Riceissa answered this on the LessWrong version of this question – the original source this facebook post by Vipul Naik.

For three different foundations: Open Philanthropy Project, Bill & Melinda Gates Foundation, and Laura and John Arnold Foundations, I calculated that the total money granted per hour of staff time is approximately $1000 - $3000. This includes all staff time (obtained by taking number of people on staff and multiplying by 2000 hours for a year, then comparing with annual grants).

Is there a reasonable argument that foundations would generally have this ratio of money granted to staff time? For instance, if we break down the cost into direct grant investigation cost + cost of time spent getting familiar with the domain and evaluating strategy, etc., are we bound to arrive at a comparable figure?

One foundation that has a much higher ratio of money granted to staff time in recent years is Atlantic Philanthropies, but they are in spend-down mode right now and I don't have a good picture of their overall spend trajectory and employee counts yet.

Open Philanthropy Project:
Grants in 2016: $50 to $100 million
Staff at year-end: ~20 (+ some shared operational staff with GiveWell)

Laura and John Arnold Foundation
Grants in 2015: $185 million
Staff in 2016: ~50 listed on their site

Bill & Melinda Gates Foundation
Grants: ~$4.2 billion
Staff: ~1500

I do not know this article but here are my thoughts on this problem, having worked at a private foundation myself.

The amount of money awarded per staff lies on a scale. On one end a foundation could just make 1 massive grant a year to one organization. On the other end, make millions of super small grants. As organizations navigate this scale from one extreme to the other, in my experience these are some of their considerations:

• Diversifying the portfolio of grants - if one does not succeed, there are still many to possibly have high impact
• Limited expertise of staff
• Limited responsibility of staff - it seems that more staff are a better system of checks and balances where corruption or poor judgement are discovered easily
• Field saturation - in my foundation, there were certain areas that we have kind of already funded to what we believed was their maximum potential. If we suddenly had twice the money, we would not have given it to the same area. We would need to research and justify a new cause area.
• Ultimately, I think that there is a sense of "wanting to know something the others do not know" or being original in some way. One could have a foundation that simply funds high quality proposals that were not funded simply due to lack of resources by other funders. Super efficient, just needs a small grants and operations team. Yet, it lacks mission and is generally unappealing to the board and founders.