This is an excerpt from Baserunning by Mike Roberts & Tim Bishop.
As with right-handed hitters, most left-handed hitters stride as the pitch is delivered, although the angle may vary. The hitter may stride into the pitch, straight at the pitcher, or even slightly toward first base. Because each hitter is different, the coach must work with each individually to perfect his mechanics when leaving the batter's box after contact and get the most out of his initial steps toward first.
If a left-handed hitter is trying to fight off an inside fastball, the hitter's balance point may be more toward his lower back or even on his heels. In this instance, the hitter may actually fall back toward the first-base dugout a fraction before the left leg crosses over to run to first base. Yet if that same hitter is trying to make contact with a slow breaking ball on the third-base side of the plate, especially from a left-handed pitcher, his balance may be toward the front of his feet with the upper body tipping over the plate. Here, the batter is over home plate and must either take a short step with the right foot to open the body so the back leg can cross over and align the runner to first base, or if the right leg holds its ground, the back leg makes a dramatic crossover step to set up the hitter to run directly to first base.
Some left-handed hitters, as with their right-handed counterparts, regardless of the pitch, after taking the swing begin their run toward first base by retracting the stride foot 6 to 12 inches (15-30 cm) toward the back of the batter's box. This causes slower times to first base. However, many more left-handed hitters than right-handed hitters hold their ground with their stride foot in the box after making contact with the pitch. This may be due to the fact that the left-handed hitter knows he must rotate his body to place it in a more direct line to first base.
A habit some left-handed hitters have after making contact is allowing the back foot to step toward or behind the plate slightly due to their momentum. This helps line up the hitter to run in a straighter line toward first base than if he retracted the stride foot. However, it does place him farther from first base as he begins to run. If a hitter is not going to maintain his balance with both feet after contact, the preferable method is to have the foot fall behind the plate instead of retracting the stride foot.
Spotlight: Ichiro Suzuki
Ichiro Suzuki is the best example of a left-handed hitter who strides in on the pitch, stays over the plate, and then allows the stride foot to open so the back foot can begin the first step sooner and more directly toward first base. Due to his great balance over the plate and ability to exit the box much quicker than almost all other hitters, his running times to first base are impressive. Ichiro usually leads the major leagues in infield hits each season and is still doing so after many years playing at the highest level. History proves athletes' speed diminishes late in their careers, but Ichiro's decline is much less notable as a veteran due to his honed technique in leaving the box as a left-handed hitter.
The best approach to an improved exit from the box and a better running time to first base is to finish the swing balanced on both feet and slightly over the plate with the stride foot holding its ground. The stride foot then swings out, possibly moving sideways instead of retracting back, which opens the body so the back foot can then take an inline step toward first base.