A computer analysis of a game in Lichess lists your "inaccuracies", "mistakes", and "blunders". An example is below:
What I don't understand is why Lichess doesn't point out my good moves. It seems there is some inherent problem identifying strong moves, which is not present when pointing out poor moves.
Question: Why does Lichess only tell me my "inaccuracies", "mistakes", and "blunders", and not e.g. my "brilliancies"?
It's really hard to tell what a brilliancy is. For example, you might try to say that a brilliancy is a move that's much better than any other move on the board. Well, if you offer me a queen exchange and I play queen takes queen, you taking back my queen is probably a much better move than any alternative, but it's definitely not a brilliancy. So maybe a brilliancy is a non-obvious move that's much better than any alternative. OK, but what's non-obvious? Maybe you could do something based on the depth you have to go in the search tree to prove that the move is good, but that probably still isn't right because a long sequence of exchanges is usually obvious but, by construction, goes deep into the tree. Or, suppose you trap my queen: by the proof depth metric, that would be a brilliancy if I can insert a long sequence of pointless checks before you take my queen, and a normal move if I can't.
In contrast, bad moves are easy to detect: if a move is suboptimal, you just compare its score against the score of the best move and use a more negative word for bigger differences.
Fundamentally, there's only one best move in any situation. As far as the computer is concerned, you either played it or you didn't. Bad moves are bad moves, but brilliancies are good moves that most players wouldn't have seen, and that's as much a statement about "most players" as it is about "good moves".
Here's why computer analysis (on any platform) can not find brilliant moves.
Now, I recognize that this seems very counter-intuitive, but bear with me. This has to do with the difference between how we (intuitively) view a chess game and how a computer (correctly) views a chess game.
When we look at a chess position, we subconsciously view the position on the board as having a certain value, and we look to improve that value.
Chess computers look at this in a completely different way.
The value that they assess the position is based on perfect play from the position forward - the only way to deviate from the perfect play is to make an error of some sort.
Example: You're losing a game by a bit, and then you find a beautiful, non-obvious tactic that nets your opponent's queen. In our human minds, we just took the game from losing to winning with our brilliancy. According to the computer, the position was already winning for you, because the computer saw the brilliancy. Any move other than the brilliancy is likely a mistake of some sort.
Non-obvious "brilliant" moves do not change the value of the position - they merely fulfill its potential.
Now, of course there are moves that we consider "excellent" or "brilliant" for one reason or another (requires a sacrifice, isn't immediately obvious, requires deep calculation, etc.). Don't get me wrong - it feels very rewarding to find one of these moves, and some moves are undeniably "!!" moves for human players. However, any analysis (on the part of a spectator or a player) that does not take into account the "!!" move is incorrect in the first place, and the "!!" move shows that.
Also, creating an objective definition of "brilliancy" is next to impossible - sometimes we "know" a move is brilliant, but we can't consistently explain why.
Your every move is being evaluated by a chess engine with super-human playing-strength. The default is to compare your performance to its own super-human performance. Since the engine always makes the move it itself has identified as the highest-valued, perforce it always makes the best move by definition. Hence you can only stray from this path of "perfection".
To leave room for brilliant moves, or better than expected performance, it is necessary that your performance be compared to something that is not "perfect" by definition, for example the performance of a weaker engine. Theoretically, given the availability of a whole range of engines with different known ratings, each one of your moves could be categorized into a specific rating bucket.
Almost all (if not all) of your brilliancies were immediately seen by the engine. If the engine always points out your moves that it agrees with, then standard opening moves would be considered brilliancies. So now the problem arises of figuring out moves that are difficult or pleasing for humans specifically, and this is beyond the normal scope of an engine's purpose.
