I guess the prefactor varied depending on which scale I was using for the other pieces (E.g. the 'classical' N=300 or Kaufman N=325).
If I would have to invent a name for the equation I would call it the "Short-range leaper law".
Formula To Estimate a Leaping Piece's Value
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Great! that's a good name. Now I also understand the purpose of the "prefactor".
Muller's Short-Range Leaper Law:
Value = α[30.0(N) + 0.625(N)²], centipawns
α = factor based on scale for other pieces
α = factor based on scale for other pieces
(1.0: classical, i.e. knight = 300; 1.1: Kaufman, i.e. knight = 325)
N = squares attacked
N = squares attacked
Now, we need the law for sliding pieces. 
I believe Muller's Short Range Leaper Law predicts values for both congested and non-congested situations. It is based on simulated games, so includes a range of densities over the course of a game. This is the same as the system for giving values to standard chess pieces (1,3,3,5,9). But when playing, position and other strategy need to be included in addition to points.
I'm sure you are right that some pieces might be weak in some situations, such as a knight not being able to capture a pawn that threatens it. On the other hand, a knight can jump over pawns to attack pieces that might be more valuable than the pawn. So there may be ways to imrove on valuations based on the Short Range Leaper Law. But to do it generally for all types of leapers, and to prove it is more accurate I think will take some very good chess theorists and mathematicians, with a lot of work. My estimate is the Muller Short Range Leaper Law will hold for about a decade until another system is indisputably proven to be more accurate. But I can be wrong.
How short does the range of a piece have to be for this to apply? And what about pieces that are restricted to a fraction of the board, such as the camel?
I assume this is meant to apply to an 8x8 board, but how would it change if the board were bigger?
Good questions. I believe the camel is a 1,3 jumper. If that's correct, there's only 4 squares on an 8x8 board where the camel has its full attacking ability. So my guess it is already near the limit of what is a close-range leaper for this formula to be accurate.
Also I'm sure the formula won't work for leapers like the Alfil-rider and the Huygens. They have unlimited attacking squares (N = ∞), so the formula would predict infinite value, but this is of course wrong.
For bigger boards, I've seen many people say the value of jumpers goes down (compared to a bishop for instance), because they can't travel across quickly, but I've never seen this actually demonstrated with data.
Any links to forums where this has actually been studied and proven would be appreciated.
I'm not aware of any other formulas to help predict piece values, nor any place that has a concise summary of variant chess piece values. But if you look for info on a single type of piece, you can usually find info (reliable or not) scattered in different places. It's all a big mess of confusing information and that's why I like variant chess games.
'Short range' here means up to two King steps away. So pieces like Camel are not included. The formula was derived by fitting empirical values measured on an 8x8 board; on such a board a Camel is practically useless. When I tested Camels, they would always get lost without compensation in the end-game, if they survived that long. The only reason they were worth anything is that there was a good chance you could fork two minors with them,and then trade it for one. On larger board this would probably be better. But pieces that have only long leaps have very poor manoeuvrability. On a piece that also has enough short-range moves, the longer leaps might be worth nearly as much as other moves, if the board is big enough to contain most of them.
I've applied this formula for sliders and it seems accurate if you divide by two the number diagonal moves.
Calculating N for a slider:
N=R+R'+R''+...
R=T*c/β
T=number of squares in a same row on a 9x9 board (9x9 for simplicity)
c= number of different colors in a row (1 or 2)
β=total posible square colors in the board (2)
obatined values:
Queen Rook Bishop
1080 640 280
Now let's calculate this for a bishop, a queen and a rook.
N(B)=R*4
R=4*1/2
N(B)=1/2*(4*2)
N(B)=8
B=(30+8*5/8)*8
B=280
N(Q)=(R*+R')*4
R=4*2/2
R'=4*1/2
N(Q)=(4+2)*4
N(Q)=24
Q=(30+24*5/8)*24
Q=1080
N(R)=R*4
R=4*2/2
N(R)=16
R(ook)=(30+16*5/8)*16
R(ook)=640
2) piece value = 31.5(N) + 0.66(N)²
3) piece value = 33.0(N) + 0.69(N)²
2) "Muller's Formula for Chess Pieces"
3) "Muller's Theorum on the Inter-Dynamic-Relationship of Fairy Chess Pieces on a Checkered Gameboard"