It seems that many WordPress web developers are unaware that you can remove the blog slug a multisite installation. This will save you from having to redirect all your posts, spilling some lovely link equity.
Where did this /blog slug come from?
When you install multisite, your permalink structure is set to the default structure, with the slug, /blog/ added before your permalinks. If you go to your settings, through the site’s dashboard, you will see the slug before the custom permalink input box.
I’ve seen this slug included in the input box, and also just before it, not allowing it to be deleted. I haven’t found a pattern or cause of this yet, but will look out for one as I install more multisite networks.
Salt on the Blog Slug
To remove the slug, go to your network admin, and to the primary site’s options > settings. Find the permalink setting, and change it to your desired url structure such as /%postname%/ like you see here.
You may need to again set your permalinks through the site’s admin as well, just make sure your links are working from the front end.
Why remove it?
If your permalink structure changes, any links to your posts need to be redirected. Although a 301 redirect is the proper way to move a page, it will filter out some of the strength of the links to the old page. This isn’t something to panic about if you really need to change your permalinks, but should be avoided if possible.