Opening, Middle-game, or Endgame, Which is most critical for improving your chess and why?

As Smyslov wrote, studying endings teaches you the characteristics of each piece, their power and potential. Their limits as well.

I’ve spent weeks standing at the edge of a board watching a young player chase a king all over the board with a queen or rook, check, check, check, … but never checkmate. For some people, this skill comes naturally. Most have to learn it.

IMO

a : Against bots I would say first the endgames then the opening then the middlegames.

On [for example] the Chessmaster program from 1100 to 1700 (apart from the fact that it is a program which normaly is not designed with an opening encyclopedia) we'll play vs bots with "a chess essential" (thanks to the lessons of notably Joshua Waitzkin) the bots present themselves as fake-weak players who play badly by giving us more or less very advantageous or winning positions then start playing well.

So what matters is rather to be good enough in tactics and to have good enough knowledge of the art of playing endgames to realize our decisive advantage.

+1800, the openings have an important role because some openings are just bad or ineffective against bots but also because if we play garbage or disadvantageous positions after the opening it will too often end in more or less painful defeats.

b : Against humans I would say first the middlegames then the openings then the endgames.

Humans play much more strategically with ideas and plans so it is important to have a background of strategic knowledge, to understand good enough positions and anticipate the attack plans of our opponents.

People don't really look at mating nets as often as they need to. But that just hides the underlying issue. Here's the trick I teach people about chess when I am trying to teach them how to play effectively:

When controlling the board, or mating, your pieces don't really exist (there are exceptions to this viewpoint, like one of your pieces blocking the way of another piece). Defensively, your pieces exist. Offensively, the one square that a piece is never able to exert influence on is the square it sits on. So, a queen is nothing, offensively, where she sits. All the power of the queen is in the rank, file, and diagonal squares the queen can reach. So stop looking at your queen, and start looking at the lines of influence. If you learn to see pieces as exerting influence around them, then seeing mating nets, control of open files, outposts for knights, etc. all become a lot more obvious.

@DiogenesDue

Influence. Something akin to a lightbulb clicked on in my mind with your analogy. I appreciate your comment, i hope to practice this immediately. (At my level i need all the help i can understand.)

Probably middle game tactics is where most players lose most often, but the endgame is vital, too. The opening is vastly less important. All the evidence deployed in this thread in favor of the opening is really about tactics.

I try to do a mixture, with my son (he's 8 years old).

I give him 5 puzzles a day to solve, setting them up on a physical board. Puzzles like this one:

These are taken from Laszlo Polgar's "Chess" puzzle book. We talk about each one afterward, just to make sure he understands the puzzle and wasn't simply guessing.

After that we set up the board to the starting position and play a game or two. We talk about "getting our pieces out so they can join the battle" (development), and putting rooks on open files "because they're like tanks who want to control the roads". I purposely hang pieces here and there, to see if he spots them and captures. Sometimes he does, sometimes he doesn't.

He still struggles with a lot of things, like seeing hanging pieces and missing recaptures ... and positional strategy is beyond his scope at this point. But he seems to enjoy it and we don't push too much beyond that. Just little bits and pieces, here and there.

I agree that there probably isn't a "wrong" way to teach chess, as long as the player enjoys the process and wants to keep playing and learning.

If I had to choose one then for me it would probably be 'the middlegame'.

You’ve never taught, have you? I’ve been teaching since the 1980s. I’ve taught students aged 3 to 75. Subjects have ranged from chess to theology, but most has been history. Chess has been a constant on a part-time basis for a quarter century.

Lessons are tailored to the learner, but I have not yet met the student who did not benefit from instruction in endgames, including basic checkmates.

A strong focus on endgames also was instrumental in lifting me from mid-1400s to high 1900s in my 40s and early 50s.

The failure was tactical, not opening theory. Obviously, a failure to develop will create problems. All my students learn from Paul Morphy’s play. https://www.chessgames.com/perl/chesscollection?cid=1042867

The quickest way to impress upon a beginning chess player the search for truth is mastery of elementary pawn endings and simple checkmates.

I would say middle game is the most crucial since that's where you shape your endgame in the future, and it mostly depends on middle game if you are having a advantage or not

Of course I’m not a stronger player. The rating difference means nothing.

The OP wanted to know which aspect of the game was most viral for improvement. No one said to neglect any phase, except you. You want to completely dismiss the endgame. The strongest players who have posted here, OTOH, have emphasized the endgame as most vital, while noting that tactics are also important. Of the three phases—opening, middle, and ending—openings are the least vital to the improving player, at least until one is battling masters on a regular basis. But, no phase of the game should be neglected.

My teaching the past quarter century has nurtured young players and a few adults in all phases of the game. My best students have been strong at tactics, followed sound opening principles, and have beaten higher rated players in tournament play because they were strong in the endgame. My best students grew stronger than me. That only happens when the foundation is solid. 
There is no foundation more solid than one built upon the curriculum José Capablanca outlines in Chess Fundamentals. Elementary checkmates, basic pawn endings, tactics, a few opening principles, then repeating the sequence with slightly more advanced training. This cycle has been my approach for more than twenty years. Some of my students have won state championships.

You’ll excuse me if I do not heed the advice of someone much lower rated in blitz than me, even if he is the better player.

Forget about blitz. Your last game that was a battle was a win where your tactical prowess gave you a superior ending. https://www.chess.com/game/live/78847503335 

In that game, you overcame a little opening problem that prevented you from castling and bringing your king’s rook into play.

Also, your rapid rating offers a better claim that you are a decent player, as you are in the top 1% on the site.