We study the average number of transitions in Glushkov automata built from random regular expressions. This statistic highly depends on the probabilistic distribution set on the expressions. A recent work shows that, under the uniform distribution, regular expressions lead to automata with a linear number of transitions. However, uniform regular expressions are not necessarily a satisfying model. Therefore, we rather focus on an other model, inspired from random binary search trees (BST), which is widely used, in particular for testing. We establish that, in this case, the average number of transitions becomes quadratic according to the size of the regular expression.