I was reading something written by one of the old greats who spent a life on the road. He always brought his own balls and tried to get them into play. He said if he couldn't get his own set of balls in play he would try to get at least his own cue ball snuck into the game. He said if he couldn't do at least that he might not want to play. I forget who this was, been many years since I read this.
One day I was playing at a very well respected pool hall. Good tables, fresh cloth when needed or before, clean place, top flight place. I happened to notice I was playing with two different pattern pool balls. Looking closer I saw I was playing with three different pattern pool balls and who knows how many different sets.
The next time I went to the pool hall I brought my own balls, a junk thirty dollar set I had bought to cut up for one project or another. It was like going from a family car to a nice sports car. Play immediately jumped a ball or more. Since this was an unexpected result I believe it was real. Later I bought some pretty decent balls. When I go to the hall I don't take the liberty of wetting down the cloth but I do keep the paper towels when I wash my hands before starting play. I wipe down the rails with these damp towels. At my favorite places they see me at a table and come wipe it down. Of course I tip nicely. It pays to take care of the house man.
Often the biggest difference between lower quality sets and higher quality sets is how finely the sets are sorted by weight. Throw multiple sets of balls together like commercial cleaners or the house man does and the value of those sets may fall sharply.
After learning for myself I have to agree with the old time road man, getting your own balls in a match is huge. Just the cue ball is pretty big. I wouldn't let somebody else use their own unless it was part of a spot. An old world billiard(three or four balls) match never came off because the players couldn't agree on the balls they would play with.
Somebody using their own bridge is something I have never seen called against although I have seen some that were a nice advantage.
Hu