on the cuescore stats what is "HB"?
Probably "high break".
Correct. If you hover your mouse over the "HB," it shows "Highest break."
"Break" is a snooker term, of course. Here it means high run. I wish they showed the high run for each player for each game rather than just the single highest run for the player in any of his games. But that's not part of the software.