An analysis of the statistics of multistage (pipeline, SAR, and algorithmic) ADCs with redundancy is performed and the ability to achieve an extra 6 dB of resolution in ADCs with half-bit redundancy is shown due to probability density function (PDF) residue shaping. This paper classifies redundancy techniques to show that only some have properties leading to statistical resolution improvements. When properly implemented, resolution gains are maintained even in the presence of large sub-ADC nonlinearity. ADC design criteria for maximizing these resolution increases through PDF residue shaping are described including improved back-end ADCs, stage comparator offset bounds, and the use of scaled conventional restoring with Z added levels (CRZ) stage redundancy. PDF residue shaped structural improvements are also quantified in relation to ideal and nonideal traditional multistage ADC structures.