WAIT STATS - high Wait Time on ASYNC_IO_COMPLETION
As mentioned


  The value for wait count is very low compared to all the other wait
  types (the lowest)


the count being only 9, i.e. the wait has only showed up for 9 times, during the run of gathering wait stats for a complete day, wont be a concern here for me.

However, its worth checking the other wait types BACKUPIO and BACKUPBUFFER .

This wait type generally shows up when you are taking the backup over the network with not a good NW connectivity or on the tape etc (i.e. any other extremely slow backup system)

We had this similar wait on one of our SQL server 2005 for backing up the database approx 200 GB in size. As the size being large and we did not had compression feature available at that time, witness lots of waits. we had to go with third party compression tool and saw those wait types count going down.So i believe it could be a good start if you start checking on the backups. Make sure you use the SQL server compression feature for backing up the databases.

However just to check if this wait type is causing any problems, you need to check for any issues in backup throughput.

May be you can go around and test the backups by doing native backups on same network as compared to other network and check for other counter values.

Also, you can refer A cause of high-duration ASYNC_IO_COMPLETION waits for more explanation by Paul on this wait.