  Assuming the source of the anomalies observed recently in $b \to s$ data to
be new physics, there is a priori no reason to believe that - in the effective
field theory language - only one type of operator is responsible for the
tensions. We thus perform for the first time a global fit where all the Wilson
coefficients which can effectively receive new physics contributions are
considered, allowing for lepton flavour universality breaking effects as well
as contributions from chirality flipped and scalar and pseudoscalar operators,
and find the SM pull taking into account all effective parameters. As a result
of the full fit to all available $b \to s$ data including all relevant Wilson
coefficients, we obtain a total pull of 4.1$\sigma$ with the SM hypothesis
assuming 10% error for the power corrections. Moreover, we make a statistical
comparison to find whether the most favoured explanation of the anomalies is
new physics or underestimated hadronic effects using the most general
parameterisation which is fully consistent with the analyticity structure of
the amplitudes. This Wilks' test will be a very useful tool to analyse the
forthcoming $B\to K^* \mu^+ \mu^-$ data. Because the significance of the
observed tensions in the angular observables in $B \to K^* \mu^+\mu^-$ is
presently dependent on the theory estimation of the hadronic contributions to
these decays, we briefly discuss the various available approaches for taking
into account the long-distance hadronic effects and examine how the different
estimations of these contributions result in distinct significance of the new
physics interpretation of the observed anomalies.
