  We prove that the exponential growth rate of the regular language of
penetration sequences is smaller than the growth rate of the regular language
of normal form words, if the acceptor of the regular language of normal form
words is strongly connected. Moreover, we show that the latter property is
satisfied for all irreducible Artin monoids of spherical type, extending a
result by Caruso.
  Our results establish that the expected value of the penetration distance
$pd(x,y)$ in an irreducible Artin monoid of spherical type is bounded
independently of the length of $x$, if $x$ is chosen uniformly among all
elements of given canonical length and $y$ is chosen uniformly among all atoms;
the latter in particular explains observations made by Thurston in the context
of the braid group, and it shows that all irreducible Artin monoids of
spherical type exhibit an analogous behaviour. Our results also give an
affirmative answer to a question posed by Dehornoy.
