Chunky vs. Smooth Strings

CJam, 19 bytes

q_1>_@.=:!1b\,d/4mO

100% chunky source code that calculates chunkiness.

Try this chunky goodness online.

How it works

q_                  e# Read from STDIN and push a copy.
  1>_               e# Discard the first character and push a copy.
     @              e# Rotate the original on top.
      .=            e# Vectorized comparison (1 if equal, 0 if not).
        :!          e# Mapped logical NOT (0 if equal, 1 if not).
          1b        e# Base 1 conversion (sum).
            \,      e# Swap with the shortened string and push its length.
              d/    e# Cast to double and divide.
                4mO e# Round to four decimal places.

Obviously, NaN rounded to 4 decimal places is 0.

Pyth, 13 12 bytes

csJnVztz|lJ1

Fully chunky code calculating chunkiness.

Demonstration. Test harness.

csJnVztz|lJ1
                 Implicit: z = input()
   nV            n, !=, vectorized over
     z           z
      tz         z[:-1]
                 V implitly truncates.
  J              Store it in J.
 s               sum J
c                floating point divided by
         |       logical or
          lJ     len(J)
            1    1

TI-BASIC, 46 bytes

Input Str1
If 2≤length(Str1
mean(seq(sub(Str1,X,1)=sub(Str1,X-1,1),X,2,length(Str1
Ans

sub(x1,x2,x3 gives the substring of string x1 starting (one-based) at number x2 and ending at number x3, then seq( builds a sequence.

Gives the smoothness value. The Ans variable is 0 by default, so we don't need an Else to the If statement, or to store anything to Ans beforehand.