Python / C, 136 chars, 136/2^((2-1)/4)=114.36191

#include <stdio.h>
#define print puts
#define pass int main (int argc, char **argv) {
#define False }
pass
print("Hello world!");
False

17 languages, 38.4167

1. (Literate) Agda
2. C
3. C++
4. Objective-c
5. CoffeeScript
6. Brainf***
7. (Literate) Haskell
8. Julia
9. Nim
10. Perl
11. PHP
12. Python
13. Raku
14. Ruby
15. Rust
16. *sh (sh, bash, zsh, ...)
17. fish

 #/*/**/if 0//<?php echo "\r";/*
 #[
 ###
 #`{{
 #=
q="""" ":" "=;q^"
true||\
=begin
 ###
 #*/
 ###]#
echo "Hello world!";##[]
exit
/* :' 
 ###
 #*/
 ###
("\n\r");?>
++++++++++[>+++++++>++++++++++>+++>+<<<<-]>++.>+.+++++++..+++.>++.<++++++++.--------.+++.------.--------.>+.>..>[
 #endif
 #include<stdio.h>
int main(){printf("Hello world!\n");return 0;}
 #if 0
 ###
 console.log "Hello world!"
 ###
=#
println("Hello world!")
 #=
\begin{code}%
open import Agda.Builtin.IO
open import Agda.Builtin.String
data Unit : Set where
  tt : Unit
{-# COMPILE GHC Unit = data () (()) #-}
postulate
  putStrLn : String -> IO Unit
{-# FOREIGN GHC import qualified Data.Text as T #-}
{-# COMPILE GHC putStrLn = putStrLn . T.unpack #-}
\end{code}%
\begin{code}
main = putStrLn "Hello world!"
\end{code}
=end
" """
 #}}
 # ^;
print("Hello world!");
 # =###
 #*/[doc=r"\"]#[doc="
 #endif //"]fn main(){println!("Hello world!")}//[]#]## #'

Explanation

Setanta & Vyxal 3, score = 37.840338686417155 (45 bytes)

>--"Hello World!",#Q(
scriobh("Hello World!")

Try it Online!

try-setanta.ie link

JavaScript (Node.js) / brainfuck , score: 88.29

console['log']("Hello, World!")+"[-->-[>>+>-----<<]<--<---]>-.>>>+.>>..+++[.>]<<<<.+++.------.<<-.>>>>+."

Try it online (JavaScript)

Try it online (brainfuck)

TI-BASIC and Pyth, 13/2^((2-1)/4)=10.93

"Hello World!

puts "Hello world!"

Works in Ruby and Tcl

Madbrain and [insert most BF derivatives here], 272 227 bytes

Just posting for fun, not to win c:

956658555658
852224222254
************
c4993c839941
1****1**+**+
01cc70776ccc
g+11+g++*11
 c003 c3c00
 1gg* 1*1gg
 0  c 0c0
 g  1 g1g
    0  0
    g  g[-]+[-->-[>>+>-----<<]<--<---]>-.>>>+.>>..+++.>>.>.<<<.+++.------.<<-.>>>>+.

NOTE: There is no TIO for Madbrain, so you'll have to trust me on this one. I did, however, write an (admittedly not really well-written (but hey, at least it works!)) interpreter for Madbrain, which is on the esolangs wiki.

Explanation

Madbrain sees: (I wrote this code c:)

956658555658
852224222254
************
c4993c839941
1****1**+**+
01cc70776ccc
g+11+g++*11
 c003 c3c00
 1gg* 1*1gg
 0  c 0c0
 g  1 g1g
    0  0
    g  g

I admit, Madbrain reaches the BF code, but it doesn't do anything, so I didn't include it here.

Brainfuck (and a lot of BF derivatives) sees:

++++++[-]+[-->-[>>+>-----<<]<--<---]>-.>>>+.>>..+++.>>.>.<<<.+++.------.<<-.>>>>+.

BF ignores everything that isn't ><+-.,[], so it ignores most of the Madbrain code. However, there are some +s in the Madbrain code (that's what the ++++++ is), so you need to add [-] after that which sets the current cell to 0.

The code after ++++++[-] is the code for printing Hello World!.

ES8, Japt, TeaScript, C#, C++, C, ESMin, score: ~8.8

main=_=>"Hello World!"();

ES8, TeaScript and Japt see "Hello World!".

JavaScript ES6, Oration, Vitsy, Minkolang score = 71.94703045766462

121 / 2^(3/4). Fun fact? I'm not trying to win, just to add as many languages as possible.

222 //X>"!dlroW olleH"Z 
shush=0
alert("Hello World!")
sorry=`
listen
capture Hello World!`
$$$
=` >###      .O$r"!"rXr<`

What Vitsy sees

"Well, I'm a 1D language, so... for now, only the first line counts."

222 //X>"!dlroW ,olleH"Z
222                      push three twos
    //                   divide twice
      X>                 drop the result and carry on
        "!dlroW ,olleH"Z standard Hello, World! program

Thanks for the cookie, Vitsy :3

What JavaScript ES6 sees

222 //X>"!dlroW ,olleH"Z

"Let's see... You put the number 222 and then put something in a comment. Alright, sure, I'll roll with that."

shush=0

"You made a variable. Noted."

alert("Hello, World!")

"Ah, I see where you're going with this. I'll display that."

sorry=`
listen
capture Hello, World!`

"Oo! A multiline string! Now we're talking, ES6 rulez, ES5 drools!"

(EOF)

"Well, I'm done. Peace out."

What Oration sees

222 //X>"!dlroW ,olleH"Z

"This wasn't on my notes...! Best not do anything."

shush=0
alert("Hello, World!")
sorry=`

"Oh, here's some extra notes."

listen

"Listen..."

capture Hello, World!`

"...Hello, World!"

(EOF)

"thinks Nothing more! Great, I'm done here. breathes deeply"

Minkolang explanation

(Too lazy to create narrative. Might do later, the code took a while.) Irrelevant code replaced with # or omitted. Also, added comments C ... C.

222 ###>"!dlroW olleH"# 
$$$  C this separates layers C
###>### #####.O$r"!"rXr<`

Layer 1, pt 1

222 ###>"!dlroW olleH"# 
222                      C push three 2s C
   _                     C space; fall to the next layer C

Layer 2, pt 1

###>### #####.O$r"!"rXr<`
   >                       C go this way C
       _                   C fall to the next (first) layer C

Layer 1, pt 2

222 ###>"!dlroW olleH"# 
       >"!dlroW olleH"   C go right and push those characters in that order C
                       _ C fall to the next layer C

Layer 2, pt 2

###>### #####.O$r"!"rXr<`
                       <  C starts here, going left C
                      r   C reverse stack C
                     X    C pop n (n = 2), and pop top n items on stack (2, 2) C
                    r     C reverse stack C
                 "!"      C push exclamation mark (for some reason, it's chopped off C
                r         C reverse stack C
              $O          C output stack as characters C
             .            C terminate program C

CoffeeScript and CJam, 46/2^((2-1)/4)=38.68

e###
"Hello, World!"
e###alert "Hello, World!"

Score of 0.84

H

Works in H9+ and HQ9+.

1 / 2 ^ ((2 - 1) / 4) = 0.84

print("Hello World!")

Works in at least Julia, Perl, PHP, Python2, Python3, Qbasic, R, Ruby ...

'Hello World!'

Runs in several scripting languages, including PHP, GolfScript, APL, ...