There have been some survey analysis done around what people are doing and correlating them to this that and the other thing, but I'm not aware of any formal studies focusing on this issue. And frankly, I don't trust the existing surveys beyond their utility as intelligence about what other entities are doing; they are not guides.
There are several compounding variables here. The major ones:
- The level of heterogeneity in the infrastructure. The more hetero it is, the more people needed to support it. If it's one big monoculture (IaaS farm, Etsy) you can get away with 3 for 10K. For an academic datacenter with a hundred random off the shelf applications purchased by departments you need many more than the IaaS farm.
- The degree of automation present. Automation saves people. This is a proxy for the first point, but it's still a very important point by itself. Some systems don't automate well (Windows), others are one-offs where automation doesn't make much sense (that Solaris 7 box in the corner that'll cost $80K to replace, but no one has that kind of money in a budget crisis).
- Service level requirements. If you need to have 24/7/365 staffing, that'll increase your head-count versus if you can get away with just emergency call-out for some hours. Which specialties need to be staffed/on-call at what hours? How many of the services supported need rapid response, and which can wait a couple hours? What failures have you engineered automated recovery for, and which need hands-on assistance?
And then there is the definitional problem. What counts as a 'technician'? Large infrastructures can count HVAC and Power people in the 'technician' count, where middling and small (100-500) consider them occasional contractors that don't contribute to head-count (or if they do, it's a fractional FTE). SAN Engineers or Database Architects may not be 'technicians' in a large environment, but are probably also the line-technicians in a medium sized one.
For infrastructures that are complex in design but simple in maintenance (such as an IaaS cloud), you need fewer people involved.
For infrastructures that are complex in design and also complex in maintenance (that Academic datacenter with 100 unique services in it), you need more people to keep it going due to the many knowledge-centers required to keep it running well.