In discussing how well the Rays are doing this year with their +95 run differential, ESPN's Tim Kurkjian said that they probably will not break the season record held by the 1927 Yankees of 371 (actually they had 376). But the 1939 Yankees had a run differential of 411. That is the record. They scored 967 while allowing 556.
As I pointed out a couple of weeks ago with Explaining The Rays Fast Start, the Rays are probably doing so well due to their performance with runners on base. Their overall OPS differential is only .084. Their hitters have a .737 OPS while their pitchers have allowed a .653 OPS. Based on an old regression I ran, the equation was
Pct = .5 +1.21*OPSDIFF
That predicts the Rays to have just a .602 pct for about 24 wins, not the .725 and 29 wins they actually do have. With runners on base, the Rays have a .831 OPS while allowing their opponents a .604 OPS.