A detailed first-principles analysis of the transport properties of different magnetic electrode materials for $\mathrm{MgO}$ tunnel junctions is performed to elucidate the microscopic origin of the tunneling magnetoresistance (TMR) effect. The spin-dependent transport properties of the magnetic materials are analyzed separately from the particular interface geometry with the tunneling barrier. We use the bulk properties of the barrier to identify the important tunneling states. For $\mathrm{MgO}$ these are ${\ensuremath{\Delta}}_{1}$-like states. From the analysis of this effective spin polarization we can predict the potential of certain magnetic materials to create a high TMR ratio in a tunnel junction. This polarization is as high as 98 and $86\phantom{\rule{0.3em}{0ex}}%$ for Fe and Co, respectively for only a few monolayers, but is very small and negative, $\ensuremath{-}7\phantom{\rule{0.3em}{0ex}}%$, for amorphous Fe. This explains the finding that for crystalline Co and Fe one monolayer next to the $\mathrm{MgO}$ barrier is sufficient to reach TMR ratios higher than 500 % independent of whether the crystalline monolayer is coupled to a non-magnetic or to an amorphous lead. However, in direct contact with $\mathrm{MgO}$ amorphous Fe reduces the TMR ratio drastically to 44 %.