How Many vav Hahipuchs (Conversive vav) are in each of the 24 books of Tenach compared with the number of letters / verses in that book. As far as I know they are only in Tenach rather than Mishna or any subsequent work. It would be interesting to see if the number of conversive vavs declines as prophecy declined in the 2nd Temple period. I'd like to compare the ratio of conversive vavs in each book with the number of letters and verses in that book.
I don't have a count, but I can give some rules about its appearance, and from that we can make an estimation.
In narrative portions, the vast majority of verbs introduced with a vav (which is most verbs) use the vav hahipuch. (This includes the beginning of verses, chapters, books, even the first word of the Prophets at the beginning of Yehoshua.) Also in commandments the vav hahipuch is used with the same frequency.
Spoken statements tend to have more verbs without the vav hahipuch, even when those verbs are introduced with a vav. (But it is used in quotations as well, for example Bereshis 3:10.)
The books of Tehilim, Mishlei, Iyov (other than the narritive at the beginning and end, and the introductions to the speeches) Shir Hashirim, Koheles and Eicha rarely use the vav hahipuch. (However, those books also don't have many verbs with a vav introducing them at all. There are instances of vav hahipuch in each of them, but you have to search for it.)
The vav hahipuch is used in the books of Ezra and Daniel as much as in other books. It is not used in biblical Aramaic.
With this in mind, let us estimate how frequently the vav hahiputo is used in each book:
1-9) In Chumash and Neviim Reshonim, the average usage is for sure more than once per verse.
10-13) In Neviim Achronim there are more prophetic passages, and fewer verbs introduced with a vav. Let us guess that this averages out to one for every two or three verses.
14-16) The poetic books of Tehilim, Mishlei, and Iyov have very few vav hahipuchs in total.
17-21) Of the five megilos, two of them, Ruth and Ester, have more than one per verse, and the other three have very few.
22-24) Ezra/Nechemia, Daniel and Divrei Hayomim all have fewer vav hahipuchs, the first two because of the Aramaic portions, and Divrei Hayomim (like Ezra) because of long genealogical passages. Let's put the average at one for three verses.
So, as you can see, most of the books with very few vav hahipuchs are from the early First Temple period (or earlier, depending on when Iyov was written,) and Eicha is from the Exile period. The more prophetic books use the vav hahipuch less than the less prophetic books, on the whole. And the books from the Second Temple period use the vav hahipuch almost as much as the earlier books.