Look at these two graphs - the first is a count of the number of times that a grammatical letter appears by position of a lexical word in Psalms, Lamentations and Job - all taken together. You can see very clearly that aleph occurs more frequently than vav as a first letter. The second shows the letters that are not used as grammatical affixes. It's a pretty clear division into two groups of 11. (Shin and sin both appear - so group 2 has an extra player.) The only one you might cavil about is tet which has one oddball use in rare conjugations. (Putnam page 271) Note how different the distribution is and how frequent ayin is a first letter and resh as a third letter. Both graphs map letter positions 1 to 6.
Here's the Putnam rule re tet: When a verbal root begins with a sibilant, the taf of the hitpael prefix and the sibilant exchange positions (metathesize). If the root begins with Tsade, the taf both metathesizes and becomes tet (partial assimilation). You can see how rare tet is from the graphs so this rule would not let tet score a run even if I let him play.