Kasparov

  • Material
  • Time
  • Quality of Position

Material, as Kasparov mentions his excellent book How Life Imitates Chess, is the ABC of chess science. If one counts all the pieces on the board and adds the value of the pieces accordingly, he will arrive at an arithmetic value of both sides' material.

Time is the counting of tempi. One side might be ahead in development, thus he is said to be ahead in time, or ahead a certain number of tempi. If one side's attack is too slow, he is down in time.

Quality of position is all the positional factors of the position like "pawn structure, strong and weak squares, active and passive pieces, two bishops, 'bad' king," etc. It's all the factors that can't be easily counted.

Znosko-Borovsky

  • Space
  • Time
  • Force

Space is the amount of squares a player controls. It must also be carefully evaluated since some squares are worth more depending on the position. In general, central squares will constitute greater importance but even this can prove misleading. The unit of measure for space is the square.

Time's unit of measure is the move. Znosko-Borovsky states in his book The Middle Game in Chess "It is no easy task to speak of things that are neither visible nor tangible." However, the idea of counting a move as a tempo makes things easier. Another distinction to make Znosko-Borovsky is that some moves are voluntary while others forced.

Force is all the pieces and how the interact with each other. A piece that controls more squares and needs less time to get to a certain square than another is more powerful.

Seirawan

  • Material
  • Time
  • Pawn Structure
  • Space

In Volume 1 Issue 8 of Inside Chess, a bi-weekly American chess magazine first published in 1988, Yasser Seirawan, the creator and Editor-in-Chief, states "We all know what annotators mean when they talk about material ("trade down when ahead in material") or time ("this is a bad move that loses several tempi") or pawn structure ("this allows me to double my opponent's pawns")."

Space is a different matter altogether because according to Seirawan, not many players know to treat space due in large part to how popular modern openings like the Hedgehog, Pirc, or Grünfeld are among grandmasters.

In that issue, Seirawan gives the reader a metric for measuring space called the "Space Count."

Smirnov

  • Principle of material
  • Principle of maximum activity
  • Principle of the center
  • Principle of the least active piece
  • Principle of attack

According to Smirnov, the driving force behind chess is activity and his principles reflect this.

The principle of material states that the side with a material advantage is going to be more active and thus better.

The principle of maximum activity suggests that one should develop his pieces as forward as possible because this gains activity as the squares in the opponent's territory are more valuable and because this takes away activity from the opponent.

The principle of the center is the idea that pieces in the center are more active than those on the edge.

The principle of the least active piece is that a player should concentrate on his least active piece and not one that is already well placed if there are others that are not doing so well.

The principle of attack states that if one can put his opponent on the defensive, he should do it as this gives him more activity and takes activity from his opponent.

All of these principles have a converse when applied to the opponent, so for instance, a player should keep his opponent from occupying the center, prevent his opponent from winning material, and avoid situations where he is on the defensive as much as possible, etc.

Krush

  • Time
  • Space
  • Harmony

According to Krush, time, space and harmony explain the game of chess.

Chess is a time-based game where you get one turn per move. And in that move a player is trying to do as much as he can to improve his position in that limited one turn.

Chess is also a space-based game because you're limited to 64 squares. Conquering space is a crucial part of the game and most times it's done by pawns but pieces can also help at times. If one player is up material then he will have an easier time controlling more space than his opponent.

Harmony is the rest of chess, how well the pieces are working together. Krush says that this is the most important element in chess.

Heisman

  • Mobility
  • Flexibility
  • Vulnerability
  • Center Control
  • Piece Coordination
  • Time
  • Speed

Heisman states there are five static elements and two dynamic ones. He also states that they can be separated into two groups, quantitative, or elements which are measured numerically, and qualitative, elements which must be measured subjectively.

"Mobility measures the number of moves of a piece, and is a key part of the new theory. Mobility is so important that all the other elements could be examined using mobility as a basis."

"Flexibility consists of keeping one's options open, maintaining many alternate paths."

"Absolute vulnerability is independent of the position of the pieces... Relative vulnerability is a piece being subject to attack that is dependent on the position of the pieces."

Center control, piece coordination, and time are self-explanatory.

"Speed is the distance a piece can travelper move, i.e., distance/tempo."

Tapia

  • Vulnerability
  • Flexibility
  • Mobility

Activity is the driving force behind chess; it can be broken down into three constituent elements.

Vulnerability is the strengths and weakness of either side.

Flexibility is the quality of having options.

Mobility is movement in the right direction.