In comments below, Peter Suber points out that the NIH has amended its estimates to $100 million/yr spent on author-side charges and 80,000 manuscripts funded -- which brings the estimated average author-side fee to $1250, well in line with the individual journal estimates I made and the published figures I found. This is an important number because it is derived from a very large sample of the scholarly literature and casts a very different light on OA author-side fees than the one that TA publishers are wont to shine on their competitors. Compare, for instance, PLoS ONE at $1300, or the standard BMC charge of $1470 -- for a couple hundred dollars more than the average cost of a TA publication, you can make your work free for all users to access, immediately and permanently. (It would be interesting to know what proportion of the $100 million is going to OA fees, though I doubt it would be large enough to make a significant dent in the average TA charge. Edit: according to Björk et al., less than 5% of all articles are available via no-embargo Gold OA; taking this into account, and assuming that the average Gold OA fee is triple the average TA fee, gives an average of $1136/article.)

But! However! There is a flaw in my reasoning!

The problem is not with the estimate of author-side charges, but in my use of that estimate to update Philip Davis' library costs study. The point of that study was to look at what libraries would pay in an all-OA model, which is why I used the fractional cost matrix¹ and graph in the first place. See the problem? Libraries don't pay the toll-access author-side charges, the NIH does! This makes the model a little artificial, perhaps, since *someone* has to pay those charges regardless of which journal levies them; nonetheless, the idea was to estimate practical library costs, so the TA author-side fees should not be included.

Here's what the updated situation looks like with the subscription/article estimate NOT adjusted for TA author-side fees (see my earlier post for details of the calculations):

The fractional cost has to drop to 0.4 before there are no libraries predicted to pay more in the OA model -- as I pointed out in the original post, there are numerous realistic combinations that will result in a fractional cost of 0.4 or lower:

The new figures also show that the fractional cost has to drop below 0.2 before all 113 libraries are predicted to save money in an OA model. That still seems to me to fall within a realistic range, given that 70% of journals in the DOAJ don't charge author-side fees and 45% of researchers in a recent RCUK study had their OA fees covered by their research funders, for a fractional cost of 0.135.

Nonetheless, it's worth taking a quick look at the libraries which are predicted to pay about the same in the OA and TA models. At a fractional cost of 0.4, they are: UC Davis, LA and San Diego, Univ Colorado, Cornell, Harvard, Johns Hopkins, McGill, Univ Massachusetts, Univ Maryland, MIT, Univ Toronto, Univ Washington and Univ Wisconsin. At a fractional cost of 0.3, only UC Davis, UCLA, Harvard, McGill, Maryland and Washington remain in the "pay about the same" category.

It's easy enough to guess what these universities have in common, and a simple analysis confirms it:

Shading the top six yellow and the next 8 blue for visibility and ranking the libraries according to FTE, serials expenditure and "estimated scholarly articles published" reveals that the 14 "pay-same" libraries have only a slight tendency to be among the larger schools, but cluster very strongly at the high end of the "scholarly articles published" ranking. In other words, research-intensive schools that publish a lot may put more pressure on their libraries in the OA world (to the extent that libraries are likely to be asked to repurpose serials costs for OA charges).

Among other things, it was in order to examine this particular concern in detail that Davis carried out his original study, and for the same reason I have here updated it with more recent estimates and assumptions. The newer numbers show that a realistic worst-case scenario is that the libraries in question (14 out of 113 total) don't save any money in the OA model.

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¹ I neglected to mention in earlier posts that I got the %fee x %funded matrix idea (of which the fractional cost graph is an obvious extension) from Peter Suber. My apologies to Peter; I'm usually more careful about crediting sources.