We have established a relationship between the viscosity activation energy of metaphosphate melts and the NMR chemical shift anisotropy of phosphorus that is measured in their corresponding glasses, and proposed a model by which the fragility of the glasses can be explained as dependent on the particular modified random network that is originated upon cooling. The increase of the modifier field strength gives rise to higher viscosity activation energy during the glass formation upon cooling, with a maximum at the calcium metaphosphate composition. The lower rates of increase of viscosity would produce network structures characterized by higher anisotropicity and be the responsible for the higher fragility of the glasses, which can be defined as a measure of the degree of difference between the structures of the glassy state and the melt from which this is obtained.