“Availability of digital object identifiers in publications archived by PubMed”, 3rd January 2017. For…

“the period 1966–2015 (50 years). Of the 496,665 articles studied over this period, 201,055 have DOIs (40.48%).”

So just under 60% are without DOIs, and that’s for biomedical in PubMed — albeit when including thirty years of pre-1995 (pre the mass Internet) coverage. More recently, for 2015, the study found that 13.5% of new content was still without a DOI.

The DOI-free figures for the humanities will be far higher, according to “Availability of digital object identifiers (DOIs) in Web of Science and Scopus”, February 2016…

“Many journals related to the Natural Sciences and Medicine with considerable impact have no DOI. Arts & Humanities WoS [Web of Science] categories have the highest percentage of documents without DOI.” … “exceeding 50% only since 2013. The observed values for Books and Proceedings are even lower despite the importance of these document types …”

As for DOI availability within articles in repositories, IRUS-UK provides a “DOI Summary” field giving “the numbers and percentages that have DOIs available” in UK repositories, although the access to their datasets is controlled. IRUS-UK has no summary infographics that I could find, relevant to DOI availability. But it would be interesting to determine what proportion of UK repository free/open journal articles have DOIs.