What does it cost to publish a paper  in a non-open access Elsevier journal? The immediate cost to the author is often zero (though page charges, and fees for colour illustrations mean this is not always true). But readers have to pay to see the paper, either directly in the case of private individuals or through library budgets in the case of university staff and students. What is the total cost to the world?

Previous attempts

It's a calculation that I've taken a couple of stabs at in public forums, but in both cases space restraints meant that I couldn't lay out the reasoning in the detail I'd like — and as a result I couldn't get the kind of detailed feedback that would allow me to refine the numbers. So I am trying again here.

The first version of the calculation was in my article Open, moral and pragmatic at Times Higher Education:

According to Elsevier's annual report for 2010, it publishes about "200,000 new science & technology research articles each year". The same report reveals revenues for 2010 of £2.026 billion. This works out as £10,130 per article, each made available only to the tiny proportion of the world's population that has access to a subscribing library.

As Kent Anderson pointed out in an otherwise misleading comment, that calculation was flawed in that I was using the total of Elsevier revenue rather than just the portion that comes from journal subscriptions. Trying to fix this, and using more up-to-date figures, I provided a better estimate in Academic Publishing Is Broken at The Scientist:

To publish in an Elsevier journal … appears to cost some $10,500. In 2011, 78 percent of Elsevier's total revenue, or £1,605 million, was contributed by journal subscriptions. In the same year, Elsevier published 240,000 articles, making the average cost per article some £6,689, or about $10,500 US.

But this, it turns out, is also an over-estimate, because it's 78% of Elsevier's Scientific, Technical and Medical revenue that comes from journal subscriptions; the other half of Elsevier, their Health Sciences division, has its own revenues.

The data we have to work with

Here's what I have right now — using data from 2010, the last complete year for which numbers are available.

Bear in mind that Elsevier is a publisher, and Reed Elsevier is a larger company that owns Elsevier and a bunch of other businesses such as Lexis Nexus. According to the notes from a Reed Elsevier investment seminar that took place on December 6, 2011 in London:

• Page 2: 34% of Reed Elsevier's total 2010 revenue of £6,055M (i.e. £2058.7M) was from "Science and Medical", which I take to mean Elsevier. This is in keeping with the total revenue number from Elsevier's annual report.
• Page 8: Elsevier's revenues are split 50-50 between the Scientific & Technical division and the Health Sciences division. 39% of total Elsevier revenue (i.e. £803M) is from research journals in the S&T sector. No percentage is given for research journal revenue in Health Sciences.
• Page 18: confirmation that 78% of Scientific & Technical revenue (i.e. 39% of total Elsevier revenue) is from research journals.
• Page 21: total number of articles published in 2010 seems to be about 258,000 (read off from the graph).
• Page 22 confirms ">230,000 articles per year".
• Page 23, top half, says ">80% of revenue derived from subscriptions, strongly recurring revenues". Bottom half confirms earlier revenue of 78% for research journals. I suppose that the "subscriptions" amounting to >80% must include database subscriptions.

The other important figure is the proportion of Elsevier journal revenue that comes from Gold OA fees rather than subscriptions. The answer is, almost none. Figures for 2010 are no longer on Elsevier's Sponsored Articles page, but happily we quoted it in an older SV-POW! post:

691 Elsevier articles across some six hundred journals were sponsored in 2010. Sponsorship revenues from these articles amounted to less than 0.1% of Elsevier's total revenues.

So for the purposes of these rough-and-ready calculations, we can ignore Elsevier's Gold-OA revenue completely and assume that all research-journal revenue is from subscriptions.

The data we don't have

The crucial piece of information we don't have is this: how much of Elsevier Health Sciences revenue is from journal subscriptions? This information is not included in the investor report, and my attempts to determine it have so far been wholly unsuccessful. Back in March, I contacted Liz Smith (VP/Director of Global Internal Communications), Alicia Wise (Director of Universal Access), Tom Reller (VP of Global Corporate Relations), Ron Mobed (CEO of Scientific & Technical) and Michael Hansen (CEO of Health Sciences). Of these, only Tom Reller got back to me — he was helpful, and pointed me to the investor report that I cite heavily above — but wasn't able to give me a figure.

If anyone knows the true percentage — or can even narrow the range a bit — I would love to know about it. Please leave a comment.

In the mean time, I will proceed with calculations on two different bases:

1. That Health Sciences revenue is proportioned the same as Scientific & Technical, i.e. 78% comes from journal subscriptions;
2. That Health Sciences has no revenue from journal subscriptions. This seems very unrealistic to me, but will at least give us a hard lower bound.

Calculation

It's pretty simple.

If HS journal-subscription revenue is zero, then Elsevier's total from journal subscriptions in 2010 was £803M. On the other hand, if HS revenue proportions are about the same as in S&T, then total journal-subscription revenue was twice this, £1606M.

Across the 258,000 or so articles published in 2010, that yields either £803M / 258,000 = £3112 per article, or £1606M / 258,000 = £6224 per article. At current exchange rates, that's $4816 or $9632. My guess is that the true figure is somewhere between these extremes. If I had to give a single figure, I guess I'd split the difference and go with £4668, which is about $7224.

Remember: this is what it costs the academic world to get access to your article when you give it to an Elsevier journal. Those parts of the academic world that have access, that is — don't forget that many universities and almost everyone outside a university won't be able to access it at all.

This is less than my previous estimates. It's still an awful lot.

Why this matters

Over on Tim Gowers' blog, he's recently announced the launch of a new open-access maths journal, Forum of Mathematics, to be published by Cambridge University Press. The new journal will have an article processing fee of £500 after the first three years, during which all fees will be waived. I've been shocked at the vehemence with which a lot of commenters have objected to the ideas of any article processing fee.

Here's the thing. For each maths article that's sent to an Elsevier journal, costing the worldwide maths community between £3112 and £6224, that same worldwide maths community could instead pay for six to twelve open-access articles in the new journal. And those articles would then be available to anyone who wanted them, not only people affiliated with subscribing institutions.

To me, the purely economic argument for open access is unanswerable. Even if you leave aside the moral argument, the text-mining argument, and so on, you're left with a very stark financial equation. It's madness to give research to subscription publishers.