In this work, the accuracy of a transformation method to estimate muscle attachments based on three bony landmarks was assessed. A concept of mathematical error was introduced and applied to a data-set of 17 muscles' attachment lines from the shoulders of seven cadavers. Within the muscles' attachment lines from the studied data-set, mathematical error and anatomical variability average percentage values were 37.3 and 62.7%, respectively, for the scapula, and 54.4 and 45.6%, respectively, for the humerus. To reduce mathematical error in the transformation method presented, the plane formed by the three landmarks of the segment corresponding to the scaled muscles should neither be too close to the origin of the global coordinate system, nor too far away from muscle attachment locations to be transformed. The procedure outlined in this work allows the researcher to analyse the anatomical variability within a data-set.