When I followed the course to become a chesstrainer, our teacher asked us to explain to him why some problems are more difficult than others. This had to be absolutely clear to us, because we had to construct our own chess puzzles for beginning chess players.
Our answer to his question was that the level of difficulty was determined by the following factors:
- the number of ply of the solution;
- the number of branches.
Our teacher confirmed that these criteria indeed determined the level of difficulty to a large degree, but added one we had missed. He used the Dutch word "ruis", which can be translated as "rustle", "noise" or "fuss".
A position becomes more difficult to solve as soon as you ad pieces to it, even when they have no bearing on the solutions number of ply or the number of branches. Adding pieces makes it more difficult to see the pattern. Often it also creates patterns that do not work in the given position, but do distract you.
Handling fuss/noise is therefore a key element in improving as a chess player. I suspect that dealing with fuss may be a big problem for anyone who has followed the circles, but has not achieved the progress he expected.
A major difference between solving positions and playing a game is that the fact that the knowledge that you are solving a puzzle decreases the level of fuss/noise enormously. This is very beneficial when solving, because it prevents you from analyzing non-forcing lines. But in a game this problem-solving mode may be the reason that you are to pre-occupied with forcing lines. This may distract you from the real issues you have to handle when selecting your move.