Does the weight and size of the balls ever vary much, and does it have an effect?
The following video describes and demonstrates all effects related to using cue balls or object balls of different weights and sizes:
“Ball Weight and Size Difference Effects – Part I” (BD, February, 2012) and “Ball Weight and Size Difference Effects – Part II” (BD, March, 2012) also cover ball-weight-difference effects in detail. Here’s another article from Bob Jewett (BD, December ’05) on the topic.
Generally, with older balls, the cue ball (CB) will be slightly smaller and lighter than the object balls (OBs) because it takes more abuse and wears faster as a result. However, if a new CB is used with an older set of OBs, the CB will be slightly heavier because only the OBs will have wear. On many old coin-operated tables in bars (i.e., “bar boxes”), the CB was often heavier and/or larger than the other balls to help the ball-return mechanism distinguish the CB from the others.
When the CB is heavier, it is easier to follow and tougher to draw. With a cut shot, the CB will go forward of the tangent line; and with a stop shot, the CB will drift forward some. This effect is called “smash through.” A heavier CB will also squirt slightly less.
When the CB is lighter, it is easier to draw the CB and tougher to follow. With a cut shot, the CB will pull back from the tangent line; also, with a stop shot, the CB will bounce back some. A lighter CB will also squirt slightly more.
When the CB is smaller or larger, the contact point on the OB will not be at the equator, the balls will also tend to hop a little, especially with faster speed (e.g., on an old bar box with a large CB, it is very easy to launch the CB off the table on a power break shot). With cut shots, the cut angle will also be off slightly (see the question and answer below), but this is an extremely small effect. And with rail cut shots, a smaller CB can easily overcut the ball, and a larger CB will usually result in a full hit.
Worn OBs will also not rack as well as new high-quality balls. Slight mismatches in size and non-spherical shape (due to non-uniform wear) will result in less-tight racks and poor break action (bad spread, more clusters, fewer balls made). Non-spherical or unbalanced balls will also not roll straight, and the direction of turn depends on the ball orientation.
Do CB and OB weight and size differences affect cut angle and throw?
See the throw ball-size effects resource page.
Assuming the ball surfaces have the same friction properties in a comparison, and assuming the same line-of-centers hits are being created in a comparison, then the amount of throw should not vary with CB or OB weight or size. However, if the weight difference is due to size differences, and a person aims the same way they normally do (with equal-size balls), then there will be different amounts of perceived throw. For example, a larger CB will create a slightly fuller hit than expected (with normal aim), and this will give the perception that the OB is being thrown more (even though it isn’t).
With a larger CB, there is a downward component of force (which can make the CB and/or OB hop and result in slower OB motion), but this would not change the OB direction (i.e., the amount of throw). Interaction between the bottom of the OB and the cloth has nothing to do with throw. Although, having the CB contact the OB above the equator does change the effective cut angle of the shot, just as it does with jump shots where the CB hits the OB while airborne (and some people might perceive this as a throw effect, but it isn’t). For more info and demonstrations of overcutting with an above-equator hit, see the jump-shot over-cut resource page.
Because the ball material is so stiff compared to the cloth, a downward CB-to-OB collision at a modest angle is really unaffected by the resulting OB-to-table collision. Per the ball-contact-time resource page, a ball-to-ball collision occurs in about 0.0003 seconds (300 microseconds). Per HSV B.44 – cloth compression and cue ball trajectory for draw shots of various elevations, an OB takes about 0.002 seconds to compress the cloth and rebound off the slate at an angle … about 7-times longer than the ball-ball collision. Therefore, the CB-to-OB collision is mostly done before any significant force builds up between the OB and the cloth.
Even though a larger CB will hit the OB above the equator, which increases the effective cut angle some (creating a thinner hit), the larger size of the CB causes a sooner hit, which decreases the effective cut angle some (creating a fuller hit). The 2nd effect is bigger than the first, creating a fuller hit than expected. If you are not convinced, draw a top view of a half-ball hit with both an equal-size CB and a larger CB (along the same CTE line). The point of contact between the balls must lie on the line-of-centers between the balls. The line-of-centers for the larger ball creates a smaller cut angle and fuller hit (even with the above-equator hit effect). Although, any reasonable and typical size differences between the CB and OBs will probably be too small to notice any cut-angle-change effects, unless you are playing on an old “bar box” with a large CB, in which case it might be noticeable to a good player.