Meta-analyses today continue to be run using conventional random-effects models that ignore tangible information from studies such as the quality of the studies involved, despite the expectation that results of better quality studies reflect more valid results. Previous research has suggested that quality scores derived from such quality appraisals are unlikely to be useful in meta-analysis, because they would produce biased estimates of effects that are unlikely to be offset by a variance reduction within the studied models. However, previous discussions took place in the context of such scores viewed in terms of their ability to maximize their association with both the magnitude and direction of bias. In this review, another look is taken at this concept, this time asserting that probabilistic bias quantification is not possible or even required of quality scores when used in meta-analysis for redistribution of weights. The use of such a model is contrasted with the conventional random effects model of meta-analysis to demonstrate why the latter is inadequate in the face of a properly specified quality score weighting method.