How much deeper do you have to calculate, and visualize to improve 100 rating points? What patterns do you have to master to do the same? Can you gain a significant number of ratingpoints without improving in both at the same time?
These were and are crucial questions in my own search for improvement and in my teaching. In my quest for an answer to there questions, I have used the stepsmethod. From my own experience I can make some estimations about the relationship between rating and mastering the steps. And I have come to the following conclusions:
Calculation level: 1 to 3 ply
Patterns: mate, capture, defend, promotion
At this level the immediate capture of a undefended piece, an immediate mate, and defending an attaked piece or square are mastered. Most exercises are 1 or two ply deep, sometimes three. I cannot give an rating assessment because I have never had a student at this level who played competitive chess in rated tournaments.
Calculation level: 2 to 4 ply
Patterns: Mate in two moves, fork, double attack, pin, mating with king and rook, discovered
attack, eliminating defense, defending against mate.
When he has mastered step 2, the student is able to use standard techniques to attack or defend. He is capable to coordinate piece action (mating with king and rook, double attack). If he has mastered these skills he should be able to reach a 1000/1100 rating.
Caculation level: 3 to 6 ply
Patterns: stalemate, mobility, eliminating defense, luring, discovered attacks.
Step three builds on the foundations of step 2. It is not as much that new techniques are added. The basics are expanded by the game setting. The position have more pieces, and more distractions. Also the solutions require more calculation because exchanges or other forcing moves are part of the solution. After mastering step 3 the student should be able to reach a level of 1200/1300.
Calculation level: 5 to 8 ply
Patterns: attacking kingside, 7th rank; pawnendgame (key squares), rook endgames (passed pawn).
Now that the student has reached a level that he is able to avoid 3 ply deep blunders, he can expect to reach the endgame in some of his games. So the basic endgame's are introduced in this step.. The 8 ply deep calculations are only necessary in very forced positions with no sidelines. The student should be able to reach a 1400/1500 level after mastering step 4.
calculation level: 7 to 10 ply
Patterns: Pawn race, seventh rank, rook endgames (Philidor and Lucena position) open files, drawing techniques (fortress), strong squares, Zugzwang, uncastled king, king side attack, small plan, Pin, discovered attack.
In step 5 the average solution is about 5/7 ply deep, but especially in the forced sequences the student has to be able to calculate up to 10 ply deep. These occur mainly in endgames (pawnrace). Mastering step 5 should get the average student to a 1700/1800 rating.
Calculation level: 9 to 13 ply deep
Patterns: mobility, drawing techniques, zugzwang, imbalances (bishop vs night), strategy (small plan), kingside attack (intermediate moves, adding pieces after sacrifice)
I am doing this step now. I score about 80% on average. So this step is fairly challenging for me (current dutch rating over 2050). The main difference with step 5 is that it is harder to recognize the patterns, and in many of the exercises there is more emphasis on preparatory and intermediate moves. About 60% of the exercises are endgame positions and themes. Mastering this step should lift you over 2000.The main conclusion I draw from this excursion is that the ability to calculate and visualize 13 ply deep is enough to reach a 2000 level. But only if you have mastered the required patterns. Mastered them so well that you can implement them in all of your (slow time control) games.
This survey confirms my suspicion that I calculate not as easy and as well than most of the players that have a comparable rating to me. More than I would like to admit, I notice in a post mortem that a player I just beat, out calculates me. The main reason that I can compete and level with those players, is that I have mastered more patterns than they have.