I have never been able to understand how Bell's Theorem disproves hidden variables. The argument I hear is that when you measure spin of a particle pair 120° ap

I have never been able to understand how Bell's Theorem disproves hidden variables. The argument I hear is that when you measure spin of a particle pair 120° apart, they agree only 1/4 times instead of the expected 1/3. But who says the expected should be 1/3? Hidden variables give you an escape that can define anything you want it to. That's the point of a hidden variable, isn't it? Maybe the hidden variable function itself is such that the interaction when measuring along 120° is not symmetrical to that when measuring along 240°, and so could yield results different from 1/3 probability.