Is game analysis based on "squares" instead of "pieces" of any value? Most all analysis I've seen in chess focuses on pieces development, and not the development of unoccupied spaces. Is there any value in analyzing game play in this way, and if so, how is this done?

NOTE: The way I look at it is: there are four types of unoccupied spaces: attackable, under-attack, attackable-AND-under-attack, and attack-free. Beyond that, really have no clue, other than I know people tend to focus on positive space, then negative space, and that the rules for positive space in chess are much more complex than the negative space; in fact, I'm only able to think of one rule that applies to negative space, that being the king may not enter an under-attack space.
I think that this is a good question, but also that the most enlightening way to answer might be to point out what I think is a slight misconception behind it. You say that most analysis you have seen focuses on the development of pieces, rather than the development of unoccupied spaces. But when one focuses on the development of pieces, what does this mean? In particular, what is the overall goal behind the development of one's pieces in the first place?

There are of course many facets to this, but one (very) rough way to put it is to say that a proper development of the pieces is just one that helps the player to gain as much control as possible of the board, or the "unoccupied spaces" as you phrase it in your question. So, long answer short, I think that your proposed two ways of analyzing game play are really just one. But I also think that your question points to a potentially very useful, guiding way of thinking about piece development.

One classic source that could plausibly be seen as particularly emphasizing this line of thought is the work of Aron Nimzowitsch (e.g. My System, Blockade and Chess Praxis), where he stresses in a pretty unified way the importance of restraining an opponent's play by developing one's pieces so as to control the center, overprotect important squares, blockade opposing pawns by plopping pieces down on appropriate unoccupied squares, etc.

Of course, one shouldn't take ideas like overprotection of key squares too far, as illustrated by Hans Kmoch's classic parody game composition Nimzowitsch vs. Systemsson (follow the link for Kmoch's crucial Nimzo-style annotations to the game):

[fen ""]
[Event "Composition"]
[Site "Copenhagen"]
[Date "1927.??.??"]
[EventDate "?"]
[Round "?"]
[Result "1-0"]
[White "Aron Nimzowitsch"]
[Black "Systemsson"]
[ECO "C00"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "48"]

1.e4 {AN INGENIOUS EXAMPLE OF MY SYSTEM by Aaron Nimzowitsch -
Anderssen started the sacrificial style, Morphy and Gruenfeld
the pure attacking style, Steinitz the positional style,
Tarrasch the scientific style, Lasker the style of styles,
Capablanca the mechanical style, Alekhine a style as brilliant
as sunlight. But it is a generally known fact that originality
and modernism were introduced by me as my own personal
inventions and enthusiastically imitated (without being fully
understood) by the whole world of chess. For the ridiculously
small sum of ten marks, the reader can confirm all this in my
monumental work, My System, published by B. Kagan. Before my
time, chess was so naive and undistinguished! One or two
brutal opening moves, each one involving a vulgar, obvious
threat, a common, banal sacrifice, a painfully elementary,
bestially raw checkmate - such, more or less, was the course
of chess games before my heyday set in. Then I appeared on the
scene and the chess world paid heed. The hegemony of matter
was shattered at a stroke and the era of the spiritual
began. Under my creative guidance, the chessmen, hitherto
nothing but highwaymen, pirates and butcher boys, became
sensitive artists and subtle instruments of immeasurable
profundity. But why waste words!--accompany me, dear reader to
the dizzy heights of the following game.} e6 2.h4 $1 {My very
oldest and latest thought in this opening. To the chess addict
nurtured on spineless convention, this move comes like a slap
in the face--but calm down, dear reader; after all, you cannot
be expected to understand such moves. (Forgive me - it is not
your fault, until now no one has opened your eyes and ears.)
Wait just a little while, and there will pass before you a
miracle of overprotection of more than earthly beauty. (I
assume that I rightly surmise that you are quite familiar with
my great theory of overprotection.)} 2...d5 { Black of course
has no suspicion of What is coming and continues serenely in
classical style. } 3.e5 $1 {A move of elemental delicacy. (We
detest, as a matter of principle, such words as "power" and
"strength"; in the first place, such banal expressions make us
uncomfortable; and, in the second place, we like even less the
brutalizing tendency which such words imply.) Wherein lies the
beauty of 3.e5? Why is this move so strong? The answer is as
simple as it is astonishing. The move is strong because it is
weak! Weak, that is, only in the traditional sense! In
reality, that is to say, it is not the move but the Pawn on e5
that is weak--a tremendous difference! In former times, it is
true, it was customary to reject any move which created a
weakness. Today, thanks to me, this view is obsolete. For,
look, my dear reader, the fact that the Pawn on e5 is weak
obliges White to protect the Pawn more and more until at last
the state of overprotection arises as it were of itself. But,
as we have seen (cf. My System), overprotection is practically
equivalent to victory. Hence it follows automatically that the
"weak" move, 3.e5, is a certain road to triumph. The rest is
more or less a matter of technique. } 3...c5 { All according
to a famous precedent.} 4.d4 {Here it is quite clear that it
is more profitable for White first to provoke c5 and then play
d4, rather than the other way round, which is the customary
course. For, if White first plays d4, there follows c5 and
White's d-pawn is under attack. But my clever transposition of
moves changes the situation completely. For now Black's c-pawn
is suddenly attacked by White's d-pawn!} 4...cxd4 {What else
can Black do?} 5.h5 $1 {All very clever, original and
decisive! Of course the ordinary run of people who envy my
every spark of genius but cannot follow my line of reasoning
for even three paces, outdo themselves in sneering at me with
the poison-dripping epithet, "bizarre." The text move creates
confusion in the whole Black army and prepares for the
annihilating invasion by the Queen 18 moves later.} 5...Qb6
{Naturally not 5...Nc6 6 Bb5! etc. Why should Black play the
French Defence only to allow the Ruy Lopez Bishop move after
all?!} 6.h6 $1 {An avaricious dullard would never hit on this
deeply conceived Pawn sacrifice.} 6...Nxh6 {After 6...gxh6,
White has an even more comfortable game.} 7.Qh5 $1 {The reason
for this becomes clear after next move.} 7...g6 {Black
threatens to begin a successful siege of the weakling at e5
with Bg7. But White forestalls this.} 8.Qh2 $1 {To every
fair-minded observer, this move must come as a revelation! All
the previous manoeuvres now become clear! White has completed
his development brilliantly and proceeds to overprotect
e5. Against this, Black is helpless.} 8...Nf5 9.Bd3 {Note the
splendid cooperation of White's forces: while the e-pawn and
the King Bishop completely blockade Black's position, the
development of the overprotective forces takes place behind
the broad backs of these sturdy blockaders.} 9...Nc6 10.Nf3
{As a rule this is a routine move. But here it is strikingly
original and as such occupies a place in the treasury of my
intellectual property.} 10...h5 {Old stuff!} 11.b3 {A deep
trap, as will soon become apparent!} 11...Bg7 {How Black must
have rejoiced when he anticipated his formidable opponent in
the occupation of the long diagonal. But...} 12.Bf4 $1 {...how
bitterly disappointed he must have been to realize that 11.b3
had only been a trap and Bb2 had not been intended at all. The
position of Black's Bishop at g7 is now quite
pointless. 11...Be7 would have been relatively better.}
12...Bd7 13.Nbd2 Rc8 {Black no longer has any good moves!}
14.Ke2 $1 {Again, an extraordinarily deep move. White sees
through Black's plans, and in addition he prepares a
particularly powerful continuation of his strategy of
overprotection.} 14...Nb4 {Just what White was waiting for.}
15.Ne1 $1 {This was the point of his previous move! Black is
now forced to exchange off the attacking Bishop at d3. But,
with that, even White's King Knight enters the fray with
fearful effect at d3, while the square f3 becomes available to
the Queen Knight. Surely a grandiose piece of strategy. The
fact is that I'm a marvellous player, even if the whole chess
world bursts with envy.} 15...Nxd3 16.Nxd3 $1 {Naturally not
16 cxd3? which would have been quite inconsistent. The Pawn on
c2 is unimportant, and Black only wastes precious time by
capturing it.} 16...Rxc2 17.Rae1 $1 {White continues his
overprotection without much ado.} 17...a5 {This counterattack
has no punch. Black would naturally like to get a passed Pawn
plus a Rook on the seventh, but it is too late for that.}
18.Kd1 $1 {Now the menaced Rook must scurry back, for capture
on a2 would be much too dangerous.} 18...Rc6 $1 {At last,
Black gets the right idea: overprotecting his Pawn at e6. But
it is already too late.} 19.Re2 Ke7 {Introduced into
tournament play by myself. See note to White's 14th move. The
King overprotects e6.} 20.Rhe1 Re8 $1 21.Nf3 $1 {Completing
the overprotection of e5 and thus deciding the fate of the
game. Black has no defence. Note the aesthetic effect created
by White's position.} 21...Bf8 {Now Black threatens to
complete the overprotection of e6 by playing Ng7. But White
has prepared a brilliant combination.} 22.g4 $1 {Much stronger
than the obvious Bg5+ etc.} 22...hxg4 23.Qh7 $1 {Now one
clearly realizes the masterly understanding of position which
went into White's eighth move (Qh2!).} 23...gxf3 {Had Black
continued overprotecting by 23...Ng7 there would have followed
24.Bg5+ f6 25.Bxf6+ Kf7 26.Ng5 mate. Black's basic error was
that he started overprotecting much too late.} 24.Bg5# {One of
my best games! I am proud of it if only because Herr
Systemsson is one of the strongest Scandinavian players. The
game made an overwhelming impression on the players and
spectators as well as on my opponent. The game has become
famous in Denmark as "the immortal overprotection game."} 1-0




Despite Kmoch's humorous exaggeration of Nimzowitsch's ideas about overprotection, a very recent top-level game brought Kmoch's parody to mind; namely, it was Caruana's destruction of Topalov during his unbelievable winning streak at the ongoing Sinquefield Cup 2014. In particular, if we compare the position after "Nimzowitsch's" move 21 above with that after Caruana's move 22 below, we see that Caruana has a similar array of forces buttressing the e5 pawn that clamps down on Topalov's position (though not the extreme-to-the-point-of-silliness buildup of every single piece directly supporting it).

[fen ""]
[Event "Sinquefield Cup"]
[Site "Saint Louis USA"]
[Date "2014.09.02"]
[EventDate "2014.08.27"]
[Round "6"]
[Result "1-0"]
[White "Fabiano Caruana"]
[Black "Veselin Topalov"]
[ECO "B46"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "61"]

1.e4 c5 2.Nf3 e6 3.d4 cxd4 4.Nxd4 Nc6 5.Nc3 a6 6.Nxc6 bxc6
7.Bd3 d5 8.O-O Nf6 9.Re1 Be7 10.e5 Nd7 11.Qg4 Kf8 12.Na4 Qa5
13.Re2 h5 14.Qf4 g5 15.Bd2 Qc7 16.Qg3 h4 17.Qg4 Rg8 18.Rae1 c5
19.c4 dxc4 20.Bxc4 Bb7 21.h3 Rd8 22.Bc3 Nb8 23.Re3! Nc6? 24.Bxe6!
fxe6 25.Rf3+ Ke8 (25...Kg7 26.Qh5 Rdf8 27.Rf6! Rxf6 (27...Bxf6 28.exf6+ Rxf6 29.Rxe6 Nd4 30.Qxg5+) 28.exf6+ Bxf6 29.Qxg5+ Kf8 30.Qxf6+ Qf7 31.Qh6+ Ke8 32.Nxc5) 26.Qxe6 Rg7 27.Qh6 Nd4 28.e6 Nxf3+ 29.gxf3
Bf8 30.Qh5+ Ke7 31.Bxg7 1-0


After Caruana's 22nd move, Topalov has no good way to create counterplay via a pawn break, because if the e5 pawn were to capture on f6, the power of his supporting pieces would be unleashed (as can be seen in the 25...Kg7 lines given above; 25...Kg7 was Topalov's original intent before he found the 27.Rf6! reply in his analysis). Because of that fact, Topalov's only productive try is to reroute his knight to d4; but he overlooked that 23.Re3! makes 23...Nc6? tactically unworkable.