This study compares publisher ratings to the visibility and impact of individual books, based on a 2017 dataset from three Nordic PRFS systems (Denmark, Norway, and Finland). Although there are Journal Impact Factors (JIFs) for journals, there is no similar indicator for book publishers. National publisher lists are used instead to account for the general 'quality' of books, leading to institutional rewards. But, just as the JIF is not recommended as proxy for the ‘citedness’ of a paper, a publisher rating is also not recommended as proxy for the impact of an individual book. We introduce a small fish in a big pond versus big fish in a small pond metaphor, where a ‘fish’ is a book and ‘the pond’ represents its publishing house. We investigate how books fit on this metaphorical fish and pond continuum, using WorldCat holdings (visibility) and Google scholar citations (impact), and test other variables to determine their predictive value with respect to these two indicators. Our statistics show that publisher levels do not have predictive value, when other variables are held constant. This has implications for PRFSs and book evaluations in general, as well as ongoing developments related to a newly proposed international publisher registry.