Marble thrones at the Theatre of Dionysus

There are 67 of these marble thrones around the edge of the orchestra, inscribed with the names of the dignitaries that occupied them. They are thought to be Roman copies of earlier versions. At the centre of this row of seats (out of shot) was a grand marble throne reserved for the priest of Dionysus.
There is a cunningly constructed drain hole on each throne that leads from the top to the front (you can see the staining where water has passed), I wonder if this arrangement is multi-purpose (especially since it doesn't seem to rain much in Athens).