Which is a kind of stupid way of measuring things, the detector systems at the LHC were developed by a relatively small number of groups at huge expense over at least 12 years, it took even longer until actual science experiments happened. A concrete example would be the Atlas trigger systems development until Higgs discovery was ~20 years, ultimately they received >50000 citations.

Anecdotal. A big grant paying off doesn't outweigh all the other countless iterative and great leaps forward that led to the detector which led to the higgs. Those efforts were also funded by small grants, graduate student stipends, or out-of-pocket in pubs and libraries.

The reason why they measured impact in that way is because that's what most funding agencies today are speculating in for their decision making processes. And as data shows, most funding agencies are getting it wrong.

Pretty much all large scale physics projects have payoff profiles like that and that is probably known to funding agencies, so I severely doubt that funding agencies have truly used this as their measure. That way to measure impact is simply wrong and would have prevented many significant discoveries in high energy physics and astronomy.

ITER, Wendelstein-X, LIGO, Planck, I could go on. In all those cases any results happened >10 years after the funding started or might still only happen in the future. In the case of the LHC, but also many other Detector experiments individual grants to research groups were typically (not just anecdotally) way beyond 700000€.

Are you claiming the impact/$ for the LHC is higher than would be expected from funding many smaller projects?

According to wikipedia the project costs about $9B, but I doubt that includes all supporting efforts and researcher salaries. That would fund 12 thousand of these smaller $700k projects.

I think "impact" as typically defined is a questionable measure of scientific value. There is no other way in which the Higgs could have been discovered except through a concerted effort of thousands of people, the technical and infrastructure work in such a project is both very challenging and expensive and usually pays only off after more than one decade of work.

You are completely missing the point. The detection of the Higgs is not the primary and absolute purpose of humanity. That it takes a massive amount of money and effort is a bad thing and it certainly isn't something we needed to do right now.

If we first invested in research to make building the LHC cheaper, we'd get more benefit for less cost. That's the only reasonable criteria for allocation of resources.

For some reason this reminds me of how hard it is to design unsupervised learning systems that don't hit a measurable payoff for a long time, so they can't easily decide what they did right or wrong.

Also, I love your username :)