Nico would start the year with Ryan Dull at closer, on the basis of his superior consistency. I think it's ... interesting to label a pitcher who has had one year and change in the big leagues more consistent than the guys behind him. In the absence of a strong opinion on this stuff, acknowledging that the roles change throughout the year based on performance, injuries, and a variety of other issues, and while generally reserving my right to protest that an inning is not a role, here is how PECOTA sees the relievers stacking up:

Best reliever: Liam Hendriks
Backup best reliever: Sean Doolittle
The next four: Ryan Madson, Ryan Dull, Santiago Casilla, Daniel Coulombe, Frankie Montas
The mopup guy: John Axford

Supposing that's a true statement of the actual abilities of those pitchers, here's what I'd do:

Designated ninth-inning guy: Madson
Andrew Miller role: Hendriks
Backup Andrew Miller / eighth inning: Doolittle
Middle relief, matchups, etc.: Dull, Casilla, Coulombe
Long relief: Montas
Mopup: Axford

Madson's plenty good enough to lock down the three-run leads in the ninth the A's will never have. Hendriks, if you believe PECOTA, is a beast, and he's a beast without any history of closing, so the team can plausibly just throw him to the wolves of the "no role" role without him complaining. The rest slot in basically as needed.

Obviously, religious faith in any one projection system isn't the best approach for your health, but you get the idea.