Factors affecting time to completion
The length of treatment needed to complete the process depends on many variables, presented roughly in order of importance:
Your choice of practitioners: As mentioned above, using someone who knows what they're doing is paramount. The better the operator, the more hairs treated per session. Plus if they're good, the kill ratio is higher, and you're done faster.
Your density of follicles: The more follicles, the more hair, the more time it will take.
Your hair coarseness: Some people's facial hair is coarser than others. Coarser hairs may take more than one treatment to come loose, and may be harder to kill.
Your pain threshold: The lower your pain threshold, the lower the machine must be set for electrolysis and laser, and the longer it will take.
Your skin sensitivity: There is a limit to how much current your skin can take. For some people this is lower than their pain threshold. Trying to use a setting stronger than the skin can handle may result in skin damage.
Your frequency/regularity of treatment: It is vital that you maintain a regular treatment schedule set up by your practitioner. Do as much as you can afford. The sooner you get hairs after they emerge, the less time they have to strengthen. Some people miss appointments because they forget, they can't afford to pay that week, or they don't want to deal with the pain that day. Sporadic treatment will greatly lengthen the time needed to finish.
Your behavior at treatments: If you stop frequently to take a break from the pain, to go stretch your legs, to smoke, or to go to the bathroom, you will be cutting into your treatment time. Also, if you fidget a lot or talk a lot (especially while you're getting work done near your mouth), your movements will slow down the whole process.
Your past methods of hair removal: If you have attempted to remove your facial hair prior to electrolysis, you may have made the task harder for your practitioner. Shaving shouldn't pose a problem, but if you have plucked your hairs, the hair roots could be curved and distorted, making it difficult to insert the probe to the necessary point.
Your androgen levels: You don't have to be on hormones for electrolysis to work, but it probably helps. While there is no definitive study on this, it is generally assumed that hormones (more specifically, anti-androgens like spironolactone) retard facial hair growth (although they have no effect on existing hairs). If you can, it is wise to get on a testosterone blocker like spironolactone before electrolysis.
Your age: There's a certain age where your facial hair is probably as thick as it will get, but this varies widely. And in general, the younger you are, the more resilient your skin is.
Your skin condition: If your skin is unhealthy or broken out, a practitioner may have to avoid an area until it's healed.
Your type of treatment: The different modalities of electrolysis (thermolysis, galvanic, and blend) and different lkinds of lasers (ruby, Nd:YAG, diode, aleaxandrite, IPL) all have their adherents and detractors. There has been no proof that one method works better than others in the long run, although you'll certainly hear strong opinions for one method or the other.
Doubling up on treatment: Some places offer work done by two practitioners at once. A reader writes, "I get twice the hours of work for the same number of hours of my lying there being tortured so it's much quicker to make progress... It definitely is worth asking around to see if any practitioners in your area work in teams."