Let A not equal A(1), A(2), I-2m be an irreducible Artin-Tits group of spherical type. We show that the periodic elements of A and the elements preserving some parabolic subgroup of A act elliptically on the additional length graph C-AL (A), a hyperbolic, infinite diameter graph associated to A constructed by Calvez and Wiest to show that A/Z(A) is acylindrically hyperbolic. We use these results to find an element g is an element of 2 A such that < P, g > congruent to P * < g > for every proper standard parabolic subgroup P of A. The length of g is uniformly bounded with respect to the Garside generators, independently of A. This allows us to show that, in contrast with the Artin generators case, the sequence {omega(A(n), S)}(n is an element of N) of exponential growth rates of braid groups, with respect to the Garside generating set, goes to infinity.