As nicely summarized on P4 in On effective degrees of freedom in the early universe here; at high temperatures where all the particles of the Standard Model are present, we have 28 bosonic and 90 fermionic (relativistic) degrees of freedom, giving 118 in total. However, as fermions cannot occupy the same state, the effective degrees of freedom for energy density, pressure and entropy density are $g_*=g_B+\frac{7}{8}g_F=28 +\frac{7}{8} \times 90 = 106.75$.
Now, consider the MSSM. According to Eqn 26 here, Low & High scale MSSM inflation, gravitational waves and constraints from Planck, the equivalent effective degrees of freedom in the MSSM are $g_*=228.75$. Unfortunately, no nice explanation there how that is added up.
Question: In a summary format, how do you end up with the MSSM effective degrees of freedom? Because I sure think my attempts below are half-baked.
Try 1) in supersymmetry: bosonic degrees of freedom = fermionic degrees of freedom, so like lecture 2 here from Jenni Adams, one might just think SUSY $g_*=106.75 \times 2 = 213.5$. However, thats surely not right, as with SUSY there are four higgsinos with two degrees of freedom each (giving $8$ DOF), but the gauge bosons swallow $3$ of the scalar Higgs degrees of freedom.
Try 2) MSSM effective DOF $g_*=106.75 + 8 - 3 + 27 + 90 = 228.75$, which adds up to the right answer, but seems to ignore the Pauli exclusion principle. So, I don't like it. Also, that would make the relativistic MSSM DOF go as: $118 + 8 - 3 + 27 + 90 = 240$
