You saw them together in the dugout in New York or Baltimore or Texas, chatting quietly for 15 minutes or so before the beginning of batting practice. Wil Myers, the hotshot rookie, and Ben Zobrist, the level-headed veteran, talking about their faith, family, baseball, life in the big leagues, where to eat after the game, anything. It was Myers who, not long after his much-anticipated promotion to the Rays, approached Zobrist about the pregame meetings. “I asked him if we could set aside 10 to 20 minutes just to talk about what’s going on with our lives, how we can help each other,” Myers said. Zobrist was impressed with both the request and what he learned about his 22-year-old teammate during their journey through the remainder of the season and to the playoffs. “He’s got his head on right,” Zobrist said. “He was very balanced for a rookie.” And that, as much as Myers’ talent at the plate and on the field, is why he is the favorite to win the Baseball Writers’ Association of America’s American League Rookie of the Year Award when the results are announced Monday. “He’s not afraid to succeed,” Rays pitcher Chris Archer said. “He believes in himself enough to not be overwhelmed with a bad game or a bad couple of weeks.” Archer is a finalist for the award along with Detroit shortstop Jose Iglesias. But Myers is expected to become the third Ray to win rookie of the year, joining Evan Longoria (2008) and Jeremy Hellickson (2011).