Links [1] and [3] are wrong, and link [2] is correct but has nothing to do with this discussion. Link [1] is so full of errors it isn't even worth discussing. The pingpong ball analogy is wrong--it's all wrong. Link [3] commits the sin of ascribing single-electron behavior to parameters extracted from the Drude model. This is a semiclassical analogy and worked essentially thanks to units.

Here's the link you're looking for. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/Fermi.html . Two electrons can't occupy the same state. In a metal of finite size, the momentum spectrum becomes quantized. Two electrons can occupy each k-state, one for spin up, one for spin down. Considering an empty metal, we can insert electrons one by one. They will find their lowest energy by packing into a sphere in k-space. Electrons inside the sphere have no states to scatter into, and there are no electrons occupying states outside the sphere. This means that only electrons on the surface of this sphere participate in conduction. The radius of this sphere is called the Fermi wavevector, and converting to units of velocity you get the Fermi velocity. All electrons participating in conduction travel at approximately the fermi velocity... at room temperature plus or minus a tiny fraction of a percent.