M - Material; ah, this is easy. Am I ahead or behind in material? The harder question is whether it matters, because sometimes even a Queen doesn't mean anything (simplest example: smothered mate)
M-factor -+...but nobody cares, as the K-factor was dominant and Black lost.
A simple system for evaluating each element of KIMPLODES
This week the M-factor: Material.
Material: basic building blocks.
Q = 9; R = 5; B = 3; N = 3; Pawn = 1 is a rule of thumb one can use for extremely rough calculations of the M-factor.
Except the pieces values are not so easily established and they fluctuate up and down over time and position...and chess engines probably calculate the value of each piece to five or more decimal places following every move...though I'm not sure what good it is to know a Bishop is worth 3.14159625 pawns in a given situation.
At one extreme, there are known openings in which one side sacrifices their Queen for two minor pieces in order to gain the initiative and decrease the safety of the enemy King. And in endgames, many prefer Q+N to Q+B because the Queen and Knight can jointly attack every square on the board, whereas the Queen and Bishop can only combine forces on 32 of the 64 squares, and that certainly won't help if none of the opponent's targets are on squares of the Bishop's color, or if the Bishop is blocked at various turns by its own pawns stuck on the same color complex. There are statistical studies that indicate whether a R+B is better than R+N, and articles on when 2Rs are better or worse than a Queen in the endgame. Usually it isn't the material itself in these instances, but some other KIMPLODES factor(s) that determine the outcome in any specific game.
Material in the opening.
Bishop versus Knight
Because Knights can develop faster (it takes two pawn moves before both Bishops can develop), the Knights can actually claim a slight Material point edge over Bishops in the early stages of the game. This can be important to realize and there is a principle that states if playing with a B+N or 2N versus 2B, then the side with the B+N or 2 Ns should attempt to maximize the value of the Knights early in the middle game, as over the long haul a pair of Bishops simply tend to gain in value. Obviously that is not the case if the position well and truly becomes blocked, with no way, barring perhaps a pawn or piece sacrifice to open diagonals for the Bishops, i.e., trading Material for Lines (diagonals) to enhance the Bishops (Officers) relative to their enemy counterparts.
One could plausibly argue that Rooks have little to no value in the opening. It will (normally) be ages before they reach an open or even half-open file, while the minor pieces and Queen may be enmeshed in full-scale warfare.
She who shall not be named (Her Majesty, the Queen)
Bring her out too early and earn the contempt of your peers, place her on the wrong square and earn the contempt of the masters, yet everyone has to respect Her Highness when she takes a stroll, wondering what plans one has in mind for her, while you have to be mindful she does not place herself in a black hole from which there is no return (the chess equivalent of the event horizon is when one's Queen is lost while chasing a Rook in the corner that, as previously noted, has no value in any case in the opening).
Material in the middle game
When tactics reign supreme, the only purpose of material for the offense is to keep the Initiative flowing, destroy pawn structures that shield the King, or simply create problems that become too difficult for the defender faced with exceedingly difficult problems in a short period of time. For the defender, the primary purpose of material is to deflect a mortal blow or initiate counterplay, or simply as a ticket to victory if the attacker has overestimated their chances. I'll offer one example from my own practice, which I have nicknamed Sturm and Drang, Variations on a Theme.
Where positional concerns reign supreme, the discussion of material is much more nuanced...some might even say the dialogue between the players is actually more interesting than a tactical sequence (this is the sporting equivalent to preferring defense in the NBA or NFL, rather than a high-octane offense). I'll offer a game relevant to this topic in KIMPLODES--Pawn structure; Part IV of IX, where the topics of Material and Pawn structure overlapped in a training game versus AlexanderRoc, but the clearly predominant theme was how pawn strucutre leads one to sacrifice an exchange (M-factor) in order to take advantage of the aspects of a pawn structure that favors Knights over other pieces.
Material in the end game
Just to make a point, a classic ending showing that Material is not everything in the end game. Many (most?) know or have heard that 2 passed pawns on the 6th rank can be worth more than a Rook. In the position below only one passed pawn is required, because the I-factor (+-) and K-factor (+-) combine to win for White, even though by stritctly quantifiable standards one could argue that M-factor is -+ since a Rook is worth far more than a pawn...but only in an overly simplistic system that says a Rook = 5 and a Pawn = 1...in this position that quantification is simply immaterial to the result.
Numerous other examples can be found, including cases in which a minor piece and pawns or Rook and pawns form a fortress that allow the defender to hold against a Queen in the ending, and of course a Rook sometimes defeats a solo Bishop or Knight...though often a draw is the correct result...if the defender knows what they are doing.In the field of tragicomedy, more than one game with B+N versus a bare king has resulted in a draw because the side with the minor pieces did not know the patterns that lead to a forced mate with this reduced set of Officers.
Because the field is so rich, I will simply recommend the notes in my drawn endgame versus chesspo in KIMPLODES: King Safety--Part I of IX as an example of an endgame where I was forced to concede a draw, despite being a Rook and Bishop ahead at the point the perpetual check ensued.
Tactics Trainer on chess.com
Chess mentor on chess.com
Any book with puzzles to solve
Dvortesky, Dvoretsky's Endgame Manual (Advanced material)