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There are many questions about changing the scaling on encounters, but I am curious if anyone knows why the designers chose 5 players as the default. FWIW, I would assume that 4e would use a 4 player party for each of the 4 roles.

Are there interviews, or a page in a book, where it's explained what their reasoning was?

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    \$\begingroup\$ Hi Jay, and welcome to RPG Stack Exchange. I've revised your request to remove invitation for speculation/guesswork. Per our quality standards, the only type of "why did the designers do this?" answers we accept are those that base their answers in the designers' actual statements, in interviews or books or so on. We specifically reject speculative answers and "here's my vague guess/theory" as unacceptable by our quality standards, and they are heavily downvoted or removed. \$\endgroup\$ – doppelgreener Jan 9 '18 at 11:00
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    \$\begingroup\$ When 4e was being developed, D&D was experiencing a renaissance of popularity - even Vin Diesel plays! Thus, the average player's number of friends went up, from 4 to 5, and the game had to be redesigned around it. \$\endgroup\$ – SPavel Feb 21 '18 at 20:33
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The short answer is that they didn't, exactly. The game is scaled for 4-6 player characters, with five being the convenient midpoint for the DM to easily scale up or down published adventure modules.

From the 4e DMG (p31):

This book provides rules and guidelines for running a group of four to six player characters. If your group varies from that size, you have some specific issues to deal with.

The sections "Smaller Than Four" and "Larger Than Six" address in what ways the game breaks down at these scales.

The slightly longer answer is that early encounter design grew out of experiences the designers had playing "more fun" engagements in miniatures combat. From "Wizards Presents: Worlds and Monsters," designer James Wyatt says,

When we started designing 4th Edition, we quickly discovered that we all shared the same experience. Encounters with multiple monsters are just more fun. So we began with a new assumption: The baseline encounter for a group of five PCs of level X is four monsters of level X.

Although that still puts the ratio in terms of players::monsters, Wyatt goes on to clarify he views encounter design from the POV of the monsters, (or more generally, the DM running the monsters) rather than the players. One such excerpt (same book):

if you design an encounter aiming for four monsters, it’s a lot easier to use all the roles. A mind flayer might have a bodyguard of advanced grimlocks—controller plus melee. A thug in an alley is supported by backstabbers lurking in the shadows—melee plus lurkers. A pair of ogres shield an orc archer and a shaman—melee, artillery, mastermind. Highly mobile drow control a giant spider that emerges from the shad- ows to pick off isolated PCs—skirmishers with a lurker. The possibilities are endless, varied, and extremely fascinating.

So from that perspective, your question ("Why did the D&D 4e designers scale everything for 5 players?") doesn't reflect the designers' initial thought process. Instead, it would be, "How many players (within the sweet spot of 4-6) are needed to deal with a fun encounter of four monsters of varied roles?"

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