Deviation from the mean. A natural first measure to investigate is the relationship of a review’s star rating to the mean star rating of all reviews for the product; this, for example, is the underpinning of the conformity hypothesis. With this in mind, let us define the helpfulness ratio of a review to be the fraction of evaluators who found it to be helpful (in other words, it is the fraction a/b when a out of b people found the review helpful), and let us define the product average for a review of a given product to be the average star rating given by all reviews of that product. We find (Figure 1) that the median helpfulness ratio of reviews decreases monotonically as a function the absolute difference between their star rating and the
product average. (The same trend holds for other quantiles.) In fact the dependence is surprisingly smooth, with even seemingly subtle changes in the differences from the average having noticeable effects.