This paper explores implications of previous work which suggested that pulp refining is achieved by a small number of impacts.As a consequence, the purpose of multiple bar crossings in refiners is to expose many fibres to a few effective cycles, not to impose many cycles on each fibre.Based on this postulate, tensile strength increase was found to be well described by a cumulative probability equation having two parameters: (a) number of bar crossings and (b) probability of a successful refining outcome at each crossing.In this paper, this concept further with additional refiner data was explored and the link between the probability term and measurable refiner variables was examined.By proposing the possibility, these two parameters may be a desirable alternative to specific energy and specific edge load for characterizing refining action.