What is the fastest rate at which you increased mileage?

Honestly one/two miles per week is just fine if you're pushing into an unknown territory.

I went from 0 to 1 mpw. An infinite rate of increase

When you first start running you will be overly injury prone. So increasing to 50mpw within 2 months of starting running might not be the most sensible idea. I'd stay at 35mpw for at least a month, then next month you can gradually go up to 50 if you feel good.

But the 10% weekly rule is nonsense after a certain point. It can take months to fully adjust to higher mileage, this really depends on what your end goal mileage is though for lets say this year. You cant just go to 80mpw by increasing 10% a week, it would be silly.

Depends on your times too, getting faster isn't just about running more. If you have some decent times for a beginner then you probably want to train smart from the start, so keep most runs easy and make sure to include threshold/tempo with some speed stimulus every week. If you are really slow currently, like 20-25 mins, then you will probably just get faster by increasing mileage.

Every time I let myself get completely out of shape (like no running for 3+ months and 20+ lbs of weight gain), I follow the same model when I get back into it.

Week 1 - 30 minutes easy every weekday, 45 minutes on Saturday, 60 minutes on Sunday.

Then every week I add 5 minutes to the weekdays, 7.5 minutes to Saturday, 10 minutes to Sunday. By the time I get up to 60 minutes every weekday, 90 minutes on Saturday, 120 minutes on Sunday (takes 6 weeks), I add workouts back in.

So, this means I start around 35 miles for week 1 and add 42.5 minutes (5-6 miles) each week. I’ve probably done this 7 different times now and have never had injury issues. If you are adding more than 10% of your mileage in a given week, I would recommend keeping workouts the same pace/intensity until your mileage gets to where you plan to keep it. I would not recommend ramping up both workouts and mileage simultaneously.

Adding mileage fast is risking injury. You could be a hobby elliptical cross trainer if you aren't conservative. I think you are over conservative though op. You could prob bump up to 40 mpw right now and then 50 in the summer. You are not at the phase where the injury risk is that high, unless you have no athletic background at all.

My answer to the question: I went from running 60 mpw to 100 mpw pretty quickly in college by adding doubles. (70 at the start of the season to 100 at the end of the season by adding a 5 mile run every day) - I ended that season with a stress fracture in my foot - but that was probably more do to too many intense workouts trying to squeeze everything out for conference and regionals, which healed in 5 weeks and was able to get back to 100 fairly quickly and train there injury free for a time.

10% rule is bad because if you're doing 10 miles per week, it takes more than 7 weeks to get to 20 miles.

I'd always take a week off after a season, then run 5 days per week the next week, 6 days per week for the next 2 weeks, and then get back into my normal 7 days per week. This probably would be 30, 50, 60, 70, 70, 80...