When Dungeons & Dragons first appeared over 40 years ago, the concept of experience points and levels was new. Today many, many different games have experience points and levels, even if they aren't really roleplaying games. Character progress is an extremely popular concept. But finding the best system to grant experience points and levels is still not easy, especially not in a pen & paper game like Dungeons & Dragons.

Of course Dungeons & Dragons has rules for granting experience points. These mostly cover the players being rewarded for slaying monsters. Every monster has an xp value, and at the end of the fight you divide the xp of the monsters by the number of players and that is how many xp everybody gets. In 5th edition there is an added element for that, a curios multiplier that goes up with the number of monsters: x1.5 if there are 2 monsters, x2 if there are 3 to 6 monsters, x2.5 for 7-10 monsters, and so on. The argument for that is that more monsters have more attacks, so 5 monsters being worth 700 xp together are more dangerous than one monster of a higher CR that is worth 700 xp alone. Where that logic fails is if you consider it from the point of view of the monster: The multiplier applies only to the number of monsters, not to the number of players. And if the danger of monsters goes up more than linearly with numbers, so should the danger of the group of players go up more than linearly with numbers. That is a permanent problem in my home campaign, which at 6 players is on the large side for adventures designed for 4 or 5 characters.

The idea of dividing xp by the number of players is also problematic if you consider that it means that a larger group goes up slower in level than a smaller group. Published adventures frequently assume that the players are of a certain level at a certain point, but if there are more players that might not be the case. Unless of course you change all the encounters to add some more monsters to keep the level of challenge for the group the same for the larger group. That doesn't always make sense, although some adjustment is certainly advisable for groups that have more or less than the recommended number of players.

In my 4E campaign, the adventure didn't give out individual experience points at all. The adventures were organized by chapters, and at the end of some chapters you were told that the players would now gain a level. That is probably the easiest way to handle level-ups, but in 5th edition the method has its issues: Because of the multi-combat nature of 5E, adventures frequently have side-quests and optional encounters. If you give out levels at certain points in the story, following side-quests becomes a whole lot less interesting. You certainly don't want a Dungeons & Dragons game to degenerate into a MMORP-style "grind for xp", but if you want to encourage players to explore, giving out experience points for the encounters resulting from exploration is a good way.

You can of course also hand out experience points for clever ideas, solved puzzles, overcome traps, or good roleplaying. This is basic behavioral economics: Give out rewards for whatever you want the players to do, and they will frequently do it. However then you'll end up with a potential other problem: Do you give out xp for everybody or individually? Players aren't equal, and every table has some players contributing more ideas and others contributing less. Give out individual xp, and you'll end up with level differences between players. To caricature it, the player already hogging most of the spotlight also ends up being higher level and stronger than the others. Not a recipe for good teamwork. Which is why I prefer to give out xp equally to all group members, even if it was not all of them who actually solved the problem.

So for my 5th edition campaign I think I will use a mix of different methods: Everybody always gets the same xp (including the person who didn't turn up for that particular session), but xp are granted for various things, not just for killing monsters. And at certain points in the story I might give out "story xp", which increases the probability of leveling up at the end of a chapter rather than right in the middle of it.