I've seen a number of recent papers that attempt to algorithmically measure patent scope by counting the number of words in the patent's first claim and comparing to other patents in the same technological field (with longer claims → more details → narrower scope). In their new paper, The Ways We've Been Measuring Patent Scope are Wrong: How to Measure and Draw Causal Inferences with Patent Scope, Jeffrey Kuhn (UNC) and Neil Thompson (MIT Sloan) argue that this measure is superior to prior scope measures.
They validate the word-count measure by comparing with survey responses from seven patent attorneys (below). In comparison, they find that previous measures of patent scope—the number of classes, the number of citations by future patents, and the number of claims—are uncorrelated or negatively correlated with their attorneys' subjective responses.
Of course, there are lots of reasons that word count is an imperfect measure, and additional validation would be helpful. (It would also be good to confirm that the attorneys in this study were blinded to the study design.) Those planning empirical patent studies should approach this variable with caution (and with good advice from patent law experts), but it is a potential scope measure that patent empiricists should at least have on their radar screens.