I always used 2x, but probably 2.5x is a sensible way to think about it in a patio11 "charge more than you think you should" mold.
This is less true following the Affordable Care Act than it used to be. The unsubsidised marketplace rate for my Kaiser health insurance seems fairly close to what I pay for COBRA from my former big tech employer.
My Kaiser almost doubled from COBRA and coverage went from better-than-platinum to high deductible gold.
Google / SF market.
Age makes a huge difference to the marketplace premiums though.
Being a subject matter expert means that you can be paid well for your work, but the numbers of jobs that require expertise in the Kura-Aras river basin can be few are far between.
When I was doing pricing for service contracts it was usually around 1.50:1 burdened billing rate vs direct labor (income)
232/1864 is a base increase of 12.5% for PTO
Payroll taxes, Medical, workers comp, etc add about 30% - though medical is flat so at higher wages like discussed here the % increase it represents goes down further
I did not have to factor in increasing skill on the job or time between jobs - but I did have to account for overhead and g&a which would be similar to time between jobs since those would be for bills
Big companies would have a lot of markup on OH/g&a/fee, but a software dev working remote for themselves on contract could competitively go down to 5-10% or less here to simply cover the minor added burden to bills.
That totals up to about a 50% increase on the salary rate. You can't outright bill someone for time you spend looking for a new job or improving your skills. You may charge a premium that you use to do such things but that would have to go under fee which tends to top out at 15% with the government, not something that can be expected to be accounted for. In my experience at least.
Again though, this was for service contracts - particularly with the US government, subject to certified cost and pricing data disclosures.
I was genuinely curious about the 2.5 number though, as i have spent a lot of time dealing with market rates in various conditions I was interested to know the context. I could see a few ways that could happen, but I wouldn't want to speculate too much