Best case: 6-6 (3-6)
The Bears crawled to a bowl game with Jared Goff and a fleet of talented receivers experienced in the Bear Raid so I don't think the ceiling is very high in 2016 as they try to replace those pieces. I will be pretty impressed if Sonny Dykes can get this team back to a bowl while reloading at the program's most-important positions.
Their non-conference schedule is tricky as they play Hawaii in Australia, at San Diego State host Texas, but if all goes right, they could run that table. In-conference is tougher as they miss Arizona and Colorado from the South (probably the division's worst teams) and face the North field. I think if they can lean on a nice run game with their talented trio of backs and underrated offensive line, the Bear Raid reloads with new personnel and the defense can keep it at least a little together, they can win a few Pac-12 games and get to a bowl game.
The key will be making sure they win at Oregon State to ensure they avoid the North cellar and then find a couple of in-conference upsets, likely at home against schools like Oregon, UCLA, Utah and Washington.
Worst case: 1-11 (0-9)
Before you sling your arrows, I reiterate this is a worse case scenario and the Bears are just a few years away from this exact record. Things could get really ugly with Cal's schedule if they can't reload at quarterback and receiver and their defense doesn't step up with their schedule. There is a good chance they won't be favored in two of their non-conference games and the only Pac-12 game they will probably be favored in (Oregon State) will be on the road.
Someone is going to have to have a really rough season in the Pac-12 and the Bears could be that team.