From Elias:
Chris Davis has 16 RBI this season, the highest total through 4 team games since RBI became official in 1920. The previous record was 12 RBI through 4 games, by Dolph Camilli (1935 Phillies), Mark McGwire (1998 Cardinals) and Charles Johnson (2000 Orioles).
from ESPN:
Chris Davis has hit a home run in each of his first four games this season, and has hit 11 in his past 11 regular season games dating back to last season. Of those 11, seven were off off-speed pitches to the outer half of the plate.