Trouble understanding why the analysis changes so drasticallly when move order is changed?

EDIT: 

I'm not sure people are understanding exactly what I'm saying so I'm gonna use a very specific example from both games. The only difference between the two games is the sequencing order for moves 10-12, the first one is what actually happened, in the second game I changed the order so I captured correctly (queen first then knight). In either case on move 12 the white King ends up on D2, from there both games play out exactly the same way, the same pieces on the same squares, literally nothing is different, so why is it then that after my opponent doubles his rooks on the C file on move 15 it judges the exact same rook moves differently? In the first game rook F8 to E8 is considered an inaccuracy and the analysis goes from +0.68 to +1.89, in the second game with the literal exact same board position and move order ignoring the single sequence that changes literally nothing about the board state, it says Rook F8 to E8 is "good" and the evaluation goes from +1.76 to +2.25.

It is the literal exact same position, so why does it judge one move as +1.1 for white and the other as +0.5 for white? Why does it have a different evaluation for the position at all if it's the exact same starting point, so why is one +0.68 and the other +1.76? This is what I'm trying to understand

I'm gonna include a picture, first game is on the right, second game is on the left the board is exactly the same and the same move has been played but it gives two different evaluations. Why is this the case? That's what I'm trying to understand.

So I recently was going over this game I played a couple weeks back; 

The game lasts 37 moves and the post game review said I made only 1 inaccuracy, where during a capture sequence I captured with a knight first instead of my Queen which would've been done with check forcing the response I wanted from opponent and giving him no counter play. I understand that no big deal, what I don't understand is why this analysis then becomes totally different if I change the capture sequence? It says capturing like I did was an inaccuracy and the only one I made, and my opponent did not take advantage of this the game played out from that capture sequence the exact same regardless of how I captured. So then why is it when I input the same PNG but with the recommended capture sequence (so Queen first then knight, literally nothing changes in terms of pieces or board positions the entire rest of the game plays out the same and it played out the same way regardless of the order) it changes the entire analysis?

So keep in mind that literally nothing changes but the capture order, so why is it that it goes from 88.1 accuracy, 2 Great, 11 Best, 13 Excellent, 7 Good, 3 Book, and 1 Inaccuracy to 81.8 accuracy, 1 Great, 10 Best, 9 Excellent, 10 Good, 3 Book, and 4 inaccuracies???? Legitimately nothing else about the games position is different by changing that capture sequence, which I changed to the correct order, so why do I suddenly have many more inaccuracies? Why does it judge the position differently despite literally nothing changing but a recommendation that it made to me??? I'll put the second analysis on the bottom, maybe I just made notation errors in the PNG but it plays out correctly so I don't see why it sees the position differently. Help understanding this anyone?

The sequence in question takes place on move 10 after he captures the black bishop with his knight.

If you want someone to look over your games and focus on a particular move sequence, it is helpful to tell them when the move sequence occurred.

At any rate, this must be the position:

If you take with the queen, you get a trade of the queens and knights and the king ends up on d2.

If you take with the knight, white can kick your queen with b4 and then take back after you retreat your queen.   It is a completely different position with the queens still on the board.

 Apologies, it's my first time posting. The sequence in question is on move 10 after he captures the black bishop with his knight ( as you obv know since you posted it), I'll edit it in to the main post though so thank you.

You're kinda missing the forest for the trees though, my point isn't about the differences between the two moves (I understand why Queen captures is better), my point is in game this transpired regardless of what happened (I captured with the Knight but he still took with the Queen immediately and then we traded and the king ended up on D2). Then the rest of the game happened. My point is that if I switch the move order to the correct one and leave the rest of the game the same it analyzes the moves and inaccuracies differently even though the exact same thing played out with the original inaccuracy of Knight takes Knight. Do you see what I'm saying? I'm not asking why the move is better, I get that, I'm asking why if the position ends up exactly the same after either sequence (due to opponent not kicking Queen) why would it analyze those moves differently?

But that's I'm not what I'm asking though. I'm not asking whether or not one move is better (I understand why Queen captures is better), I'm not asking if its the correct thing to do in the first place, I'm asking why the analysis comes to two different conclusions from the exact same starting position, midgame, and ending.

Both games come out worse in analysis than the game review says but it also makes no sense they should come out differently at all from each other, since from move 12 of white (capture on D2 with the King) the game is the exact same, so why is the analysis different? Why is the analysis different from the game review in the first place?

"Accuracy", "great", "excellent" and other labels are all meaningless. The chess.com script that assigns these titles is extremely dumb and is full of bugs.

See I can understand that, I just don't understand how a system that's effectively an input/output (input moves and position of pieces, out put "accuracy") would produce different results with the same info is all. Appreciate the fact it's just bs but sorta confused why it wouldnt put out the same results for the same position unless it's just totally made up but if that's the case why even have an analysis section basically?

Im trying to understand your print screens in your first post?

Help me out here.  What is the difference between them?

That's actually what I'm pointing out, there is zero difference in the position at all and yet it gives two different evaluations for the exact same move, the only difference between the two games at all is a capture sequence from move 10-12 (one is sequenced Knight Takes, Queen takes, Queen takes, King takes and the other is Queen takes, Queen Takes, Knight Takes, King takes) but that's it, exact same position is reached and the same game plays out from there (cause it's just a PNG of the game with those 10-12 moves swapped). Which is why I'm so confused that it gives different evaluations for the same position and moves. I get if the eval is just fluff for the most part but I am confused why it wouldn't output the exact same info in the exact same position.

If you got any insight on this I'd appreciate it

I understand your question, I've encountered the same many times. The short answer to your question is: it's just output variance, because the engine is not 100% reliable.

I don't know exactly what happens under the hood during engine calculation, but I guess it has to do with performance optimization. Calculating all possible positions takes an enormous amount of effort and time. To speed up the process engines takes shortcuts. Instead of literally calculating everything with brute force, engines make smarter decisions (things like alpha beta pruning). As a result, the output can change a little bit depending on circumstances.  

In this example, the engine spent more resources on calculating the Nxd2 b4 line than on Nxd2 Qxb2. 

You can see this effect a little bit every time you analyze a specific position. If you recalculate the engine evaluation for each position of a game, the evaluation for each position will be slightly different from the evaluations shown in the full game report.

The point about engine analysis is it uses brute force and programming to analyse as many moves as it can, but there are provisos :

1. Time. The longer you allow it to run, the more accurate it may be. Most "reviews" use a pretty short time of engine analysis because you wont want to sit around for an hour waiting for it to complete.

2. Depth. The more moves an engine analyses for any given path, the more accurate it may be. But even asking an engine to examine one more move for each path will add a very considerable amount of moves to be calculated. This will both add time to the analysis and/or lead to some candidate moves being discarded.

3. Path choices. During engine analysis, there will be points where two or even more candidate moves are evaluated equally. The engine will be programmed to pick one and analyse it further (it does not have the time to evaluate them all).

In the example in your first post, I expect this is what has happened. The same engine, working to the same time/depth constraints has followed two separate paths. After analysing both paths one says +2.25 and the other says +1.89. Both answers are correct.

If you do some googling you should be able to find examples of a board position where a 1 minute analysis gives the advantage to white, a 3 minute analysis gives it to black, and a 10 minute analysis gives it back to white again.

No chess engine is powerful or fast enough to calculate all possible moves in board positions like your example.

I get what you’re saying Henry. It will just be a quirk of the analysis. Something like one of the two sequences encouraged the machine to look shallower but more broadly and the other one it decided to start looking deeper but narrower, and it’s come to a different conclusion - just because the two final positions are identical, it doesn’t mean it’s considering the exact same things going forward from that point in both scenarios.

To be honest you’re better off downloading Stockfish to run locally on your PC as that’s much better than the cloud version that’s inbuilt into chess.com 

This was a very concise answer, I appreciate you taking the time to explain this to me as it has help solve something that was rattling in my head. Thanks again.

Yeah, that's a very good question.

The answer is the output is noisy at first (it jumps around). If the engine is allowed to calculate on a single position for long enough the output will settle to nearly the same value every time (let's say within 0.10)... which raises an interesting question, why doesn't it settle to the exact same value every time, and that answer is more technical, but it usually gets very close.

Anyway, chess.com auto-analysis is extremely fast. Far faster than the engine needs to give high quality analysis... but most users are beginners so analysis doesn't need to be anything serious. If I'm interested in a game beyond elementary tactics I may have missed, I'll use stockfish on my PC (as @jamescoleman said, you can download stockfish for free).

(too bad getting an answer to your question was so difficult...)

Nah it's no big deal, I clearly over complicated the initial post in the hopes of being very direct and answering a lot of questions before they happen but also I'm very grateful so many people including yourself were happy to drop some input and help me understand. This all started because in the initial game it said I made one inaccuracy and I was interested in how my "accuracy" would be graded/changed and how much weight would be given to not playing an inaccuracy given the move in questions resulted in no actual difference in the position.

Thank you for taking the time to respond =)

 I am a beginner and I am a student of maths, and there is a topic called Markov Chain, if you change the ocorrence of one event from before or after the things are gonnna be differente. I hope this is a explanation, search for markov chain.