Domain administrators have full visibility to the message statistics for their services. 

The following statistics are available:

Email Gateway / MX Backup / Email Forwarding

You can access the logs in the User Portal

Under each configured email service you will be able to click on the View Message Log button. 

Once you are viewing the logs, there is a statistics button on the navigation bar. 

And then you will have access to the graphs and statistics about your mail delivery.