 Solution

Represent the ranking criteria by a tuple in decreasing priority:

type Weight = (Int,Int,Int)

weight :: Results -> Weight
weight (Results _ scores) =
  (sum (map points scores),
   sum [gf - ga | (gf,ga) <- scores],
   sum (map fst scores))
  where
    points (gf,ga)
      | gf > ga   = 3
      | gf == ga  = 1
      | otherwise = 0

The components are total points, total goal difference and total goals scored. The Haskell Ord class compares tuples in lexicographic order, so a greater first component dominates all later components; only ties reach the next criterion. Exactly equal triples remain tied because no further ranking criterion was specified. In the supplied fixture data the descending triples are $(6,13,15)$, $(4,3,5)$, $(3,0,3)$, $(1,0,0)$, $(1,-3,4)$, $(1,-3,0)$ and $(0,-10,0)$, respectively for United, Athletic, City, Albion, Rovers, Corinthians and Thistle.