I haven't come across any stats or traditional methods that can be used to calculate Bitcoin's fair value, but does that mean Bitcoin doesn't have a fair value?
The total market value of a currency, its "monetary base", is driven by two things, transactional demand and reservation demand.
1. Transactional demand - Daily transaction volume.
2. Reservation demand - Hoarding/long-term investment.
It is expected that with more merchant adoption the transactional demand would increase.
3. Hurdle rate - Rate of return required to compensate for the risks associated with holding Bitcoin. Yeah, technopolitical hurdles or backlash from a country can have an impact on Bitcoin's expected value.
Theoretically, the fair-market value of one BTC should simply be the dividend of its predicted future monetary base (total market cap) and BTC in circulation, discounted by a "hurdle rate."
All three of those make sense--I can see how each would contribute to bitcoin's value/price. But I don't see how one could possibly come up with any kind of formula/analysis method to say how they actually do contribute. For #1, you at least have some data that you can try to use, but I think #2 and #3 are impossible to calculate. Even worse, I think they all interact and feed off of each other. For example, if people see higher transactional demand (#1), they may decide to hold their bitcoin longer (#2). Or if a country tries to ban bitcoin (#3), that could lead to more transactions (#1) and less investment (#2) as people sell, but then there would be fewer users so the transactions would go down (#1), which would discourage people from buying (#2), except that price has now fallen a lot, so more people see it as a good buy, so investment starts to climb again (#2), and on and on we go....