Assume a market with two players and equally distributed market share; and . Now compare that to a situation with three players and again an equally distributed market share; , note that like the situation with two players. The market with three players is less concentrated, but this is not obvious looking at just H*. Thus, the normalized Herfindahl index can serve as a measure for the equality of distributions, but is less suitable for concentration.
assume a market with two players and equally distributed market share; and  now compare that to a situation with three players and again an equally distributed market share;  note that like the situation with two players the market with three players is less concentrated but this is not obvious looking at just h* thus the normalized herfindahl index can serve as a measure for the equality of distributions but is less suitable for concentration