We apply the Bayesian concept of ‘evidence’ to reveal systematically the nature of dark energy from present and future supernova luminosity distance measurements. We express the unknown dark energy equation of state w(z) as a low-order polynomial in redshift and use evidence to find the polynomial order, thereby establishing the minimum order required by the data. We apply this method to the current supernova data, and with a prior −1 ≤w(z) ≤ 1 and Ωm= 0.3 ± 0.05, obtain a large probability of 91 per cent for the cosmological constant model, with the remaining 9 per cent assigned to the two more complex models tested. We also investigate the use of evidence for future supernova data sets such as distances obtainable from surveys like the Supernova Acceleration Probe (SNAP). Given a low uncertainty on the present-day matter density, we find that, if the underlying dark energy model is only modestly evolving, then a constant w(z) fit is sufficient. However, if the evolution of the dark energy equation of state to linear order is larger than |w1|≳ 0.5, then the evolution can be established with statistical significance. For models where we can assume the prior −1 ≤w(z) ≤ 1, the correct polynomial order can be established even for modestly evolving equations of state.