The problem with average per song is that you "use up" words in every new song, so all things being equal each marginal song has progressively fewer new words.
I bet you could get something insightful from plotting "unique words" versus "total words" - That might give a good idea of the amount of repetition over time, the length or quantity of output, and the total vocabulary.
If a rapper released one song using n distinct words their score would be n/1, and if they released a second song using the same set of words their score would halve, to n/2, despite the fact their demonstrated vocabulary is still n words.
In fact, if their first song used n distinct words and their second used a completely distinct set of words, but the second song was shorter than the first, their score would drop.
That would be unusual behaviour for a measure of vocabulary.
I don't think that's what the poster meant. By "average unique words per song" I take it to mean, within each song words are only counted once, but across songs, words can be counted multiple times. So if song A had the words "I like cats" and song B had the words "I like dogs", then the average unique word count would be ((3 + 3) / 2) = 3, not ((3 + 1)/2) = 2.
That's definitely one solution, but it still wouldn't quite capture it. As an extreme example, if rapper A produced 100 songs, each with exactly the same lyrics, they should surely be penalized compared with rapper B producing 100 songs with no shared words— even if rapper A's average unique-words-per-song is higher than rapper B's.
