I love this debate. It is similar to, "How many times should I mow my lawn every week?" and the answer is the same - that depends. Some weeks you will mow it 2x per week, sometimes you will not need to mow it for months.
I don't want to act like I do not care about the scientific studies here - but keep in mind that science is not limited to people in lab coats. ANYONE can use the scientific principles to create a working model of their world. If this were not the case you can imagine this:
Person A: There is this invisible force in the universe that attracts all objects of mass to all other objects of mass.
Person B: I cannot see it, prove it. Magical forces don't seem real to me.
Person A: There are a bunch of studies saying that people in white coats show it exists, and all scientists agree.
Of course, this isn't how science works. The real response would be, "Here, test for yourself. If I drop something, it falls to the earth."
Sometimes the studies are the best pieces of evidence we can rely on, sometimes, not so much.
I think loganyy is actually on the right path for more people than we like to admit - but a lot of assumptions about other variables are being made. I also agree with Resolve to some extent - again, depending on the assumptions being made for other variables. Sorry @choclateclen, somewhat disagree here with you. The fact a "scholar" says something has no bearing on if it is true or not anymore than if a 4 year old says something doesn't determine if it's true or not.
I agree that loganyy is on the right path. MOST people in the gym are overtraining in some manner. Generally, most people are not working very hard, so they make up for that with volume. And let's face it, if you ARE working hard, it won't be for very long and your volume will be low. You can work hard or you can work long, but you cannot do both.
So if you're doing a ton of volume, by definition it is low intensity. You may have a high RPE on a given set, but you are not actually achieving high intensity. If you doubt this, go do some squats with your 10RM in a squat rack until you get stuck on the safety bars, have a training partner help you with 4-5 forced reps and then tell me how many sets you're going to do of those. Sure, you could drop the weight and keep going, but the weight is going to drop precipitously. IF you are training with that level of intensity, yeah - 2X per week is probably not going to be good for a natural trainer.
Many people don't train like that though. They come up shy of 100% intensity - usually leaving at least a rep in the tank and normally 2-3 reps. Good news though, studies do show there is benefit to this type of training. And these trainers can probably use a little volume and see benefits.
And beyond that group you have the majority of trainees who don't have hardly any intensity, and have tons of volume - and who really cares how often they train? That's like asking how many times you have to tap a stick of dynamite with a pencil before it will go off - it doesn't matter, it's not effective.
So, I've typed this long, probably boring, post to basically say - it's ALWAYS a balance between intensity, volume and frequency. High intensity will require lower volumes and frequencies. Higher volumes will require lower intensities and frequencies. Higher frequency will require lower volume and intensity.
So how do you find a balance? A training journal and progression. Progression is king.
The theory is that there are 3 steps:
1. Provide a effective stimulus.
2. Recover
3. Super Compensate.
So, you log your progress - if you did 5 reps with 100 pounds last week and this week you do 7 reps with 100 pounds - you made progress and you are doing what you should be. If you do 5 reps or less this week, you should question those 3 parts of the process. Did you provide an effective stimulus for muscle growth? If not - then change the stimulus. If you know you did and you still have not grown this workout then you know the reason for no improvement is in steps 2 or 3 - you need more time for recovery, more sleep, more food and/or you did not allow for super compensation to occur (more time and sleep and food - but it is NOT recovery, it is a second step that only happens AFTER you recover).
And if this is constantly happening and you know you're eating what you should and getting sleep, etc. - then what is your volume and intensity like? Do you need to drop one or both back? Do you need to try less frequent workouts?
Further, for some people - these factors will be very individualized. Some people will require a lot of time between workouts in order to recover, while other people will need a few days and be ready to go again. Some people do well with workouts spread over 2 weeks even.
I can agree with loganyy because I've tried a lot of different workouts and I know everyone on here always says, "2X per week is best. " and that's the dogma and it's been written - but I've tried everything, including very low volume 3X per week training and I can tell you that while short term gains can be good - after a very short period (a month or 6 weeks) I stall pretty hard and get nowhere.
I get the logic - if you can run the stimulate, recover, grow cycle 1X per week you get 52 growth cycles per year. If you can run it 2X per week you get 104 cycles per year - obviously better. The trick is being able to run all 3 steps of that cycle 2X per week and that means - modulate intensity and volume.
Second, the "protein synthesis is elevated for 48 hours" means nothing to me. Big whoop. All that means is that you have the fastest rate of recovery for the first 48 hours - after that, any recovery that still needs to be accomplished will occur much more slowly. In other words, if you use high intensity and/or a lot of volume and you HAVEN'T fully recovered and super-compensated in 2 days (which is unlikely) - then you are going to need even more time off before you're ready to hit the gym. If anything, this could very well be an argument for 1X per week training in my mind. I am sure you get a similar response from surgery - someone cuts you open and in the first couple days post surgery your skin heals at a fast rate and the wound may have started to close in just a few days - but the wound won't be fully healed for weeks because after that initial spike in repair rate, things slow down.
Of course, this doesn't mean there aren't other methods. One thing I like about Doggcrapp, which I would consider a 90-95% intensity program, is that you rotate exercises so that, sure you're hitting the same muscle group 3x in 2 weeks - but you're not doing the exact same thing. I think this is a good break for the nervous system and I think it is especially helpful with deadlifts and squats which can be taxing - you hit them 1 workout, but then maybe do leg presses the next workout and hack squats the next workout and then you rotate again. This greatly reduces the CNS strain.
And, of course, as other have pointed out - the workload of the rest of our days should also be considered, especially mental stress. We often forget that our brains/nervous system is a huge energy consumer and if we have a stressful job and a tough schedule, our training strategies may require adjustment.
So, after that long, rambling post, I think the ideal training frequency for everyone is 1.639832 times per week.