For the user’s point of view, in large environments, it can be desirable to have Information Retrieval Systems (IRS) that retrieve documents according to their relevance levels. Relevance levels have been studied in some previous Information Retrieval (IR) works while some others (few) IR research works tackled the questions of IRS effectiveness and collections size. These latter works used standard IR measures on collections of increasing size to analyze IRS effectiveness scalability. In this work, we bring together these two issues in IR (multigraded relevance and scalability) by designing some new metrics for evaluating the ability of IRS to rank documents according to their relevance levels when collection size increases.