diff --git a/lib/matplotlib/font_manager.py b/lib/matplotlib/font_manager.py
index 91fe97e128f4..a0a695bf268e 100644
--- a/lib/matplotlib/font_manager.py
+++ b/lib/matplotlib/font_manager.py
@@ -1099,15 +1099,18 @@ def score_family(self, families, family2):
         Returns a match score between the list of font families in
         *families* and the font family name *family2*.
 
-        An exact match anywhere in the list returns 0.0.
+        An exact match at the head of the list returns 0.0.
 
-        A match by generic font name will return 0.1.
+        A match further down the list will return between 0 and 1.
 
         No match will return 1.0.
         """
         if not isinstance(families, (list, tuple)):
             families = [families]
+        elif len(families) == 0:
+            return 1.0
         family2 = family2.lower()
+        step = 1 / len(families)
         for i, family1 in enumerate(families):
             family1 = family1.lower()
             if family1 in font_family_aliases:
@@ -1117,12 +1120,11 @@ def score_family(self, families, family2):
                 options = [x.lower() for x in options]
                 if family2 in options:
                     idx = options.index(family2)
-                    return ((0.1 * (idx / len(options))) *
-                            ((i + 1) / len(families)))
+                    return (i + (idx / len(options))) * step
             elif family1 == family2:
                 # The score should be weighted by where in the
                 # list the font was found.
-                return i / len(families)
+                return i * step
         return 1.0
 
     def score_style(self, style1, style2):