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PHRED scores are confidence values associated with each basecall generated by sequencers. The score is defined as a monotonic function of the probability that the basecall is incorrect. The calibration of PHRED scores has previously been examined by evaluating errors made in reading known sequences. We investigated the calibration of the Illumina MiSeq instrument PHRED model using data from a large dataset. We also derive calibration methods for the PHRED scores in datasets similar to those produced by the Global Hepatitis Outbreak and Surveillance Technology (GHOST). The GHOST protocol uses a short amplicon, resulting in many positions having two base calls, one coming from each of the paired reads. A maximum likelihood model of redundant base calls that match each other was used to estimate corrected probabilities of the PHRED scores. The PHRED scores showed only small absolute deviations from their target values. These differences are statistically significant deviations (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo> </mml:mo><mml:mo><</mml:mo><mml:mo> </mml:mo><mml:mn>0.0001</mml:mn></mml:mrow></mml:math>) from being calibrated. The accuracy of the scores varied significantly between the MiSeq instrument runs. Recalibration produced quality scores that improved Brier scores for the dataset by an average relative improvement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2.83</mml:mn><mml:mi>%</mml:mi></mml:mrow></mml:math>. Methods developed to create calibration curves for PHRED scores will be useful in improving error-correction pipelines based on redundant deep sequencing of amplicon data. However, quality scores are relatively uninformative of substitution errors. The quality scores assigned are determined more by the global error rate of the sequencing run in the current machine cycle than by the characteristics of the specific base call.