If I had a penny for every time a politician asked “why doesn’t [our country] set up a super innovation agency like DARPA?”, I could probably afford to set up my own.

Policymakers’ interest in the immense US defence research agency isn’t surprising. DARPA played an important role in many of the great innovations of the last 50 years, from the Internet and the graphical user interface to GPS and self-driving cars. It makes big bets on breakthrough technologies, which can seem much more exciting than the more incremental projects that most countries’ innovation agencies support.

The idea of setting up a big blue-skies research organisation working perhaps not on defence (as DARPA does), but on something nicer, like health or climate change, has a certain allure for politicians bored by the niceties of R&D incentive schemes or knowledge transfer networks. At this point, someone usually points out the role of CERN in the invention of the World Wide Web, and policymakers’ excitement builds.

Not so fast. There are a couple of major problems with the idea of setting up a DARPA-alike, which are worth putting down for the record.

First of all, there’s the question of how successful organisations like DARPA really are. SPRU’s Paul Nightingale makes the point that there’s massive selection bias at work in the popular account of organisations like DARPA. For every successful project we hear about, there are dozens we don’t (and perhaps never will). Of course all innovation runs the risk of failure. But unless we have some idea of how many failures there are and how big they are (and defence tech failure can be an expensive business), it’s worth tempering our enthusiasm. Are your politicians willing to accept this level of risk?

But for me the bigger problem is one of scale. Unless you can replicate DARPA’s scale, it may not be possible or sensible to emulate DARPA. And most countries can’t.

DARPA is very big. It spends about $3 billion a year, about four times the budget of Innovate UK or similar organisations in other rich countries.

Not only is DARPA itself big, but it’s plugged into the overall US defence procurement budget. At $600 billion, it's nearly as large as the annual spend of the entire UK public sector. And a long-standing part of American defence doctrine is being technologically superior to the rest of the world. What’s more, DARPA sits alongside a constellation of other funding bodies, such as the Office of Naval Research, so if DARPA misses something, other funders can step in. (Big science institutions like CERN are famously un-cheap too: finding the Higgs Boson cost a cool $13 billion.)

Replicating something like DARPA in all its glory, along with all the other things that make it work, in a country like the UK would be a vast undertaking. If politicians really have the desire and the ability to spend very serious money on it, then that’s great. (It'd be interesting to speculate what the minimum viable size of a DARPA-a-like would be: my guess is a few hundred million dollars or more, not counting supporting institutions.) But most DARPA-enthusiasts aren’t proposing that. Instead, what they are really proposing is to copy it at a significantly smaller scale.

And here’s the problem. A big part of the reason DARPA works as well as it does is its size, and the size of the system it works within.

When you’re huge, you can make big bets safe in the knowledge that one or two will probably succeed and will pay off many times over. You can attract talent by virtue of the size of your ambition. And the breadth of the system helps too: because the US can afford other funders, funding options exist for good projects DARPA misses.

With this in mind, I’d like to propose a new idea: the quantity theory of innovation policy.

The quantity theory of innovation policy holds that if you implement any non-absurd innovation funding policy at absolutely massive scale, it’ll work, in the sense that you will discover some useful and important things.

Defence, particle physics, healthcare would all work as topics… In fact, I suspect if you spent several billion dollars on orthodontics research or medieval history or butterfly taxonomy you’d also discover some useful things out of a combination of serendipity and brute force.

Massive innovation programmes may not be efficient (it’s hard to tell whether DARPA or CERN are). But if you have enough money to spend, you’re fairly sure of some good outcomes even if the policy itself leaves something to be desired.

The flip side of this is that anecdotally successful projects that involve spending Smaug-like heaps of money on research don’t necessarily work if you scale them down to a size that most countries can afford.

So there you go. As Stalin supposedly said, quantity has a quality all of its own. And that makes massive innovation organisations a poor guide for the innovation policies of small countries.