JS_Harris - 5:10 am on Mar 18, 2010 (gmt 0)
If you submit a page to 10 directories and the article is then sent out to 90 sites you have a potential for 100 incoming links. From that you can ultimately expect 1 qualifying backlink and 99 duplicates and the value of your backlink will depend on which site Google ultimately chooses to call the owner of that article.
It's also likely that article directories are somewhat discounted so there is a chance you end up with no qualified backlinks at all in the long run. Some may show up temporarily but they likely will fade away in time, especially when the article becomes buried in a sites archives.