It is natural to assess the legal argument strength qualitatively orquantitatively. In the first case we express the strength by some relevant modalqualification of the argument conclusion, in the second case — by value of its logicalprobability. The quantitative assessment presupposes explication: 1) by which formulashaving known initial data to calculate logical probability of the argument conclusion;2) how to find all necessary initial date including structure, probabilities of the initialreasons, and strengths of logical links in the argument. Some formulas which permitunder given initial data to calculate the argument strength are discussed in the paper.But it is pointed out that diagramming of legal reasoning and assignment of the basicdata necessary for calculations in nontrivial cases constitute a matter of intuition orapproximate qualitative assessments ex datis partially. It creates an essential challengeto the argument strength quantitative assessment, particularly in prospect of completeelectronic justice.