Let's put this thing under the microscope. I'll attempt to keep this as short and to the point as possible.
For the majority of the music world, there exists a standard pitch reference that makes it possible for all instruments to play in tune together. You may have heard the term A440. This represents the speed at which a string vibrates to create the note named 'A'. On a piano, it's the 'A' above middle 'C'. I use a tuning computer that measures the speed of that 'A' on the piano in question.
From training, and years of experience, a piano needs a pitch raise (or pitch correction) when that measurement is at or below 437Hz. Yes. Even that seemingly small difference requires a pitch correction. Here's why: a piano is under 18+ tons of tension. To attempt to tune a piano without first equalizing the tension throughout the piano first is literally a battle; lots of going back and forth between previously tuned notes and sections of the instrument. Whew!
Keep in mind that a piano is mostly wood. The iron plate helps to equalize all that string tension, and is a reason pianos are so heavy! Wood flexes, expands and contracts according to the environment. Add to this, the technician yanking, pushing and pulling on strings, and we're dealing with one big heavy pressure cooker! While tuning in an ascending manner from the lowest note to highest during a pitch raise, previously tuned notes are usually disturbed by all this flexing and must be tweaked again.
The pitch raise service involves tuning the piano twice: once to equalize the tension; then a second time to fine tune it. Rarely is there a third time, at least in my experience, but really flat pianos need lots more tweaking. The beauty of the tuning computer is that it calculates an 'over pull' that is slightly above 440Hz. Equalizing the tension and the pitch in this manner makes the fine tuning process much easier. This is the nutshell version. How far out of tune the piano is at the outset makes a difference as to how long this entire procedure takes, which can still only be estimated. It ain't over til it's over!
440Hz is the standard. 437Hz-436Hz is what I call the cringe factor. For example, if a guitar is tuned at 437 or 436, you would clearly hear the clash with an instrument tuned to 440. 415Hz is a half step down, G#. Think about this: if 437-436 requires a pitch correction, just imagine the drastic adjustments in tension from 415 to 440! It can be a longer process too. Pitch corrected pianos, especially drastic ones, tend to go out of tune sooner than anticipated. A minimum once per year tuning service helps to stabilize the tuning around 440 and are thus much easier to fine tune. Plus, you won't have to pay the additional pitch raise labor costs.
Other factors to consider are the integrity of the pin block and the condition of the strings. Weak pin blocks make fine tuning more difficult; the tuning pin is more difficult to set and stay in the intended position because the grip of the pin block is looser around the pin. Older strings aren't always an issue, but rusty ones can be, being more prone to breaking.
The technique of the technician is about sensitivity and finesse, and knowing how to apply strength as needed. It's a skill that can only be developed with experience, and lots of it.
If you'd like more detail, use the Contact section to request my document "The Piano: A Look Under The Hood of the World's Most Beloved Instrument".