word count - Quantifying the amount of change in a git diff?

Question

I use git for a slightly unusual purpose--it stores my text as I write fiction. (I know, I know...geeky.)

I am trying to keep track of productivity, and want to measure the degree of difference between subsequent commits. The writer's proxy for "work" is "words written", at least during the creation stage. I can't use straight word count as it ignores editing and compression, both vital parts of writing. I think I want to track:

 (words added)+(words removed)

which will double-count (words changed), but I'm okay with that.

It'd be great to type some magic incantation and have git report this distance metric for any two revisions. However, git diffs are patches, which show entire lines even if you've only twiddled one character on the line; I don't want that, especially since my 'lines' are paragraphs. Ideally I'd even be able to specify what I mean by "word" (though W+ would probably be acceptable).

Is there a flag to git-diff to give diffs on a word-by-word basis? Alternately, is there a solution using standard command-line tools to compute the metric above?

Answer 1

Building on James' and cornmacrelf's input, I've added arithmetic expansion, and came up with a few reusable alias commands for counting words added, deleted, and duplicated in a git diff:

alias gitwa='git diff --word-diff=porcelain origin/master | grep -e "^+[^+]" | wc -w | xargs'
alias gitwd='git diff --word-diff=porcelain origin/master | grep -e "^-[^-]" | wc -w | xargs'
alias gitwdd='git diff --word-diff=porcelain origin/master |grep -e"^+[^+]" -e"^-[^-]"|sed -e's/.//'|sort|uniq -d|wc -w|xargs'

alias gitw='echo $(($(gitwa) - $(gitwd)))'

Output from gitwa and gitwd is trimmed using xargs trick.

Words duplicated added from Miles' answer.