The Distribution Effect is proposed for the HELP PUF that is based on purposely introducing biases in the mean and range parameters of path delay distributions to enhance entropy. The biased distributions are then used in the bitstring construction process to introduce differences in the bit values associated with path delays that would normally remain fixed. Offsets are computed to fine tune a token's digitized path delays as a means of maximizing entropy and reproducibility in the generated bitstrings: a first population-based offset method computes median values using data from multiple tokens (i.e., the population) and a second chip-specific technique is proposed which fine tunes path delays using enrollment data from the authenticating token.