The mechanics underlying a billiards ball strike is just wonderful. A quick youtube search revealed an interesting video doing both high-speed and infrared imaging.

In the above image, the player does a slight jump shot with a 30 degree strike. The stick does the majority of the flexing after impact (I always had this feeling that the lighter 16 oz sticks had an exaggerated flexion), and the yellow ball goes airborne. Now the player struck the ball so hard, that the yellow ball impacts the white ball in the same manner, and both go for a aerial trip. Where's the flexion in the second case?
 
By the way, if you're pretty sure your aim and ballstrikes are proper, but you're still missing, that cue stick flexion is one of two possible causes. The cue stick might be squirting the ball off trajectory. Alternatively, the roll of the cue ball naturally has a friction contact with the object ball - that can throw the object ball a slight amount. Yes billiards starts getting complicated, here's a technical note on squirt:

(download)

In this thermal image, extreme draw was applied. In fact the angle of incidence of the stick suggests that the player also might have messed up the table. The table rise about 3 degrees in temperature (I believe this is an underestimate) based on the camera calibration. Notice how focal the spots are on the table, and yet how linear the heat friction pattern is on the ball - that probably means that the ball is rotating at a ridiculous rate.
 
Ever wonder why you get white spots on a fast billiards table or those same spots on a pool table where people break? Players strike the ball so violently that it's thought to induce local melting of the nylon on the table cloth (~90% worsted wool and 10% nylon).
 
Here's the video for the first two images, it's really neat.

 
One last video, at 2:45" shows the always interesting draw shot in slow motion. The cue ball rotates in place 5 times before friction forces the ball to draw back. By the time that happens, the 1-ball has traveled about 20 inches.