My intuition says that it "weighs" both the current proportion of success "x" and current proportion of failure "(1-x)": f(x;alpha,beta) = constant*x^(alpha-1)*(1-x)^(beta-1). Where the constant is 1/B(alpha,beta). Alpha is like a "weight" for success's contribution. Beta is like a "weight" for failure's contriubiton. You have a two dimensional parameter space (one for successes contribution and one for failures contribution) which makes it kinda difficult to think about and understand.