Why would the agents need flight stats when they are likely to have a very good flight information system. Of course the issue lies when aircraft are in holds etc and were all expected in at the same time.
I have no doubt they are also linked in to the ground radar so they would be able to see the likelyhood of which aircraft it likely to be on stand first.
I'm guessing if an aircraft is early then the team expected to turn it round maybe stuck on another aircraft. Also if a plane is late then you have to deal with that delayed aircraft as soon as possible.
In an ideal world with endless pot of money to dip in for turnaround teams to be sat around waiting for an aircraft to arrive so it's on stand immediately however things have changed and there is likely to be very little slack in the system when things go off schedule.