This paper discusses issues that arise when considering what is meant by the expression ‘research quality’ in universities. Popular measures of research quality are often based on determining the quality of a published journal paper, or of using these to publish journal league tables based on the assumption that the journal quality represents the quality of the papers published by the journal. This paper argues that measuring the quality of a research publication cannot be done. Therefore a journal league table also has no meaning. The issue of the use of the surrogate of Journal League Tables is used to exemplify some of the issues that need to be addressed by the community to avoid the inequality quality trap. A number of suggestions are made to establish a sounder basis for dealing with real quality properly. This is not an information systems crisis paper or similar nonsense, but one possible positive way forward.