A couple of things here that suggest that there may be more going on than your simplistic explanation (but no i don't have numbers):
1. Humanities (e.g. arts programs) along with sports are large generators of alumni donations. These are certainly large chunks of money that aren't even considered "science funding saves the world" type thinking.
2. Humanities and other non-science programs contribute to the overall prestige of a school. Whether or not this is deserved is different from the truth of it -- a good reputation is good for all forms of grants.
3. A simple thought analysis on how much overhead a humanities professor really needs compared to his science counterparts shows there is a huge lack of cost from the humanities groups: no equipment to house and power, no labs (but books, galleries etc, i don't know where more money would be needed: a good lab building or a good library), fewer RAships (but roughly equal numbers of TAships), no need for extra infrastructure to be built (cooling towers for compute clusters, etc), no need for special legal teams to cover the risks, no need for special accounting to sate the governments crazy reporting needs, no need for non-academic staff (programmers, lab specialists, etc). Im sure there are others.
Basically, from the universities I've worked at, the vast majority of overhead goes to general building/grounds maintenance, specialized services for the groups bringing grants, student programs, general infrastructure, and sure, some to the humanities, why not -- all those LAS majors probably don't pay tuition at all.
1. Humanities (e.g. arts programs) along with sports are large generators of alumni donations. These are certainly large chunks of money that aren't even considered "science funding saves the world" type thinking.
2. Humanities and other non-science programs contribute to the overall prestige of a school. Whether or not this is deserved is different from the truth of it -- a good reputation is good for all forms of grants.
3. A simple thought analysis on how much overhead a humanities professor really needs compared to his science counterparts shows there is a huge lack of cost from the humanities groups: no equipment to house and power, no labs (but books, galleries etc, i don't know where more money would be needed: a good lab building or a good library), fewer RAships (but roughly equal numbers of TAships), no need for extra infrastructure to be built (cooling towers for compute clusters, etc), no need for special legal teams to cover the risks, no need for special accounting to sate the governments crazy reporting needs, no need for non-academic staff (programmers, lab specialists, etc). Im sure there are others.
Basically, from the universities I've worked at, the vast majority of overhead goes to general building/grounds maintenance, specialized services for the groups bringing grants, student programs, general infrastructure, and sure, some to the humanities, why not -- all those LAS majors probably don't pay tuition at all.