We show how the critical point and the ratio ~,/u of critical exponents of the finite temperature deconfinement transition of SU (2) gauge theory may be determined simply from the expectation value of the square of the Polyakov loop. In a similar way we estimate the ratio (a-1 )/~. The method is based on a consistent application of finite size scaling theory to results obtained with the density of states technique. It may also be used in other lattice theories at second order transitions.