The new 2016 Schedule is out! The new 2016 Schedule is out! Forgive us for channeling Steve Martin's Navin R. Johnson character from The Jerk. But the MLB 2016 schedule is out. The Red Sox will play the following National league teams at Fenway: the Giants, the Braves, the Rockies, and the Diamondbacks. In addition, the Sox will play the Dodgers, Giants, Braves snd Padres on the road next year. The full schedule can be seen HERE.