How potent is my piece?

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This is the hypothesis:
All kinds of positional topics like piece activity, king safety, outpost, color complex etc.. can be described using only a few elements. Space and time are two of them.

If I am able to express every topic in these same few elements than I can compare them on a realistic basis in stead of awarding them with arbitrary statistic bonuses. I want to stretch matters even further, even the tactical elements can be expressed using these very same few elements. Everything isn't worked out completely yet. That's the reason for this post. Let me give it a shot.

What happens when a piece is dumped on the board?

Diagram 1























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In 7 tempo's, the King can reach every square of the board. That must be his potential in the shortest time from his position on h8.
Potential from h8:

• Space = 64 squares
• Time = 7 tempo's

That shows immediately that there must be better squares on the board. If you place the king in the center of the board, for instance on e4, he becomes even more potent.
Maximum potential:

• Space = 64
• Time = 4 tempo's

Even if you give the king more tempo's, he cannot accomplish more than reaching 64 squares.

I'm a bit afraid that you might find these posts a bit boring. For me they are very important though. Without them I would never be able to find the third element as I just did:

• Position on the board.

Only on d4, e4, d5 and e5 the king will have his full potential and hence his greatest future possibilities.

What happens when other pieces are being dumped on the board? It is evident that they can only limit the full potential of the king by influencing the elements.

Diagram 2























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The blocked pawns are lengthening the pathways of the king. To go from h8 to g7 the king needs 15 tempo's. To go from h8 to h7 he even needs two tempo's more.
The king can still reach all 64 squares. But he needs an incredible amount of tempo's to do so.
It is possible to place the pawns in such way that a certain part of the board isn't accessible to the king at all.

Conclusion for now:
The position to strive for is to maximize the difference between the current potential of your own pieces and the current potential of the pieces of the opponent. Potential can be expressed in squares and tempo's. Not every square has equal potential for a piece. Hence the inclination for some pieces to head towards the center.

Hanlon's razor:
Never attribute to malice that which can be adequately explained by stupidity.