We show that for any rooted directed tree T, its reversible pebble game number is always just one more than the edge rank coloring number of the underlying undirected tree U of T. It is known that given a DAG G as input, determining its reversible pebble game number is PSPACE-hard. Our result implies that the reversible pebble game number of trees can be computed in polynomial time. Using this connection as a tool, we also address several questions including that of finding the number of steps required to optimally pebble various families of trees.