I actually have hired, specifically for what is described here, so I'll use some examples from software engineering.

While I agree that experience will give you more - expertise in subject matter, people skills, and well-roundedness - I believe that all these points can be (and are) typically clarified in the job description. I can say I'm looking for specifics in these areas, and keep the field open to a larger pool.

So... what's experience?

It's having had the time in the field to see the feedback loop caused by your own decisions.

Particularly in engineering, you'll (and your team) will make various decisions about how you'll do the work, what the design will be and other basic assumptions. You'll go along proceeding with some sort of plan, which is inevitably flawed. Show me a plan that worked perfectly and you'll be showing me either a very small project, or a very unperceptive engineer. No plan survives contact with reality, and even a very good plan may work well in unexpected ways and poorly in others.

As time goes on, you'll adjust the plan, people and technologies will come and go, and reality will not trod along in a predictable fashion. The team will come up with new solutions and changes to the plan to compensate for what they've learned.

This feedback loop is what seasons an engineer. Much like a hands on lab is usually much preferred to book learning and rote memorization - experience living through a product lifecycle (or several!) gives the candidate more practical information about what works - both for their team and for themselves. It can include design heuristics, ways to improve development processes, good work habits, research tricks, and experience with how to get things done across an organization.

Variation in years

It's not a fixed thing - in fact 3-7 sounds about right. There's a point after 2 but before ...8? where there's a significant number of cases where an engineer says "Oh... that did not work before, let's try some other way" some significant portion of the time. And yet they are not so burned by experience that they can't see the hope in trying new things and going with new strategies. After 10, I see a sweeping difference - usually from a diversity of work experiences that means that what the engineer sees applies not just to their main area of work, but to the pieces of the organization around them.

It definitely isn't a fixed number. Here's some samples in variation:

An engineer who's switched between many projects over a very short span of time, never having seen the full release of any of them is likely to have less experience from this perspective.

An engineer who's worked several internships and then 1-2 years with the same group may have more than the standard 2 years of experience since he's seen that group survive 3-4 years worth of history, regardless of having been there for fixed time spaces (say a summer internship during schooling)

Someone working in a very small shop with lots of DIY may gain richer experience faster. I don't see too many of these operating as strongly experienced on the short end (2 years), but I do see it start to factor in in the 7 vs. 13 year range - a person from a small startup who has had to do just about anything shows more experience than a guy who's worked for 13 years always doing a small piece of the business, never questioning the process never going beyond his small bit of the world.

Is there an Equation?

Nope... but did you really expect a yes?

It is definitely a factor of:

Time working + experiences survived + nature of role & responsibilities + lessons learned

I'd say most roles have an instinctive scoring factor. And it can be as much related to gaps in the current team as the nature of the work they do. I don't need customer facing skills, for example, on a huge defense contracting team where all customer contact is buffered by management. And types of customer contact are very different between sales engineering and IT technical support. Experience with one at some level does help with the other, but someone who fits the desired profile more closely but with fewer years may well get the higher rating.

In essence some of the "experience factor" comes down to saying (as a hiring manger) - "how easily can I jam this square peg into my triangular hole?" as well as "will it be easier or harder than with this circular peg?"

Interviewing for the Experience

The difference between experience and "not enough experience" or "not the right experience" come down, for me, to questions of "what did you learn doing the things on your resume?".

If in response to these questions the answer is:

well, I haven't been working long enough to have learned much.

I have no clue, I keep changing projects and never followed up with the people on the projects to see what happened.

Then I'm probably going to say - "doesn't have the experience".

If, however, I get:

I keep switching projects, but I noticed that when they released the product, it had XYZ reactions, which made me glad/regretful that we did ABC.

Well, I haven't made it through a full lifecycle, but I have a pantheon of ways not to kick off a project, so far we've failed at the last 5 attempts, but we learned not to do E, F, G, H, and most especially I.

Some thoughtful insights about ways to improve process after a true lifecycle is completed

Then I'm going to rate the candidate more favorably. Note - failure is pretty common. Experiencing failure is often even more powerful than experiencing success. If you join a humming, successful, complex project right off the bat and do a fine job, you may actually have less experience just because you haven't seen a major disaster, nor have you learned how to survive it. We all should be so lucky!

Can I beat the system?

Maybe. Could you have an in depth conversation about the strengths and gaps in your skill-set? How your own experiences and biases have helped and hindered your teams so far? How your projects have succeeded or failed or been less efficient on more than a "the textbook says it, therefore it must be true" level? Then the challenge is largely conveying that in the interview.

Keep in mind that the job rec was written based on at least one person's experience. Probably several. There are myriad strategies for how a job rec is written and each company can be different - but the 3-7 range is canonical enough that there's some group think out there on why this time in the field matters. If you are going to sell an alternate idea, realize that you may have to go above and beyond to show why you, particularly, are the outlier and that you are somehow more seasoned than the years you have would normally indicate.

Also realize that they are considering you in light of a pool. If someone with all your skills walked in for the same job the next hour after you left the room, but they had some experience you hadn't had yet -- then there's no reason to compromise.