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whether anyone has followed, whether these tokens have any relation to the size of the fan base of a particular club? also, whether there is any connection between the value of the token and the activities of the club, new signings or the results of the competitions?
which parameter is generally crucial for the value of such tokens (except Bitcoin price of course)
You have to know the utilities of these fan tokens first before you can answer those questions. They seem to have some sort of a governance like what we see in DAO voting plus some exclusive perks. Bottom line is that the value of the token depends on how happy these fans are for their club. Everything the club do affects the fans and that may also affect the price.
Investing in different tokens are mostly associated with risks. So if you decide to invest in those fan tokens, not only the utility cases that you have to consider but also the security of those coins as i think they are mostly dependable on the outcome of what the club is into. I think it's better to invest on established coins than to risk your money in those tokens who have not yet proven their real utilities, as they can easily lose their value and might end up with the same fate of other useless tokens.