Beast combat in Scenario 19 (The Beastmaster)
Consider the number of pips showing on any rolled die as a success.

Then, a standard creature/character rolling one die has a range of possibilities from 0-2.  Let's say a creature got to roll one die, but had one additional succcess.  Then that creature rolls a die (normal 0-2 distribution) and adds one.  So, their overall distribution is 1-3.

The impact of this is that the creature will always have some successes that must be defended against.