A lot can be said about the number of people in your I.T. department. There are too many, too few, and of course, "We don't need more because Other School XYZ and/or Competing Business XYZ has fewer."
In my experience, the reality is that the staffing is more about perception and budgets than anything else. When management sees I.T. as a cost center, they give as few resources as possible to it. When management sees I.T. as a way to make staff more efficient or make instruction more effective, then more resources are allocated -- including staff. New hardware is "sexy" and everyone likes being "Santa" by providing new gadgets. The effects of proper staffing, on the other hand, are usually overlooked.
Consider this: How often does your computer break down, confuse you, or require an update? Include any time that you're working for the computer, instead of the other way around. Let's say you lose a full 8 hours to "overhead" out of every 2000 hours. That sounds pretty generous, right? You probably have computer-headaches much more often than that, right? Well, that is roughly one full working day per 1 working year. If you assume 52 weeks per year minus some time for vacations, holidays, and sick days, you have 200 - 240 working days per work-year. (Less if you're in education.) From that, we get 200 to 240 days times 8 hours per day, or 1600 to 2048 hours per year. So at least one full day out of every 200-240 full days is lost to computer overhead like fixing things, figuring out how to do something, installing new software, replacing dead parts, installing upgrades, etc.
This isn't terribly scientific, but its a start. You should have one full time I.T. worker (1.0 FTE) per 200-240 computers. That is just in regards to the PCs, laptops, and tablets. You still need staff for your networking, servers, website, phones, printers and photocopiers, projectors and TVs, document cameras (a.k.a. "Elmos"), streaming video (a.k.a. "Apple TV"), and so on. After all, why have computers if they can't print, share files, access your databases, use the web, or send email to customers?
Yes, that is a lot of staff. Yes, that is a lot of money.
Let's look at a parallel idea for a moment. The cost of a bigger office building is more than just additional rent. Its electricity for the lighting, janitors, and cleaning products. If a manufacturer short staffs the assembly line, then fewer products can be built each week and fewer sales are made. Everything has upkeep costs. Computers are the same. If your staff is really good, you could get away with short-staffing for a while. Of course, good staff will move to jobs that give them less stress. At that point, since there weren't enough I.T. workers, the institution will really feel the pain of the loss. In addition to things taking even longer to get done while searching for a replacement worker, the institution will suffer a brain-drain. The new worker will take months to figure out how things are implemented. A sudden loss of a worker that doesn't have a fall-back co-worker with the same knowledge and skills can cripple a company. Also, what do you do when one of your All Star team of three gets into a car accident or catches bronchitis and needs several weeks to recover?
Its a touch choice. You need staff to keep things running, but staff costs money that you want to use elsewhere.
If you're reading this and you're in management, my suggestion is that you start a dialog with your I.T. department. I think you'll be surprised at how many things they maintain and how deeply dependent on them your institution is. More importantly, ask them what they wish they could do for the institution. Chances are good that they can improve the company or school in ways that you haven't even considered yet. The I.T. department isn't just a cost center. They can be -- and want to be -- a profit center. Most I.T. workers became excited about the field because they thought they could help people and be heroes. Let them. They'll make you look good if you give them a chance.
If you're reading this and you're in I.T., my suggestion is to start a list of things you and your team do. Don't be shy; be realistic. If something goes wrong with the copiers, phones, or TVs, are you going to be asked to help? If so, put it on your list. Then break up your list into visible (user-facing) and invisible (back-end) systems. For the invisible ones, list out the impact of it going down. If the boot disk in your Active Directory server dies, what does that mean to your computers, phones, copiers, wireless networking, BYOD, instructional environment, etc? You're not trying to make it scary, but be honest. The day will come when this list will be helpful. You want to have it ready, because if you have to think of things on the spot it won't be accurate or complete.
Other lists to consider include projects that you think would improve any part of your workplace for your coworkers (new services, consolidate systems, ways to make work easier), ways to make your team or anyone else more efficient, ways to decrease downtime (including scheduled maintenance and redundancies like UPSs, RAID, and VM), and ways to decrease costs. If you know of any legal regulations, keep a list of those, too. For example, K-12 public schools should know about FIRPA, COPA, CIPA, eRate, software licensing regulation, etc.
Whatever you do, you should start with the question of what your institution wants to have running and at what level of reliability. You can work backwards from that and find the right number of staff. Chances are good its not the same number that you have. If you keep an open mind, you might even realize why it takes so long to get a reply from your I.T. department.