As I understand it there's a number of variables that regulate Roberts flow:
River Call: When the South Platte is free or under a very junior call, I wouldn't expect Denver to use the Roberts. You can check calls here: Colorado's Decision Support Systems
Cheeseman outflow: Cheeseman and the Roberts seem to operate hand-in-hand; when outflow from Cheeseman is high, Roberts is low or off; when outflow from Cheeseman is low, Roberts is more often on. Below Cheeseman gage: Detail Graph
Denver Weather: When Denver is hot and it hasn't rained for a few days, the Roberts is more likely to be on.
Reservoir levels are mixed in on this website: Division
In general: Dry years = more Roberts Tunnel, Wet years = less Roberts Tunnel
Good article on the Roberts: ftp://dwrftp.state.co.us/cdss/swm/tm...s_20040406.pdf