Thank you!
However, I will admit that I think there are practical problems with your intuition. You see, strategical understanding appears to improve gradually and almost linearly with rating, and so it is difficult to come up with a non-arbitrary cutoff point; for example, opening principles ─ a strategical concept ─ are one of the very first things one learns as a chess player, and even 1200s know that isolated doubled pawns are undesirable. Obviously, knowing which side to play on is a bit more advanced, but perhaps not as advanced as knowing when it's okay to keep the king in the middle with both queens on the board. It's easy to look at a game and say "neither player knows what they are doing ─ this isn't how either of them is supposed to be playing this position", but this is a statement that one can apply to literally all levels of online chess, just to different extents. How many times have you heard Hikaru say "my opponent is completely misunderstanding this position, his plans are all wrong"? when facing 3000+ opponents? Yeah, exactly.
The only mechanism for demarcating a reasonable cutoff on this continuum that I can think of is by introducing another, non-linear function of strategical understanding and locating a turning point there. One such function is understanding of the basics. The way it looks like from my perspective is that strategical understanding is like a jigsaw puzzle in which basic concepts are the pieces. Bad players will struggle to even locate the pieces; good players have all the pieces and can begin to solve the puzzle, although will often fail to do so; and better players will be able solve the puzzle with a higher frequency. The "good players" in this analogy would be the 1500+ cohort. Before this point, most players are either unfamiliar or unproficient with at least some of the basics such as the concept of weak squares, colour complexes, bishop pair advantage, etc; however, at right around 1500, most players seem to consistently demonstrate awareness of most of the basic elements of strategy, even if combining these elements (which your example of identifying which side of the board would require ─ you'd have factor in many different elements such as weak squares around your king and your opponent's king, pawn storm potential for either player, piece activity around either player's king, etc) often proves too tall of a task.
So I actually stand by my original suggestion. To me, 1500s don't look like they are shuffling pieces aimlessly; it rather looks like a battle of logical ideas but poor execution and lots of blunders. Watch Northerlion as one example. He has a very logical plan for almost every position, even if he often misses even better plans that might be obvious to a better player and makes lots of one-move blunders.
Yeah, my personal feeling definitely has practical problems, and the first one that comes to mind is as you said e.g. with Hikaru criticizing other GMs for not understanding anything.
There's a similar problem with when play becomes recognizable. I've seen 800 rated players play games that "look normal when you skim through them" as you put it... even then it depends on the standards we use. In Hikaru's comments sometimes people point out that during e.g. sub battles, Hikaru and Levy compliment a 1000 rated player for playing well, but then during their own games criticize a 2500 for playing like an idiot, clearly grading on a curve for the low rated players.
I like your #2. After a certain level you can't expect to win material simply because you make a series of simple 1 move threats, or because your opponent was careless and threw away a piece. I think of 1300 as the OTB rating where players are consistently not making simple blunders, and it's easy for me to imagine 1500 is the online equivalent.
I know I'm very late, but my answer is pretty definitive: 1400-1500. There is a number of things that is special for this rating range:
1) It is the lowest rating at which most players have full grasp of the fundamentals (basic tactics, opening principles, and basic positional principles like king safety).
2) It is the lowest rating at which it is no longer possible to win consistently by making moves that don't improve the position (e.g. by simply waiting for a blunder to happen) or address opponent's ideas.
3) It is the lowest rating at which, visually, the games look "normal" when you skim through them; at lower ratings, the games immediately stand out as amateurish even after the most cursory of looks.
4) It is the lowest rating to which highly advanced players (such as International Masters and Grandmasters) have a non-zero chance of losing.
5) It is the lowest rating at which it is possible to beat most casual players consistently. At lower levels, such as 1200-1400, you'd still beat most casual players a good majority of the time, but will often slip up.
So, for me, the 1400-1500 range is by far the strongest candidate. Two other potential candidates are the 1700-1800 range and 2000+. The former marks the first time that tactical oversights stop being the dominant decisive factor in most games (it is still an important factor at that rating range, but it's no longer the only one). And the latter is a big round number, officially demarcates experts from non-experts in many countries such as the US, and marks the first time theoretical knowledge becomes a significant factor. But still, at least for me, both of these candidate ranges are a lot weaker than the 1400-1500 range.
I agree a lot with this... not 100%, but it's a quality post with good reasoning.
As for my answer,
My personal feeling (and this is just my subjective feeling) is a player isn't "good" unless they're at least starting to incorporate basic correct strategic ideas... for example in a position where they should attack on the kingside, they at least try to attack on the kingside. The moves can be bad, but the basic understanding is there at least.
If they're just aimlessly shuffling pieces, then try some desperate attack... I guess that's where the pejorative "wood pusher" comes from. They're just pushing pieces around without understanding what's going on.
Thank you!
However, I will admit that I think there are practical problems with your intuition. You see, strategical understanding appears to improve gradually and almost linearly with rating, and so it is difficult to come up with a non-arbitrary cutoff point; for example, opening principles ─ a strategical concept ─ are one of the very first things one learns as a chess player, and even 1200s know that isolated doubled pawns are undesirable. Obviously, knowing which side to play on is a bit more advanced, but perhaps not as advanced as knowing when it's okay to keep the king in the middle with both queens on the board. It's easy to look at a game and say "neither player knows what they are doing ─ this isn't how either of them is supposed to be playing this position", but this is a statement that one can apply to literally all levels of online chess, just to different extents. How many times have you heard Hikaru say "my opponent is completely misunderstanding this position, his plans are all wrong"? when facing 3000+ opponents? Yeah, exactly.
The only mechanism for demarcating a reasonable cutoff on this continuum that I can think of is by introducing another, non-linear function of strategical understanding and locating a turning point there. One such function is understanding of the basics. The way it looks like from my perspective is that strategical understanding is like a jigsaw puzzle in which basic concepts are the pieces. Bad players will struggle to even locate the pieces; good players have all the pieces and can begin to solve the puzzle, although will often fail to do so; and better players will be able solve the puzzle with a higher frequency. The "good players" in this analogy would be the 1500+ cohort. Before this point, most players are either unfamiliar or unproficient with at least some of the basics such as the concept of weak squares, colour complexes, bishop pair advantage, etc; however, at right around 1500, most players seem to consistently demonstrate awareness of most of the basic elements of strategy, even if combining these elements (which your example of identifying which side of the board would require ─ you'd have factor in many different elements such as weak squares around your king and your opponent's king, pawn storm potential for either player, piece activity around either player's king, etc) often proves too tall of a task.
So I actually stand by my original suggestion. To me, 1500s don't look like they are shuffling pieces aimlessly; it rather looks like a battle of logical ideas but poor execution and lots of blunders. Watch Northerlion as one example. He has a very logical plan for almost every position, even if he often misses even better plans that might be obvious to a better player and makes lots of one-move blunders.