Q:

How to adjust CR of a campaign?

So I'll be GMing for the first time ever. All of us except for the previous GM (who will now be playing) are very inexperienced.
We just got done with first major campaign, and me being new, decided to run a the Carrion Crown campaign. All of the newer players are bummed that they're going to have to start over at level 1.
To compromise I told them I was runt he game at fast character level advancement per this chart. Carrion Crown is supposed to be run at the medium level advancement pace.
What are some general tips for increasing the challenge as the campaign goes on and my PC's out level the suggested challenge rating. Add more NPC's? Swap out some NPC's for more difficult creatures?
Any tips would be appreciated. At some point I'd also like to take some of the other official adventure paths and tweak them to start at higher levels, like starting at level 10 instead of level 1.

A:

The CRs in 3.PF are wildly variable in their accuracy (which makes sense, considering that the power level of parties of a given level are also wildly variable), so don’t put too much faith in CR. No matter what the numbers say you’ll have to tailor the encounters for the party based on their power, even if their level says it should match the encounter’s CR. They can easily be much, much more or less powerful than those opponents, and that’s not even getting into the possibility that they’re more (or less) powerful in general but those specific opponents are particularly well (or poorly) suited to fighting them.

