It is well known that the hydrophobic effect is the major factor that drives a protein toward collapse and folding. We analyze the variation of the solvent-accessible surface area of amino acids in small fragments of protein $(3⩽N⩽45)$. In this way, we look into 5526 protein chains deposited in the Brookhaven Protein Data Bank. The accessible surface area behaves as a power law for $N⩾9$. The comparison between the loss of accessible area and the self-similar behavior gives us a measure of the possibility of an amino acid to have apolar or polar side chain. It is therefore possible to infer about amino acid hydrophobicity, i.e., if one amino acid has a hydrophobic side chain or if it has a hydrophilic one. Furthermore, the present findings indicate that the variation of the accessible surface area describes an alternative hydrophobicity scale.