There have been a number of questions such as this one:
I wonder if there is any data available that indicating what the tangible impact has been. Do the site's statistics show the affect on new users of having their questions closed during their initial contact with the site?
One measure I can think is users with only one or a few questions that were closed and their reputation points have stayed or their participation in the site has effectively ceased. There must be better ways of finding suitable measures, but this is what I have come with off the top of my head.
It would help discussions about problems of closure on especially new users if some figures were available.