So government isn't very good at running research programs then?

The standard argument in favour of government running research programs is that the product, knowledge, is a public good. That is, it's non-rivalrous and non-excludable and thus the private sector will underproduce it. Simply on the grounds that non-rivalrous and non-excludable goods are difficult to profit from and thus a profit seeking private sector won't do very much of that activity. Thus government should step in to produce the socially optimal amount of whatever it is.

There are most certainly areas where we agree with the argument. It is exactly the logic which produces the patent and copyright system for example. However, the wider logic of government intervention in the provision of public goods is not the same as concluding that government must provide that item. We think, for example, of the herd immunity provided by a vaccination campaign. The US does it largely by insisting the children cannot enter public education without having been vaccinated - the UK by the NHS directly providing the vaccinations. We think that second system works a little better. But that is not necessarily true of all public goods.

Which brings us to biomedical research. The Zuckerbergs are funding $3 billion of such. This is welcomed as the field currently rather suffers: 

Success rates for NIH grant applications are at the lowest they’ve been going as far back as the 1970s. When the money for science is this tight, researchers don’t take big risks. Instead of making innovative leaps in science, researchers early in their careers are typically among the most risk averse, taking on bits of studies designed by their senior mentors. Writing a successful grant application often requires preliminary data – in other words, you need to have already done a chunk of the research you’re proposing to do. Even then, about 20-25% of academic biomedical researchers’ time (in my experience) is spent applying for grants to support their projects. Much of their mental effort goes into grantsmanship, which is not at all the same thing as creativity.

Academic researchers are promoted on the basis of “achievement” – grants won and papers published. Volume is what matters here, not necessarily impact. According to Adam Grant, a professor of organizational psychology at the Wharton School of Business, “The greatest originals are the ones who fail the most, because they’re the ones who try the most.” But biomedical researchers can’t afford to have failed experiments because they’re not publishable. Furthermore, they need to take as much of the credit as possible for that “productivity” to count towards their advancement, so there’s an incentive against working with too many other people. Biomedical research is highly siloed in parallel with the grants funding it. An added challenge is that the gold standard for medical research – the randomized clinical trial, ideally conducted in multiple sites and settings – is very expensive.

The NIH spends 10 times as much per year as that entire Zuckerberg gift. And yet we're told that government does this job of funding research rather badly.

Or as we might put it more widely. That we've identified a possible market failure does not mean that government is the solution - for there is such a thing as government failure too.