There is a clear undeniable relationship between CR and encounter guideline building, the fact people are trying to deny this is baffling.
People aren't trying to deny that there's a relationship, but by far the more important factor is XP and numbers of foes, and you prove that yourself.
The monster manual makes the base assumption that the relationship between CR and encounter difficulty is that one monster of CR equal to the parties level should be a 'challenging' encounter for 4 party members.
This table illustrates what happens when you take a monster of CR equal to the party level (against 4 party members), and divide the encounter budget by how many monsters of that CR are expected in that encounter.
Apart from the fact there is a CLEAR relationship, this also tells you:
To get an easy encounter to use roughly half a monster of CR equal to the party level.
To get a medium encounter you use roughly 1 monster of CR equal to the party level.
To get a hard encounter you use roughly 1.5 monsters of CR equal to the party level.
To get a deadly encounter you use roughly 2 monsters of CR equal to the party level.
Alright: let's start with the MM's assumption and work our way down from there. The
only assumption the MM makes is that "An appropriately equipped and well-rested party of four adventurers should be able to defeat a monster that has a challenge rating equal to its level without suffering any deaths." That's it. In the example provided it says the monster should be "a worthy challenge", but what does that mean? Should it be a medium encounter, to account for the fact that there should be no casualties? Perhaps it should be a hard encounter, to account for the fact that nobody should die, but the threat should be there if there's a particularly bad streak of the dice?
Personally I'd tend towards it being a hard encounter, because it says they
shouldn't suffer any deaths (leaving the possibility open) and the description of a hard encounter says "[In a hard encounter] there's a slim chance that one or more characters might die". If so, then the only metric that matters is the one in the seventh column in your table: the number of CR-equivalent monsters required to make an encounter "hard". If not, then what are
you looking for in your table?
Now we can look at the table. It's fascinating, really. Using the
experience guidelines from the DMG (see, even if you think CR is an equivalent for XP you still use the XP rather than CR value), we can see how many monsters of a CR equal to level are required to make each difficulty of encounter for your hypothetical party. Level 1 is relatively clear-cut: "You need 1 monster of CR 1 to provide a medium challenge for a party of four 1st-level adventurers". Levels 2 through 20 are considerably less so. "You need 1.11 (repeated) monsters of CR 5 to provide a medium challenge for a party of four 5th-level adventurers". What does that mean? How am I supposed to find 1.11 repeated monsters? Perhaps an ooze is 1.11 times bigger than normal? Maybe a marilith has 1.11 times as many arms as a normal one? Maybe it instead means that I have to throw a monster of CR 5.55 repeated at the party?
This table goes to illustrate that CR is useless in terms of determining the difficulty of a given encounter. Why? Because a monster of CR 5-7 is an
easy encounter for a party of 4 level-appropriate adventurers, while at every other level, a level-appropriate monster is a medium encounter; if CR was a reliable indicator of a monster's strength against an equal-level party, it would be consistent from 1-20, and lie in the same region of a "medium" encounter (ie they're all medium tending towards easy, or medium tending towards hard). What if I wanted to throw a CR 5 monster at a 4th-level party? The CR can't account for that, so I'd have to look at the XP values to see where it would come on the tables (and so XP>CR). What if I'm tired of throwing enemies at my players one at a time? The CR can't account for that, so I'd have to look at the XP values and start using the multipliers to figure out the correct number of enemies, as well as the CR of those enemies, in the encounter (and yet again, XP>CR).
CR, XP, and numbers of monsters
must be integers. If you need to use "roughly half a monster of CR equal to the party level" to make an easy encounter, does that mean I cut a bugbear in half to make a 1st-level party have an easy fight with it? Should I use the top half or bottom?
Perhaps you should simply use a monster of half the intended CR, then. This works at level 1 (one CR 1/2 monster), but once you reach, say, CR 6, this doesn't work in the slightest: a CR 3 monster is nowhere near half the XP given by a CR 6 monster, and the discrepancy gets larger as you progress up the table.
And this probably explains why the whole encounter building guidelines are so messed up. 2xCR1 monsters against a 1st level party WILL be deadly. 2xCR20 monsters against a 20th level party will be a cakewalk.
Yeah... No. The encounter building guidelines are messed up if you use them without the assumptions they make for determining a party's power. If you use them correctly, they seem to work perfectly fine.