So what's a good proxy for estimating the value that an incbuator provides to startups? Perhaps time. Iterating through product ideas, getting introductions, and getting help with legal work & administrivia probably shaves somewhere from months to years off of getting to a good product-often to the point where the product/business would have been abandoned before getting traction.
Let's pick a completely arbitrary amount of time saved-one year. Most of the value of YC's portfolio comes from AirBnB & Dropbox. It's hard to get good revenue numbers, but based on users, nights booked, and other heuristics their growth rates are estimated at around 100%-500%.
If we take an estimate of 350%, that means that we could attribute roughly 70% of the value of YC's portfolio companies to YC itself. I'm not sure if these assumptions are all accurate (especially the 1 year saved figure), but this can give us a starting point to estimating YC's impact on their portfolio companies.
ETA: the amount of time saved is probably the most important variable. If we assume YC saves each company 6 months instead of 12, then YC's impact drops from 70% to 47%. With 3 months, it's about 27%.