2088 potential work hours in a year
Less 88 hours holiday
Less 80 hours vacation
Less 56 hours sick
=1864 hours (these are federal guidelines under the Service Contract Act regs)
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
I think the number is pretty dependent on the flow of jobs. If you work in some kind of incident response, for example, it's going cost more than if you've got downtime between 6 month contracts.