I think the greatest effect is the surface condition and size of the balls. Worn out, dull balls don't break as well. Seems like there's more throw because of the higher friction. More skids and such. That could be my imagination though. But the breaking part is not.
The cue ball wears down the fastest and the most. On an old set, it's the smallest ball on the table and that changes the point of impact. It's not as severe as the effect seen on a barbox with large cueball, but it's enough to change shots requiring extreme precision.
People would be very surprised if they ever measured the worn out balls they play with using A) a micrometer B) a scale accurate to at least .05 of an ounce.
They'd find they're smaller than 2.25" and are underweight according to spec.
At the local pool room, many of the cue balls are so worn that the red-circle is fading and almost gone. It's more of a crescent on many of them. With those, everyone looks like a superstar doing table length draw shots. Until I bring my brand new Super Aramith Pros and all of a sudden things change.
At least that smaller cue ball is proportionally closer to the old worn set than say a new one. When they began swapping out cue balls for brand new ones, the sets remained the same but now there are new cue balls. Small object balls, large cue balls. Much more difficult to draw a ball. Cut shots are different etc.
The bangers don't even notice. I can feel the difference. If I need to get a stop shot or a few inches of draw down the length of the table, it's not happening with that CB unless I really juice it. Players unaware of this scratch their heads in wonder when what they thought was draw or stop shot to avoid a scratch ends up with the CB following the OB into the pocket.
By far the most annoying of all factors about worn out balls in a pool room, aside from not breaking and spreading well...is that they don't rack well.
If they are in really bad shape, you can never get a good rack. This pool room runs a 9-ball league and tourney. That means the 1-9 gets 2 days more use each week than the rest of the object balls. And that's above and beyond the fact that even without a league and tournament, the 1-9 is used more as a result of people playing 9-ball throughout the week.
Add that up over the course of 7+ years and 1-9 is smaller than the 10 - 15.
There's always gaps in the rack when racking for 8-ball, straight pool or one-pocket. This further exacerbates the problem with breaking. Not only are the balls dull, chipped, dinged and rough - but they vary in size and there are gaps throughout the rack.
That's why you hit them with a cannon of a break and they spread poorly, and sometimes clusters are left right where they were racked.