We find that the fragility can be correlated to the eutectic instability and the glass forming ability in binary metallic glass formers under growth controlled conditions via a dimensionless parameter beta defined as DfT0/2(T-e - T-0), where D-f is fragility parameter, T-0 is Vogel-Fulcher-Tammann temperature, and T-e, is eutectic temperature. It is shown that the large beta value, which results from high Df and from that T-0 is close to the eutectic temperature, can lead to small interface growth velocity and undercooling of eutectic structure, and good glass forming ability. This indicates that high beta leads to small characteristic diffusion length resulting from sluggish material transport that governs the glass forming ability. The results might provide an in-depth insight into the glass formation mechanism and be helpful for searching new glasses in growth controlled process. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4721405]