The group of Mark Buehrle, Jake Peavy, Gavin Floyd, John Danks and Freddy Garcia is so crucial to the team's success that they will stay as close to on schedule as humanly possible.
"I really could tell you the whole Spring Training, if nobody gets hurt," said Cooper, sitting in his golf cart and watching workouts on Thursday. "We have some split-squad games, and we might have some 'B' games. You never know. Maybe Charlie Leesman or [Daniel] Hudson or [Carlos] Torres or [Daniel] Cabrera will get a start there, in those situations.
"Otherwise, our starting pitchers will be doing all the starting."
Floyd gets the opening call for the White Sox in Tuesday's "B" game against the Dodgers. Danks has the honor of Thursday's Cactus League opener against the Angels in Tempe, with a rare 4:05 p.m. CT first pitch.
The thought process for these opening two pitchers was fairly simple, according to Cooper.
"It's their day to throw," Cooper said.
Although the first full roster workout isn't scheduled until Friday, most of the position players were in camp on Thursday. That strong early turnout allowed the White Sox to go through their first round of live batting practice, with Peavy and Floyd each working two rounds against three hitters in each session.
One highlight was Peavy shattering Brent Lillibridge's bat, while Floyd continued to throw with impressive velocity, especially in the first week of Spring Training. Ozzie Guillen also pointed to Cabrera for his strong work in this debut session.
"I want him to worry about one pitch -- the fastball right in the middle of the plate, and then take care of the rest," said Guillen of the hard-throwing Cabrera, who struggled mightily with control issues last year for Arizona and Washington, walking 42 and striking out 23 in 51 innings. "I don't see why this kid with that kind of arm is bouncing around all over the place.
"Maybe too much coaching. Try to be perfect. Too much stuff. Here, our philosophy is throw as hard as you can, try to hit the middle of the plate and go for it."
Cooper listed Cabrera as one of the numerous candidates to fill definitely one spot in the bullpen, and the pitching coach said possibly two. That group includes Hudson, Torres, Sergio Santos, Freddy Dolsi, Lucas Harrell and left-hander Erick Threets, along with incumbent lefty specialist Randy Williams.
They will get plenty of work. But with the starting spring spots saved primarily for the big five, even extended innings usually will come in relief.
"Hudson is going to be getting as much work as we can get him to keep him stretched out," Cooper said. "The same thing goes with Harrell, Torres and Cabrera. We are giving them the best opportunity to show us what they can do.
"We really won't make the decision. They ultimately will make it. We are going to pick the 12th guy to best help us win games."
Scott Merkin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.