Phred quality scores  are logarithmically related to the base-calling error probabilities  and defined as 
This relation can also be written as 
For example, if Phred assigns a quality score of 30 to a base, the chances that this base is called incorrectly are 1 in 1000.
The phred quality score is the negative ratio of the error probability to the reference level of  expressed in Decibel (dB).