Previous work suggests that the size factor may be the most crucial one on the glass forming ability (GFA). But the alloys in a system have significant deference for GFA. A criterion,, is defined in the present work to comprehensively evaluate concentration dependence of GFA of alloys in a system. It is found that the values of lambda(n) of bulk glass formers with greatest GFA in Zr-, Pd-, Mg-, Nd- and Fe-based systems are nearly constant of 0.18. Based on the mathematical description of regular polytopes and the dense random packing of hard sphere (DRPHS) model, a cluster model is suggested. This model provides the physical meaningful origin of the lambda(n) from the view of free volume. The glass structure of bulk glass formers with lambda(n) approximate to 0.18 has optimum defect concentration within the framework of the cluster model. In the term of lambda(n) criterion, an alloy with lambda(n) of about 0.18 will be one of bulk glass former candidates, which is verified by the experimental result of Zr-Al-Ni system. (C) 2003 Elsevier Science Ltd. All rights reserved.