Exactly four? No. But it did assume a ballpark of 3-5 encounters in terms of balance. That's how they arrived at the number of healing surges and balanced player abilities. They didn't just pull that number from the aether.
Can you tell me where this
assumption is stated?
To put it another way: it is one thing to build a system so that it is able to perform within certain parameters. It is another to build it with the goal being to fit within, or be balanced solely within, those parameters.
For instance, here is a run-down of an "adventuring day" from my 4e game, when the PCs were mid-paragon:
Recently, the PCs in my game took on the following sequence of encounters without an extended rest:
*Comp 2 L14 skill challenge (as a result of which each PC lost one encounter power until their next extended rest);
*L17 combat;
*L15 combat;
*L7 combat;
*L13 combat;
*L15 combat;
*Comp 1 L14 skill challenge;
*L16 combat;
*L14 combat;
*L13 combat;
*Comp 1 L15 skill challenge;
*L16 combat (the L15 solo was defeated by being pushed over a bridge down a waterfall);
*L15 combat (the solo returned later in the night, having survived the fall and climbed back up).
The PCs started this day at 14th level, and finished it at 15th.
Admittedly some of the encounters involved waves/split opposition rather than a unified force; but equally, in some of the encounter the PCs were split and couldn't bring all their power to bear simultaneously or in a co-ordinated fashion.
I continue to find 4e PCs very resilient.
It's not a coincidence that 4e is very forgiving/flexible vis-a-vis the length of the adventuring day: the amount of mechanical capacity a 4e PC can bring to bear in a given interval between short rests is only loosely related to the amount of mechanical capacity that PC can bring to bear in a given interval between extended rests. This is because most "oomph" comes from encounter powers (and other encounter-based resources, like action points); and the significant cap on hit point recovery tends to be the availability of healing powers rather than of healing surges.
This means that an encounter can be very challenging and dramatic even if it does not consume many "daily" resources (eg because the terrain, or the manoeuvrability of an opponent, or the fictional context of a skill challenge, made it difficult for the players, via their PCs, to bring their abilities to bear upon the situation).
The same phenomenon is also what makes mechanical balance relatively easy to measure and achieve: because no significant allowance needs to be made for the difference between nova-ing or not. (At least, not significant compared to AD&D, 3E or 5e.)
Which means that the encounter-building guidelines are just as useful in the context of the "adventuring day" that I just posted, or in the context of an adventuring day in which only a handful of encounters takes place. They don't need to rest on any assumption about 3 vs 5 vs (by my count of the above) 9 encounters at or around the PC's level between extended rests.
In 3e and 4e, baseline encounters were designed so you wouldn't face that kind of unfair fight that required lateral thinking. Encounters were a tactical puzzle that could be "solved" through coordinated use of powers.
I can't comment on 3E, with which I have only limited experience.
As for 4e and "lateral thinking", you need to tell me what you mean by "lateral thinking": some people think that AD&D players using burning oil to do mass AoE damage (3d6 at 1st level) is lateral thinking; I think of it as standard operating procedure. I don't know whether you regard a 4e fighter leaping onto the back of a flying dragon so as to gain OAs when it moves and thereby knock it prone thus driving it to the ground (in the fiction, pinning a wing) as "lateral thinking" or not - but to me that is as "creative" or "lateral" as using oil or smoke or the other standard techniques for dealing with the Keep; or the flying thief on a rope to deal with the ToH.
Please refer to page 58 and 59 of the DMG. Really, pages 56-59+ layout a by-the-book encounter. Which is what I'm talking about, designing encounters by following "the rules".
You seem to have a much lower threshold for calling something "a rule" than I do.
Page 58 of the 4e DMG introduces those examples thus:
Here are templates you can fill in with monsters of your own choosing that combine different roles and levels into dynamic encounters. . . .
The example encounters given in this section serve to illustrate the sorts of adversaries you can produce from the creatures in the Monster Manual.
To me that doesn't read like a rule. They're examples. There are other examples in the MM that don't fit any of these templates. (For example, the first suggested encounter in the 4e MM is on p 9. It suggests 1 aboleth slime mage (level 17 artillery), 2 aboleth lashers (level 17 brute) and 9 kuo-toa guards (level 16 minion). This does not fit any of the DMG templates.)
Pages 56 and 67 do not set out any "by-the-book" encounters either. They give advice on correlating encounter level to difficulty:
An easy encounter is one or two levels lower than the party’s level.
A standard encounter is of the party’s level, or one level higher.
A hard encounter is two to four levels higher than the party’s level.
There is no
prescription as to what level encounters a GM should use. What I regard as the key advice is found on pp 56, 101 and 104:
Building an encounter is a matter of choosing threats appropriate to the characters and combining them in interesting and challenging ways. . . . Encounter-building is a mixture of art and science as you combine these threats together. . . .
Know the characters’ capabilities so you can build encounters that test those resources. . . . Know what the characters are capable of, and then design to reward the clever use of those powers. . . .
When you’re building an adventure, try to vary the encounters you include, including combat and noncombat challenges, easy and difficult encounters, a variety of settings and monsters, and situations that appeal to your players’ different personalities and motivations. . . .
An encounter with five different kinds of monsters is complex for the players and for you, so mix those up with wolf pack encounters (a group made up of a single
kind of monster; see page 59 in Chapter 4) as well as more straightforward encounter types. . . .
The specific
advice on encounter difficulty is found on pp 56-7 and 104:
You can offer your players a greater challenge or an easier time by setting your encounter level two or three levels higher or one or two levels lower than the party’s level. It’s a good idea to vary the difficulty of your encounters over the course of an adventure, just as you vary other elements of encounters to keep things interesting . . .
The majority of the encounters in an adventure should be moderate difficulty—challenging but not overwhelming, falling right about the party’s level or one higher. . . .
Hard encounters are two to three levels above the party, and can include monsters that are five to seven levels above the characters. These encounters really test the characters’ resources, and might force them to take an extended rest at the end. They also bring a greater feeling of accomplishment, though, so make sure to include about one such encounter per character level.
My own experience is that, at tiers above Heroic, this advice is overly conservative; particularly at Epic tier.
the rules tell you the maximum difficulty for an encounter. If you're playing by the rules, you're not going to put a party against an encounter with a budget outside of their expected level range.
There is no
rule that caps encounters at 4 or fewer levels above the party's level. And I suspect that I'm not the only GM who has found that, at epic tier, level +6 to level +8 makes for a suitably climactic combat encounter.
That said, the context of an encounter can be very significant. As described
here, when I ran G2 in my 4e game a 27th level dragon encounter for 26th level PCs was more challenging than some higher-level encounters, because the aerial circumstances favoured the dragon over the PCs in their Thundercloud Tower.
To me, this reinforces my view that what makes encounters interesting and memorable is not the encounter level per se, but the fiction, which - at least in 4e, given the nature of PC building and action resolution in the system - will include the clever stratagems and surprises pulled out by the players (via their PCs) to try and get the better of the situation.
One encounter that I remember pretty well despite GMing it years ago involved
5 level 10 PCs against a single cave bear. I remember it because the players decided to have their PCs tame, rather than kill, the bear; and the player who initiated that approach said, at the end, "I feel good about not having killed that bear".
When I try to think of the last boring encounter that resulted from my use of the 4e encounter-building guidelines, I have a lot of trouble. Maybe a one-on-one arena battle between a PC and an ogre, around 4 years ago.
Straight fights can be fun to play. But there's nothing inherently special with them.
Provided the fight is an appropriate challenge, the difference between a couple orcs in a 10 ft x 10 ft room and two dozen balors in a 100 ft x 100 ft platform is largely numbers. Nothing in a balanced encounter makes it memorable. Nothing in a standard encounter is special. It's just going through the motions. It's fun to play and could have a wide variety or story implications and roleplaying moments, but nothing in a straight fight becomes fun to retell. It's just that fight where everyone rolled expected numbers, used an appropriate amount of resources, and took an average amount of damage. We've all had that fight a dozen times and there's no point in telling that story. It's just not memorable.
What makes a fight memorable is everything else. All the stuff that isn't in the book, that isn't covered by the encounter building rules.
If those are your ideas of a "standard" encounter than no wonder they're not memorable! I haven't had that fight a dozen times. I've never run an encounter like that in 8 years of GMing 4e.
I've followed the key advice that I identified above (plus advice on terrain, stakes etc found in the two DMGs), and that has given me pretty good results.
But it wasn't enough to strain resources, so they tended to be pretty spectacular displays.
