How far a batted ball travels depends on how fast it's moving when it leaves the bat, a variable known as batted ball speed, or BBS. Increase BBS, and you increase how far a fly ball will travel. BBS itself depends on two factors: swing speed and the weight of the bat. A corked bat results in higher swing speed, an effect that would tend to increase BBS. But at the same time, such a bat weighs less, which means it transmits less power upon collision and leads to a decrease in BBS.
In 2011, a team led by Alan Nathan and Daniel Russell, two physicists who frequently study the science behind baseball, investigated just how these competing qualities of corked bats affect the velocity of batted balls. Their research focused on something known as collision efficiency, or q, a value related to a bat's ability to turn an incoming pitch into a solid hit. For an unmodified bat, the team found q to be about 0.214. For a corked bat, the value for q was 0.193 [source: Nathan et al.]. Next, they calculated batted ball speed via the following equation:
BBS = (q)(pitch speed) + (1 + q)(bat speed)
For an unmodified bat, the math might look something like this:
BBS = (0.214)(94 mph) + (1.214)(70 mph) = 20.116 mph + 84.98 mph = 105 mph
For a corked bat, it looks like this (note that the 3-mph increase is an educated guess on our part):
BBS = (0.193)(94 mph) + (1.193)(73 mph) = 18.142 mph + 87.089 mph = 105 mph
Notice that the batted ball speed is the same for both bats! The research suggests that the gains associated with increased bat speed are negated by the losses associated with decreased bat weight. In other words, the net effect of a corked bat is zero -- it has no real impact on the speed of batted balls and, as a result, how far they'll travel in the air.
Unfortunately, this doesn't end the controversy, because corked bats probably have another advantage. A good hitter doesn't just swing a corked bat faster. He can also swing the bat with greater acceleration, meaning he can move the bat from 0 mph to its top speed in a shorter amount of time. This allows him to wait longer on the pitch, to see a pitch better and to make necessary adjustments in his swing. He may not hit more home runs, but he'll make solid contact more regularly and likely have a better batting average.