  We prove that, for any irreducible Artin-Tits group of spherical type $G$,
the quotient of $G$ by its center is acylindrically hyperbolic. This is
achieved by studying the additional length graph associated to the classical
Garside structure on $G$, and constructing a specific element $x_G$ of $G/Z(G)$
whose action on the graph is loxodromic and WPD in the sense of
Bestvina-Fujiwara; following Osin, this implies acylindrical hyperbolicity.
Finally, we prove that "generic" elements of $G$ act loxodromically, where the
word "generic" can be understood in either of the two common usages: as a
result of a long random walk or as a random element in a large ball in the
Cayley graph.
