How often do funding agencies require funded authors to publish their work in open access venues? Some funding agencies such as the Gates Foundation require funded authors to publish their work in open access venues.

Is there any research/study/survey that tried to quantify the percentage of funding agencies that require funded authors to publish their work in open access venues. 

I am interested in any data that could share some light on that question, e.g. historical trends or weighting by funding agency size.



For example, 
The RoMEO Journals database contains thousands of journals, labeled with their archiving policy (preprint/postprint/publisher's version):



One could imagine a similar database for funding agencies with paper  access policies.
SHERPA, which produces RoMEO, also produces a database on funders' open access policies, called SHERPA/JULIET. There is a statistics page on the JULIET website. 

According to this page, 26% of funders worldwide require publication in an open access venue, 30% encourage this, and 41% have no policy.

When it comes to archiving the publication in an open access repository, 68% of funders require this, 12% encourage, and 17% have no policy.