Crazy Librarian's Amazing Sorting System

APL (132)

{⎕ML←3⋄⍵[⍋{2='R'+.=↑¨⍵⊂⍨⍵≠' ':!99⋄↑(+/⍎¨'0',⍵⊂⍨⍵∊⎕D)-⍨((+/∊1.5 1×(⍳×∊⍨)∘⍵¨G)-+/⍵∊(⎕UCS 32+⍳94)~'`',⎕D,∊G←(⊂⎕A),⊂⎕UCS 96+⍳26)÷⍴⍵}¨⍵]}

Since everyone else is doing the same thing, this too is a function that takes an array of titles and returns it sorted, e.g.:

      titles
┌─────────────┬──────────────────────────────────────┬────┬────────────────┬───────┬────┬────┬────┬───────────┬──┬───────┬───┬───┐
│War and Peace│Reading Rainbow: The Best Unicorn Ever│Maus│Home for a Bunny│Matthew│Mark│Luke│John│Revelations│42│9 Kings│1:8│7th│
└─────────────┴──────────────────────────────────────┴────┴────────────────┴───────┴────┴────┴────┴───────────┴──┴───────┴───┴───┘
   
      {⎕ML←3⋄⍵[⍋{2='R'+.=↑¨⍵⊂⍨⍵≠' ':!99⋄↑(+/⍎¨'0',⍵⊂⍨⍵∊⎕D)-⍨((+/∊1.5 1×(⍳×∊⍨)∘⍵¨G)-+/⍵∊(⎕UCS 32+⍳94)~'`',⎕D,∊G←(⊂⎕A),⊂⎕UCS 96+⍳26)÷⍴⍵}¨⍵]}titles
┌──┬───┬───────┬───┬─────────────┬────────────────┬────┬────┬───────────┬────┬───────┬────┬──────────────────────────────────────┐
│42│1:8│9 Kings│7th│War and Peace│Home for a Bunny│Mark│John│Revelations│Luke│Matthew│Maus│Reading Rainbow: The Best Unicorn Ever│
└──┴───┴───────┴───┴─────────────┴────────────────┴────┴────┴───────────┴────┴───────┴────┴──────────────────────────────────────┘
  
  
  

Explanation:

• ⎕ML←3: set ⎕ML to 3 (for ⊂)
• ⍵[⍋{...}¨⍵]: sort the input by the values returned from the inner function
  • ↑¨⍵⊂⍨⍵≠' ': get the first character of each word
  • 2='R'+.=: see if two of these are 'R'.
  • :!99: if so, return 99! (≈ 9.3×10¹⁵⁵). This is not quite infinity, but it'll do: a title can never have a score more than 38 times its length (ZZZZ...), so as long as no single title is bigger than about 2×10¹³⁰ yottabytes, it is guaranteed that these will be at the end.
  • ⋄: otherwise:
  • (...)÷⍴⍵: divide the score by the length of ⍵ after calculating it:
    • G←(⊂⎕A),(⎕UCS 96+⍳26): store in G the uppercase and lowercase letters
    • (⎕UCS 32+⍳94)~'`',⎕D,∊G: the printable ASCII characters, except letters, digits, spaces and '`', which are the characters for which a point is subtracted. (This is shorter than writing them all out, because G is used later on.)
    • +/⍵∊: count the amount of these characters in ⍵
    • -: subtract this from:
    • +/∊1.5 1×(⍳×∊⍨)∘⍵¨G: the sum of 1.5 × the scores for the capitals, and 1 × the scores for the lowercase letters.
  • -⍨: afterwards, subtract the total of the numbers in ⍵:
    • ⍵⊂⍨⍵∊⎕D: find the groups of digits in ⍵
    • '0',: add '0', to prevent the list being empty
    • ⍎¨: evaluate each string
    • +/: find the sum

Lua 5.3, 366 364 Bytes

r={}for i,s in ipairs(arg)do n=0 s:gsub("%l",function(a)n=n+(a:byte()-96)end):gsub("%u",function(a)n=n+(a:byte()-64)*1.5 end):gsub("%p",function(a)n=n-1 end):gsub("^R?.- R.- ?R?",function()n=math.huge end)m=n/utf8.len(s)s:gsub("%d+",function(a)m=m-a end)table.insert(r,{s=s,n=m})end table.sort(r,function(a,b)return a.n<b.n end)for i,v in ipairs(r)do print(v.s)end

This code only works in Lua 5.3 because it needs to deal with Unicode characters. If you don't care about Unicode, then replace "utf8" with "string" and it will work fine with Lua 5.2 or 5.1.

It takes its inputs from command-line arguments, so either run it from the command line or put this code above my answer:

arg = {"Title 1", "Title 2", "Title 3"}

JavaScript (ES6), 210 218 251

As a function with an array argument, returned sorted.

f=L=>(S=s=>([...s].map(c=>t-=(a=s.charCodeAt(l++))>32&a<48|a>57&a<65|a>90&a<96|a>122&a<127?1:a>64&a<123?96-(a<96?a*1.5:a):0,l=t=0),s.split(/\D/).map(n=>t-=n,t/=l),t/!s.split(/\bR/)[2]),L.sort((a,b)=>S(a)-S(b)))

//TEST

test1=['War and Peace','Reading Rainbow: The Best Unicorn Ever','Maus','Home for a Bunny']
test2=['Matthew','Mark','Luke','John','Revelations']
test3=['42','9 Kings','1:8','7th']

;O.innerHTML=f(test1)+'\n\n'+f(test2)+'\n\n'+f(test3);

// The comparing function used to sort, more readable

Sort=s=>(
  t = 0, // running total
  l = 0, // to calc the string length avoiding the '.length' property
  [...s].map(c=>{
    a=s.charCodeAt(l++);
    t-=a>32&a<48|a>57&a<65|a>90&a<96|a>122&a<127
      ? 1 // symbols (ASCII char except space, alphanumeric and backtick)
      : a>64&a<123 
        ? 96-(a<96?a*1.5:a) // alphabetic both upcase and lowcase, and backtick
        // lowcase: 96-a, upcase (64-a)*1.5=>96-a*1.5, backtick is 96 and 96-96 == 0
        : 0 // else space, non ASCII, and numeric : 0
  }),
  t = t/l, // average
  s.split(/\D/).map(n=>t-=n), // sub number values
  f = s.split(/\bR/)[2], // split at words starting with R, if less then 2 f is undefined
  t/!f // dividing by not f I can get the infinity I need
)

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