Inverse grading in hard sphere granular flow is described by an effective stochastic process for the vertical displacement of particles in time. By pure, parameter-free data analysis, we extract an underlying stochastic Langevin equation for the heights dynamics of large and small particles. Fixed points of the deterministic vertical dynamics of individual particles are determined and show that within this macroscopic description of a granular flow. inverse grading of large particles is due to a deterministic effect. These results may be used as an efficient alternative to time consuming direct numerical modelling of inverse garading.