Is there any metric to rate the overall complexity of a position/game?

I am trying to determine if I play well in simple positions or in chaotic ones, and I thought it would be nice to see if there was an engine metric that could tell me this information.  

The score would be something like 

Extremely Straightforward (1) to Extremely Chaotic/Complex (10) 

What one player finds complex, another might see as a clarification of the position.

That's why I thought an engine could standardize it and take out the human difference

If youre looking for an engine to evaluate positions. What metric do you want it to use?

Do you want stockfish to use its 3800+ rated ability? No one would understand it.

As LieutenantFrankColumbo points out, an objective and impartial assessment is worthless if Human minds cannot think in those terms.

In that respect, it is quite similar to the physicist's dilemma regarding the "Theory of Everything". Even if it turns out to be possible to encapsulate all of the known physical laws in a single set of equations, that's just an exercise in futility if nobody can possibly SOLVE the equations.

Well I can turn that on you also, if I am using default Stockfish to analyze a game its doing so from a perspective that can beat every human on earth yet we still anaylze with it. 
Imagine two armies fighting in straight lines like at Fredericksburg (simple) and then imagine two armies with units flanking, retreating, and staying still, Gettysburg Day 2 (chaos).
A simple "you thrive in choatic positions" would be so helpful.

That again gets us back to what one chess player finds "chaotic" another wont. Also back to my first post: What one player finds complex, another might see as a clarification of the position.

How you, I blueemu, Carlsen and billions of others evaluate a position, and what we think of it will be dramatically. Just my .02 but I think you're trying to apply static rules to a dynamic game.

That's neither here nor there, for the computer sees it neutrally. If a computer can make an accuracy calculation (based on the best, excellent, good, etc.. moves compared to all possible moves) it can make what I ask which would be some formula based on some of the following metrics:
all possible moves: all possible captures: all possible checks: all possible tactics: etc..
Magnus does this quite a bit, he will make some random moves to confuse the opponent and tax their clock - it is a valid strategy. So is playing safe and predictable.

Hello

I suck and want to get bette

Engines do evaluate all possible moves, captures, and forcing moves.

Carlsen does not make random moves. What he will do is not make the "best" engine move. But making random moves against the world best players is a recipe for disaster.

Chess engines do not see all positions as neutral. If they did all evaluations would be 00.00. Which is why they assign a numeric evaluation.

All this "best, excellent, good, etc." is completely useless when it comes to learning and growing. Its nothing but an ego feed.

Magnus has opened with Nh3 many times, it gives an evaluation of -.6 - it is made to confuse, especially in bullet

Yep and that is normal engine analysis. And 2018 Carlsen can play that against Dreev in a rapid game here. But their is also a reason you dont see him play it in a world championship match.

When a GM is explaining an opening and says, "This move leads to a complex position," are you claiming they are making it up or that it is immeasurable? Clearly, they are using some internal system to analyze the complexity of the board. I mean, they are using their experience to make a professional evaluation. 

What is "complex" to a GM, and to the rest of the world is a huge difference. I want to make sure im understanding what youre asking for.

I assume you want to see something that can evaluate any position as "complex"..."intricate"...and any other wording youre looking for. So my obvious question is this: "complex"..."intricate"...and any other wording...for who? For GM's? For beginners? For a certain rating range? I just do not see how that can be done for several reasons.

What is the definition of intricate?

What is the definition of chaotic?

What is the definition of intense and any other word?

And another big question. How is that supposed help someone improve?

Spitballing some ideas for building a “simple to complex” scale … there’re a good number of counter examples to each of the following elements, but you might be able to sort some of that out by combining multiple measures into a single metric. Anyway, here’s where I’d start:

• More pieces on the board for both colors will probably tend to be more complex.
• How many moves are within x pawns of the best move (e.g., within 0.5 pawns). This gets at positions that have many good plausible moves (although some simple winning positions will also have many moves nearly as good as the best move).
• How deeply does the engine need to analyze before its evaluation of stabilizes? Deeper probably being more complex.

"More pieces on the board for both colors will probably tend to be more complex."

What if you're a beginner and do not know how to win a KP vs. K ending? Who has the first move?

What if its a Rook pawn?

I wrote assuming that by “complex” OP meant something along the lines of “positions in which it’s difficult for a strong GM to find the best plan."

And that is the point I was trying to get across.

Fixed above.Not GM, rather an Engine.
I think you both are missing two critical points:

1) Chess.com is surely already using such an evaluation of complexity to determine issues of fair play. A GM making a best move in a complex position is different from a 1200 making the same move, same position.

2) What players find complex is irrelevant in 2025; engines conduct analyses now. I am sure there is already a part of what I request built into accuracy scores. I am simply asking it to be made more public and transparent.