The observed ratio of RGfree to RGwork. The expected RG ratio is the value that should be achievable at the end of a structure refinement when only random uncorrelated errors exist in the data and the model provided that the observations are properly weighted. When compared with the observed RG ratio it may indicate that a structure has not reached convergence or a model has been over-refined with no corresponding improvement in the model. In an unrestrained refinement, the ratio of RGfree to RGwork with only random uncorrelated errors at convergence depends only on the number of reflections and the number of parameters according to sqrt[(f + m) / (f - m) ] where f = the number of included structure amplitudes and target distances, and m = the number of parameters being refined. In the restrained case, RGfree is calculated from a random selection of residuals including both structure amplitudes and restraints. When restraints are included in the refinement, the RG ratio requires a term for the contribution to the minimized residual at convergence, D_restr, due to those restraints: D_restr = r - sum [w_i . (a_i)^{t . (H)}-1 a_i] where r is the number of geometrical, displacement-parameter and other restraints H is the (m,m) normal matrix given by A^{t.W.A W is the (n,n) symmetric weight matrix of the included observations A is the least-squares design matrix of derivatives of order (n,m) a_i is the ith row of A Then the expected RGratio becomes sqrt [ (f + (m - r + D_restr))/ (f - (m - r + D_restr)) ] There is no data name for the expected value of RGfree/RGwork yet. Ref: Tickle, I. J., Laskowski, R. A. & Moss, D. S. (1998). Acta Cryst. D54, 547-557.}