Matt Eddy of Baseball America has a great article on the specialized situation of left handed relievers dominating against left handed batters.
The reason more teams have left handed specialists in their bullpens (those players whose job is to get out one or two left handed batters in key situations) is that statistically this match up works.
The basic stats:
Platoon Split, 2011-13
SO%
Left-on-Left
22.8%
Right-on-Right
20.0%
Major League Average
19.4%
Batter Advantage
18.5%
Platoon Split, 2011-13
ISO
Left-on-Left
.118
Right-on-Right
.140
Major League Average
.146
Batter Advantage
.154
Platoon Split, 2011-13
AVG
Left-on-Left
.235
Right-on-Right
.249
Major League Average
.254
Batter Advantage
.261
The open question is why are so many lefty pitcher more dominate against lefty hitters than their righty on righty counterparts?
First, there are more right handed pitchers in baseball. Nine out of ten people are right handed.
Second, as such, right handed hitters are more plentiful than left handed hitters.
Third, right handed hitters get more practice hitting against right handed pitchers so their ability to get contact is improved (thus a higher batting average).
With a batter advantage (a right handed hitter against a left handed pitcher) is a matter of sight lines; the ball is being thrown from an area across the plate toward the strike zone. This open view of the pitch allows for quicker adjustment by a batter than a pitch coming toward him directly (inside).
Every team bullpen now has at least one lefty specialist.