There seems to be a lot of reading material, be it books, blogs, dedicated websites, on the strategy behind a roll up but I have failed in my attempts to find any material on a Roll-up valuation.

Does buying 10 x $2M EBITDA companies that are "performing well" automatically drive value via arbitrage? E.G. 4x EBITDA per company is now 8x EBITDA per company because you have acquired 10 of them?

Secondly has anyone found any noteworthy information on the interwebs or other, related to this topic?

Thank you in advance.