Actually, it is the concentration you give to the mysteries.
It all works together.
There’s an old saying: The beads are for the sake of the prayers; the prayers are for the sake of the mysteries.
The beads occupy the hands, and help count the prayers, freeing the mind from counting. The prayers occupy the lips and free the mind from “self talk,” the inner monologue we are always carrying on, so that the mind can focus better on the mysteries.
The beauty of vocal prayer is explained by St. Thomas Aquinas: A vocal prayer is “complete” at the instant it starts. That is, the prayer is really located in the INTENTION, which is complete even before the words are said. Thus, there need be no anxiety that a prayer “doesn’t count” if the mind wanders during it. Many people are never able to concentrate, and many elderly people are less able to do so as they age. I have explained this in confession many times, to people who confessed that they were “distracted” during prayer.