user6987: What exactly is the logic behind the concept of “overprotection of a piece”?
Wikipedia says that it "...provides greater freedom of movement for the pieces protecting that square."  If the protected pieces moves, then one of the protecting pieces leaves and that seems like it goes against the concept. What is the actual logic?

user167: From the cited Wikipedia article:

The strategy of protecting a pawn or specific square of the chessboard more than is immediately necessary. This serves to dissuade the opponent from attacking that specific point and provides greater freedom of movement for the pieces protecting that square.

The sense in which overprotection provides "greater freedom of movement for the pieces protecting that square" is that, with multiple defenders already in place, no one of them is necessarily tied down to defense.
What follows isn't the greatest example, but I think it illustrates the concept fairly well. (I'm not claiming any of these moves are the best or are necessary; I've chosen them specifically to illustrate overprotection.)
[FEN "r1bq1rk1/ppp1npbp/3p1np1/4p3/2P5/2NPP1PP/PP2NPB1/R1BQ1RK1 w - - 0 1"]

1.Kh2 
    {Overprotecting h3, and thus creating a genuine threat against b7 by 
    the Bg2. That makes it so that the Bc8 can't develop immediately.}
    ( 1.Rb1 {In this variation White leaves the Bg2 as the only defender 
    of h3, and so Black can immediately develop the Bc8 if she likes.} 
    1...Be6 2.Bxb7 Bxh3 3.Bxa8 Qxa8 4.e4 Bxf1 5.Qxf1 )
1...Rb8 
    {Black responds by overprotecting b7 herself. Again, having this 
    second defender frees the Bc8 to develop.}
    ( 1...Be6 $2 2.Bxb7 )
2.Rb1 Be6

The Wikipedia entry continues:

[Overprotection] can cause an opponent to pursue a faulty plan or no plan at all.

I'm not sure about that wording, but I think the intended meaning is this: the opponent might press on against the overprotected piece/square in what will be a futile attempt thanks to the overprotection (faulty plan) or will be forced to abandon that endeavor and look for something else to do (no plan at all).
For example, in the basic structure of my position above, it is very common for Black to line up a Be6 and Qd7 to harass the h3 pawn (or just try to trade off the light-square bishops if the pawn is still on h2); but once White has played h3 and Kh2 as above, Black won't really be able to effect that plan. She might press on and ultimately be unsuccessful (faulty plan), or instead need to figure out something else to do in the position (no plan).

6987: <p>What exactly is the logic behind the concept of “overprotection of a piece”?</p>

<p><a href="http://en.m.wikipedia.org/wiki/Glossary_of_chess#Overprotection" rel="nofollow noreferrer">Wikipedia</a> says that it "...provides greater freedom of movement for the pieces protecting that square."  If the protected pieces moves, then one of the protecting pieces leaves and that seems like it goes against the concept. What is the actual logic?</p>
 167: <p>From the cited Wikipedia article:</p>

<blockquote>
  <p>The strategy of protecting a pawn or specific square of the chessboard more than is immediately necessary. This serves to dissuade the opponent from attacking that specific point and provides greater freedom of movement for the pieces protecting that square.</p>
</blockquote>

<p>The sense in which overprotection provides "greater freedom of movement for the pieces protecting that square" is that, with multiple defenders already in place, no <em>one</em> of them is necessarily tied down to defense.</p>

<p>What follows isn't the greatest example, but I think it illustrates the concept fairly well. (I'm not claiming any of these moves are the best or are necessary; I've chosen them specifically to illustrate overprotection.)</p>

<pre><code>[FEN "r1bq1rk1/ppp1npbp/3p1np1/4p3/2P5/2NPP1PP/PP2NPB1/R1BQ1RK1 w - - 0 1"]

1.Kh2 
    {Overprotecting h3, and thus creating a genuine threat against b7 by 
    the Bg2. That makes it so that the Bc8 can't develop immediately.}
    ( 1.Rb1 {In this variation White leaves the Bg2 as the only defender 
    of h3, and so Black can immediately develop the Bc8 if she likes.} 
    1...Be6 2.Bxb7 Bxh3 3.Bxa8 Qxa8 4.e4 Bxf1 5.Qxf1 )
1...Rb8 
    {Black responds by overprotecting b7 herself. Again, having this 
    second defender frees the Bc8 to develop.}
    ( 1...Be6 $2 2.Bxb7 )
2.Rb1 Be6
</code></pre>

<p>The Wikipedia entry continues:</p>

<blockquote>
  <p>[Overprotection] can cause an opponent to pursue a faulty plan or no plan at all.</p>
</blockquote>

<p>I'm not sure about that wording, but I think the intended meaning is this: the opponent might press on against the overprotected piece/square in what will be a futile attempt thanks to the overprotection (faulty plan) or will be forced to abandon that endeavor and look for something else to do (no plan at all).</p>

<p>For example, in the basic structure of my position above, it is very common for Black to line up a Be6 and Qd7 to harass the h3 pawn (or just try to trade off the light-square bishops if the pawn is still on h2); but once White has played h3 and Kh2 as above, Black won't really be able to effect that plan. She might press on and ultimately be unsuccessful (faulty plan), or instead need to figure out something else to do in the position (no plan).</p>
