I don't think the actual formula for ball speed versus stick speed was ever mentioned above.
The faster the stick moves, the faster the ball moves. Twice the stick speed, twice the ball speed.
In addition to that simple relationship, there is a multiplier that is related to the weights of the ball and stick. This multiplier says how much faster the ball will be moving than the stick was moving just before contact. Yes, the ball typically goes out at a faster speed than the stick comes in.
Ball_speed = Multiplier * Stick_speed
For a six-ounce stick, that multiplier is one, so the ball comes out at the stick speed and the stick stops dead.
For a ten-ton stick, the ball will have twice the speed of the stick, and the stick will slow down a tiny, tiny amount.
For more interesting cases, you can use the formula:
Multiplier = (Stick + Stick)/(Ball + Stick) where Ball and Stick are the weights (or masses) of the ball and stick.
For an 18-ounce stick and a 6-ounce ball (more or less normal) we get Multiplier = (18+18)/(6+18) = 36/24 = 1.5
That means that the ball will come off with 150% of the incoming stick speed.
In the real world, sticks and tips are imperfect and some energy is lost and the speed of the ball is reduced from the ideal. If you want to increase your break ball speed, the easiest way to do it is to get a more efficient tip. Hard tips seem to be more efficient. That change alone will probably give you more speed improvement than a two-ounce change in your break cue, if you currently use a typical playing tip.
Another source of energy loss is in spinning the cue ball. More energy into spinning the cue ball = less energy into its speed forward. The standard WNT break shot uses a lot of spin.