Balance holes are an effective way to change the motion of a bowling ball. What you are doing, by drilling a balance hole, is replacing ball material density with a lighter density material (AIR). This will change the RG, Int. Differential, and Total Differential numbers of the ball. These changes in numbers will change the motion of the ball. Pay attention to the white tape on the ball. The white tape is placed on the Pin, this will help show the influence of the core on ball motion. Static weight number have been left out. I did this on purpose. On one side are those who believe ending static weight means everything and on the other side are those who believe ending static weight means nothing. I'm in the middle, everything done to a bowling ball will influence its motion as it travels down the lane, as to how much the effect is, is open for debate.
Video on the left shows the effect of balance holes on a symmetrical core ball. Video on the right shows the effect of balances holes on an asymmetrical core ball.