As-fan is a R&D term to describe how a booster pack looks like "as fanned", i.e. spread out across the table in a fan-like shape. It assigns a number to the actual frequency of certain cards in booster packs.
The number "as-fan" is a combination of the rarity of the card, the number of cards with the same rarity and the set number of cards with that rarity in a booster pack. Each booster pack (on average—there can be variance) has ten commons, three uncommons, a land (usually basic), and one rare or mythic rare. Fifty commons will show up much more because ten of the fifteen slots are allocated to common while only one slot is allocated to rare (and one out of eight times it gets replaced by a mythic rare). For example, this can result in 2 gold cards as-fan, meaning that on average each booster contains two gold cards. Simarly, each color has a different creature as-fan, with white being 60% and blue—being the lowest—at 47%.
Mark Rosewater used to say that “If your theme’s not at common, it’s not your theme”. This came from a time where rarity was the only tool to control as-fan. With modern collating technology to do things like a guaranteed card per booster pack, there's now other ways to guarantee the theme is recognizable with just a few packs opened. Innistrad began with double-faced cards with one in each pack. Dominaria's legend theme was set with an uncommon or higher legendary in every pack, which was later also done with Planeswalkers in War of the Spark. Zendikar Rising later combined these two with its MDFCs, upping the "land" count and theme without saturating rarities with nonbasic lands. Strixhaven: School of Mages had another variation, where the mythic, rare and common Lessons are on one sheet and guaranteed one each pack, while uncommon Lessons are distributed as normal.
- Mark Rosewater (November 7, 2016). "A Few More Words from R&D". magicthegathering.com. Wizards of the Coast.
- Mark Rosewater (May 09, 2011). "The Issue Is Legen—Wait for It—Dary". magicthegathering.com. Wizards of the Coast.
- Mark Rosewater (June 10, 2013). "A Few More Words from R&D". magicthegathering.com. Wizards of the Coast.
- Sam Stoddard (February 20, 2015). "Presidents, Kings, Role of the Leads". magicthegathering.com. Wizards of the Coast.
- Mark Rosewater (May 21, 2016). "Still don't know what as-fan really means.". Blogatog. Tumblr.
- Mark Rosewater (March 10, 2019). "You've stated repeatedly that if it isn't your theme at common, it isn't your theme.". Blogatog. Tumblr.