The typical Challenge Ratings and DC charts in the DMG don't really work, in my experience. Maybe we're doing it wrong, but it seems like the battles that are supposed to be Hard end up being either Easy or Deadly, and I can't figure out why. And the skill DC charts never seem to account for highly-optimized characters loaded to the teeth with feats and multiclass options, either: past 8th level, my players are never challenged by a DC 18 ability check.
So I've cooked up my own chart for DCs, depending on the players and their characters. For skills:
"Easy" would be about a 90% chance of success. So if the rogue has a +7 to Thieves' Tools, and assuming he makes the check at Advantage (through the Help action, or the Guidance cantrip), a trap with a disarm DC of 14 or less would be "Easy." (14 - 11 = 3, so the player would only fail with a roll of 1 or 2 on 1d20---a 90% chance of success.) The players make certain that the rogue is the only one who will ever be making that Thieves' Tools check, and will always be doing so at Advantage...so I make certain that all Easy traps in my dungeon have a disarm DC of 14 or lower.
"Medium" would be a 60% chance of success. Same as above, but the DC would be 20. (20 - 11 = 9, the player would fail on a roll of 8 or less.)
"Hard" would be a 30% chance of success. Same as above, but the DC would be 26.
"Deadly" (or "Impossible") would be about a 5% chance of success. Same as above, but the DC would be 31. The player would need to roll a natural 20 in order to succeed, which would only happen about 5% of the time.
Combat is harder to pin down mathematically, though. I'm still working on a system that better estimates how to model it, but I figure an Easy encounter should use up about 10-25% of the party's daily resources. A Medium one should consume about 30-50%, a Hard one should consume 60-75%, and a Deadly one should consume 90-100%. ("Daily Resources" means hit points, spell slots, magic item charges, and special abilities, basically everything that recharges in 24 hours.) If anyone has a system that can easily track these resources in this manner, I'd love to see it...because Challenge Rating just isn't working for me.