Overall, 18% of fully open journals appear to be sponsored [diamond], but their proportion and number have been decreasing. . . . Among society-run journals, sponsored titles account for more than double the market average, for non-society (commercial) journals they account for just under half. Societies’ greater proportion of sponsored titles and their not-for-profit status could therefore place them in a stronger position than their commercial competitors if we see a large scale move by funders to require publication in journals without publisher fees and — as some noises from European funders suggest — which are not for profit.