Standard model describes three interactions (strong, weak, electromagnetic) of elementary particles. Coupling strengths are free parameters.
There are several arbitrary parameters in the scalar sector, which are:
1. Symmetry breaking SU(2)xU(1) .--> U(1) proceeds through the VEV of the Higgs scalar =v. This is a free parameter.
2. Higgs field interacts with fermions through trilinear Yukawa couplins of the form fermion-fermion-scalar. There are, six quarks and three leptons, consequently there are nine Yukawa couplings.
3. Higgs self interaction strength is a free parameter.
4. Cabbibo-Kobayashi-Maskawa mixing matrix has three angles and a phase, giving four parameters.
Furthermore there is an unknown theta term in QCD Lagrangian giving rise to strong CP problem.
In total there are nineteen of them. Except four parameters of CKM sector, the remaining fifteen parameters are complex.
Because these parameters are fixed by experiments, one thinks that there is a strong motivation for carrying out studies beyond the standard model in a direction which will have more predictive power and fewer free parameters.