So, before I had to actually build my own encounters, I always assumed the APL and monster CR had something to do with each other, but it seems like they don't. Now that I'm not running something out of a module, I have to build my own encounter, so I went to the CRB to read about how to do this. In the CRB it gives the example that a CR 10 encounter (which would be challenging for the party which was APL 9) would include a CR 8 monster and 4 other CR 4 monsters. This blew my mind. They came to this using an XP budget \ buying system. Is this really a reliable way to build encounters? What's the point of individual monster CRs? I'm trying to build a couple encounters for a party of APL 4, 3 lvl 5 characters.
something to keep in mind is action economy. a single CR 10 monster is going down easier than a CR 8 + minions because it has 1 turn of actions/# of PCs.
Other than that, the CR system seems to be generally perceived as flawed. As I understand it, it's balanced against a party of 4 with the standard party makeup (fighter/rogue/cleric/wizard). An encounter can be a cakewalk for one party of adventurers but be a slog and TPK for another. Building encounters is an art more than a science and it's about learning to build encounters that are the appropriate level of challenging for your party of adventurers. Sometimes you'll be surprised by how an encounter turns out in play.
The CR system has some issues, but on the whole is reasonably reliable. Party composition and player skill all have an impact - no system can account for those. Also there are a few outliers to keep it interesting - those creatures that are under or over CR'd. Single creatures often struggle to match their listed CR.
The problem is Pathfinder is not a linear system.
If you didn't have individual CRs you wouldn't have any basis at all to work out the combined CR of an encounter.
Individual monster CRs matter because it’s a matter of fewer, more powerful, enemies vs. more, less powerful, enemies. For example, with your APL 4 party, an average difficulty encounter would have a total CR of 4 (awarding a total of 1,200 XP). You might have them fight a single Forest Drake (CR 4, taking up your entire XP budget), or instead decide to split the XP up between a pair of cheetahs (each one is CR 2, awarding 600 XP each for a total of 1,200).
The CR of a monster gives its rough xp value , it is not additive.
So 4 CR1 Creatures so using your example a CR 8 creature is worth 4800 xp and each of the CR 4 creatures is worth 1200 xp , for a total of 9600 xp which happens to be the total of a cr 10 encounter.
It is a decent start for building an encounter but the CR system does not work perfectly , it depends on your party composition,number of pc's, point buy and how optimised your pc's are.
With 3 pc's you should use slightly weaker encounters as your party only has 3/4 of the expected actions and abilities. Aim for a budget of around 7200xp for a CR 10 encounter which would give each pc what they would have got in a 4 man party vs CR10
But the baseline assumption is 15 pt stat buy and badly designed characters of your players have a higher pt buy of stats or are well designed then they will be able to deal with higher CR opponents. Also some creatures or combinations of creatures are particularly strong or weak against a specific party.
I expect my 4 PC team to defeat encounters much more effectivly than the rules allow as I give a high point buy and they build effective characters and then fight with good teamwork.
So while the encounter builder is a guideline you have to use your judgement to some degree and adjust as necessary to maintain a threat.
So for your 3 character level 5 party some APL encounters would be
1 CR 4 Monster Flail snail or 2 CR 2 Alligators
For a APL +3 Encounter I woudl budget that as 3600xp as 3/4 of a CR8 Encounter for a 4 character party for instance 2 alligator pets and a Seawater Merrow
In the CRB it gives the example that a CR 10 encounter (which would be challenging for the party which was APL 9) would include a CR 8 monster and 4 other CR 4 monsters. This blew my mind.
Why? Were you expecting that to be a CR 24 encounter?
The CR/APL system says for every two CR / character levels you go up, your power level basically doubles. Experience values are proportional to power, so they double at the same rate.
For example, a CR 8 monster is worth 4,800XP. Two CR 8 monsters are worth 9,600XP, which is the same as a CR 10 monster is worth.
If you're trying to make a CR 10 encounter, you can use a single CR 10 monster, or two CR 8s, or a CR 8 and two CR 6s, or a CR 8 and four CR 4s, or a CR 8 and eight CR 2s, or just four CR 6s... Any of these combinations should be moderately challenging for a level 9 party.
Other people have explained how encounter building works well enough, I probably shouldn't try to add anything unless you say you need clarification.
Here's a spot of advice, though. After you build the encounter, if you're worried that it's too tough for the PCs, run through it yourself using the PCs' stats, to see how hard it really is.
In the CRB it gives the example that a CR 10 encounter (which would be challenging for the party which was APL 9) would include a CR 8 monster and 4 other CR 4 monsters. This blew my mind. They came to this using an XP budget \ buying system. Is this really a reliable way to build encounters? What's the point of individual monster CRs?
I use the XP budget method for a few years now - works pretty well. Individual monster CRs are relevant for this method, because they are totally tied to the monster's XP value (CR 1 equals 400 XP, CR 2 equals 600 XP etc.).
Technically you could ignore CR and work just with XP, since they are interchangeable with each other. But the rapidly growing XP values are more difficult to grasp (is 100,000 much?), and more difficult to compare to the party (is 100,000 tough for a level 9 party?).
A handy way to figure out the CR of a group of monsters is the rule that for X greater or equal to 1, two groups of monsters of CR X working together creates a CR X+2 encounter. CR 1/4, 1/3, and 1/2 use different math.
To calculate the CR of a CR 8 lamia matriarch teamed up with four CR 4 sea hags, first group the hags into pairs. A pair of sea hags has CR 6. Next pair the two CR 6 pairs. That creates a CR 8 group of four sea hags. Now we can easily pair the CR 8 group of four sea hags with the CR 8 lamia matriarch to create a CR 10 encounter.
Combining a CR X group with a CR X+1 group gives a CR X+2.543 group, for those times the GM wants an enounter harder than CR X+2 and easier than CR X+3. Combining a CR X group with a CR X+2 group gives CR X+3.170 group, which we can round to CR X+3. Combining a CR X group with a CR X+3 group gives CR X+3.874, which we can round to CR X+4. Combining a CR X group with a CR X+4 group gives CR X+4.644, which is too small to round to CR X+5, sorry. I used logarithms, 2*log_2(1+2^(difference/2)), to derive these numbers.
But the CR system is only a rough approximation. Some creatures are strong for their CR. Other creatures are weak for their CR. More significantly, some parties dominate monsters of one type and crumble before monsters of another type. To truly judge the difficulty of an encounter, the GM must know the strengths and weaknesses of the party.
For example, suppose a party wanders into the Valley of the Giants. At low levels, they encounter a Giant Frog (CR 1), a Giant Crab (CR 2), and a Giant Eagle (CR 3). After battling enough giant insects and animals to level up several times, they encounter Hill Giants (CR 7) and Stone Giants (CR 8). They master battling these large, trong creatures, specializing in Power Attack, reach weapons, and battlefield control methods that neutralize Strength. Then, unexpectedly, their next enemies consist of CR 8 halfing ninjas. The ninjas use the vanishing trick to turn invisible for sneak attacks and escaping. Even while visible, the ninjas' high Dexterity, small size, and enchanted armor make them hard to hit. The party will be overwhelmed by the unfamiliar tactics even if the CR is the same as the last group of Stone Giants they defeated. The party's specialization in fighting giants will work against it this time.
Thanks to everyone for their responses. Before really looking into it, as I had to do recently, I knew that parties had APLs and that monsters had CRs and that encounters had CRs also, and that if the CR of an encounter was the same as the party's APL, is was a medium difficulty encounter. But I thought that, since they were called the same thing, that a CR 8 monster made a CR 8 encounter, and that if you wanted a CR 10 encounter, you got a CR 8 monster and a CR 2 monster (for example). That's why I was so surprised to the example in the CRB of a CR 10 encounter being made up of a CR 8 monster and four CR 4 monsters. I'd also never heard anyone talk about XP budgeting for building encounters they way they do in the CRB. I think simply because they used the same name (Challenge Rating) the describe the difficulty of monsters and of encounters, I thought they were basically the same or had a 1:1 relationship to one another. Otherwise, why would they give monsters CRs if it didn't relate to the encounter CRs in some way? Anyway, this all makes a lot more sense now.