The PPCG Handicap System

Mathematica, 244.719 (245 bytes)

f[l_,n_]:=x/.Solve[d=Rest@Import@"QueryResults.csv";LinearModelFit[#.#2/Tr@#&@@{#~Max~-1&/@#4+1,#3}&@@Thread@#&/@{#,#~Cases~{_,l,__}}&/@d~GroupBy~Last/@#[[;;,1,5]],x,x,Weights->Tr/@#[[;;,;;,4]]]&[d~Cases~{_,l,_,v_/;v>=0,_}~GatherBy~Last]@x==n,x]

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Test case

f["mathematica", n]   (* { .820033 (n + 53.4263) } *)
f["mathematica", 245] (* { 244.719 } *)

What about other languages?

f["c++", n]           (* { .821181 (n - 79.5437) } *)
f["java", n]          (* { .717579 (n - 56.0858) } *)
f["cjam", n]          (* { 2.21357 (n + 2.73772) } *)
f["pyth", n]          (* { 4.52194 (n - 8.82806) } *)

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Alternative model: \$\log(c)=\log\left(\frac{n-B}V\right)\$

One notable feature of code golf (and probably other coding problems) is that the distribution of the lengths of programs tends to be exponential distribution (in contrast to uniform distribution). Hence model \$\log(n)=\log(Vc+B)\$ is much more likely to balance the influences between points with large \$c\$ and small \$c\$.

As we can see in the graphs below, the distribution of points are suitable for fitting in logarithmic scale.

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Results of the new model

Language       V       B

Python       1.365   -19.4    
Javascript   1.002     1.6
Ruby         0.724     1.7
Perl         1.177   -32.7
C            1.105     1.5
Haskell      1.454   -24.5
Mathematica  1.319   -39.7
PHP          1.799   -62.0
Java         1.642     4.4
C#           1.407     4.5

CJam         0.608   -12.5
Pyth         0.519   -11.4
Golfscript   0.766   -18.0
J            0.863   -21.4
APL          0.744   -17.7
K            0.933   -23.3
Retina       1.322   -37.9
MATL         0.762   -13.3
Jelly        0.965   -23.8

We have found two exceptional language - Ruby with \$V=0.72\$` and Retina with \$V=1.322\$, and a criterion of being a popular golfing language - having a large negative boilerplate.

Python3, 765.19 (765) bytes

Probably some room for golfing here. Requires numpy for matrix stuff. Reads from stdin, formatted as follows: [lang] [bytes/n]. Stops when you send q.

import numpy as n,csv
L={};Q={};X={};D=n.dot;f=open('QueryResults.csv',encoding="utf8");R=csv.reader(f);f.readline();Z=list.append;M=n.matrix
for r in R:
 if r[1] not in L:L[r[1]]=[]
 if r[4] not in Q:Q[r[4]]=[]
 Z(L[r[1]],r);Z(Q[r[4]],r)
for l in L:
 b=[];a=[];v=[];t=[]
 for r in L[l]:
  if int(r[3])>-1:
   Z(b,int(r[2]));o=[]
   for q in Q[r[4]]:Z(o,int(q[2]))
   Z(a,sum(o)/len(o));Z(v,int(r[3])+1)
 for k in a:Z(t,[1,k])
 if len(t)<1:continue
 A=M(t);T=A.transpose();W=n.diag(v);y=M(b).reshape((len(b),1));e=D(D(T,W),A)
 if n.linalg.det(e)==0:continue
 i=n.linalg.inv(e);X[l]=D(i,D(D(T,W),y))
p=input()
while(p!="q"):
 S=p.split()
 if S[1]=='n':print("(n-("+str(X[S[0]].item(0))+"))/"+str(X[S[0]].item(1)))
 else:print(str((int(S[1])-X[S[0]].item(0))/X[S[0]].item(1)))
 p=input()

Results

I might have done something wrong at some point; I get different results than the Mathematica answer:

python3 808 -> 765.19
python3 n   -> (n-(32.41))/1.01

c++ n        -> (n-(71.86))/1.17
cjam n       -> (n-(-14.09))/0.51
java n       -> (n-(18.08))/1.64
pyth n       -> (n-(1.42))/0.28
jelly n      -> (n-(-4.88))/0.34
golfscript n -> (n-(-0.31))/0.44