The band-gap reduction caused by heavy impurity doping in a semiconductor can be written as δEg(x)~xα, where x is the mole fraction of the impurities, and α is the scaling exponent. It is well known that α=1/3 for n- or p-type (i.e., charged) doping, where the isolated impurity center forms bound states. In contrast, the incorporation of isoelectronic impurities into a semiconductor commonly results in alloy formation. In this case, the impurities do not form any bound states (with small cluster sizes), and one finds that α=1. However, for the case of nitrogen doping in GaAs, although isolated nitrogen impurities do not form bound states, nitrogen impurity pairs do, and we find α=2/3. The scaling rule revealed here demonstrates that the dominant mechanism for the large band-gap reduction observed in GaAs1-xNx is the formation of an impurity band associated with nitrogen pair bound states.