A regular normalization will only help you to compare the scoring distribution among queries (and theirs retrieved lists).
You cannot simply normalize the score to compare the performance between queries.
Think of a query which all retrieved documents are highly relevant and received the same (high score), and on another query that the retrieved list comprise barley relevant document (again, with the same score) - now, no matter the per-query normalization you make - the normalized score will be the same.
You need to think on a cross-query factor that can bring all the scores to the same level.
For example - maybe computing similarity between the query and the whole index, and use that score somehow along with the document-score