision. This usually translates to mainly relying on moves that don't have a lot of lag, but defensively this concept is invaluable. If you just got hit off the stage and your opponent is waiting for you to get back on, many players will try to time an aerial so they hit the person trying to edgeguard them. You take the risk of being sent even further off the stage, whereas it is MUCH less risky to wait for them to approach you and air dodge back on the stage.
On a side note, doing these things alone probably won't win you games. You need to find creative ways to hit your opponent. Forget about terms such as "mindgames", which gets thrown around way too often. Just worry about playing smart. The majority of youtube brawl videos I see look more like turnbased RPGs than smash brothers. One person attacks, then another person immediately approaches and attacks, and on and on. You need to be able to have enough control over your game that you can prevent yourself from immediately executing a command. This is why rolling works so well against so many players. Players are unable to pause even for a moment in their flurry of attacks and movements.
In order to combine these principles effectively, most people must abandon bad habits which initially will most likely make you perform worse. This also means that you will probably have to slow your game down. Furthermore, playing against computers nonchalantly reinforces committing to attacks, spamming, and poor spacing because they do not tend to punish you for your mistakes. You may have heard the popular phrase, "practice makes perfect". I do not agree entirely with this adage, but feel that Vince Lombardi was closer to the truth: "practice does not make perfect, only perfect practice makes perfect". If you are going to practice against a computer, I find the most effective way to do this is by playing a level 1-3 (no higher) CPU and take it seriously. Make every move hit, and make sure every move is intentional. Don't worry about combos and flashiness. Worry about being in complete control of your character. Move around, put yourself in awkward situations. You don't have to constantly be attacking as if you were recording a combo video. Slow your game down and you will think of different things to do in different situations.
In summation...don't get hit.