Change Adventuring day and Short Rest to Adventure and Milestone.

Change the names. Then give rules and XP budgets for the different modes of play. Why adventure and milestone. Because both words have DD history now and neither are intrinsically tied to time or space.

Milestone= 5 minute of rest or 2 encounters
Adventure= 24 hours
XP Budget= 100% per day

This is the default. We know how it works.

Action Oriented
Milestone= 5 minute of rest or 2 encounters
Adventure= 1 hour
XP Budget= 50% per hour

In this mode of play, characters get all their resources quickly but the face a lot more obstacles in a shorter duration. This lets them nova but action economy is against them. The DMG would suggest additional modules for keeping balance between the classes such as free power attacks and Injuries.

Hack 'n' Slash
Milestone= None
Adventure= 5 minutes
XP Budget= 25% per 30 minutes

This is Action with more action. Diablo/Gauntlet mode. The cave doesn't have 30 goblins, it has 100. And it is balanced. The DMG would sugggest swarms, summons, and numerous potions.

Milestone=  24 hours
Adventure= 1 week
XP Budget= 15% per day

In this mode of play, characters get all their resources slowly but they face a lot fewer obstacle sover a longer duration. This lets them deal with many weaker issues but they refresh powers at a slower rate and learn to conserve. The DMG would suggest additional modules for keeping balance between the classes such as maximum HP and daily action points.

Milestone=  1 hour rest anywhere but a large city
Adventure= 1 hour rest in a large city
XP Budget= 100% per day

In this mode of play, the PCs' power is location based. The wizard is stronger when he can go back to the arcane library every hour. The fighter can get magically healed up after every fight in the metropolis.  But outside of town is less accommodating. Mapmaking tools and even finer laocation bonuses would be offered by the DMG.

etc etc.

Then at the beginning of play, the DM and players can decide which mode they wish to play. The DM could also switch modes during play or even say PCs are in Classic mode while adventuring and Novel mode in town. This would lets the group tailor the game mechanics to the narrative in which ever way they prefer. This is the only way I could think of that building to such a large assumption of an XP budget would work.

Orzel, Halfelven son of Zel, Mystic Ranger, Bane to Dragons, Death to Undeath, Killer of Abyssals, King of the Wilds. Constitution Based Class for Next!

I like the idea of making the recovery periods into dials, to suit the campaign style and context.
What I don't agree with is associating the term 'adventure' with a time span. I rather think the 'adventure' should be defined by achievements (explore the dungeon, recover the artifact, discover the killer identity...), as devised by the DM. 
Just add a narrative adventure/milestone and this is pretty much awesome. A milestone could be completing a minor quest/goal while an adventure would be finishing a major plot point.
...or something like that.
But seriously, another great idea, Orzel.
"What's stupid is when people decide that X is true - even when it is demonstrable untrue or 100% against what we've said - and run around complaining about that. That's just a breakdown of basic human reasoning." -Mike Mearls
I had a vague idea about something like this when they first started talking about adventure budgets, but I hadn't really tried to flesh it out. I like this presentation and the different variety game modes.

This works for me, regardless of whether they add it or not, but having some back-up in the DMG would be great
Nice work.
Viva La "what ever version of D&D you are playing right now!"
Adding few more ideas to this vaulable thread. 
Note that I'm using the term Milestone here is a different meaning than the OP.
As in the OP the daily system is assumed to be the baseline (core) option, with these being availbale as options in a module.

Milestones instead of Days

Expose the math behind the adventuring day (either in terms of number of encounters or combat rounds) and let the DM set milestones upon them to grant the party full recovery of their resources.

The DM effort is about designing milestones in a way that makes sense in the context of the campaign and story (alternatively if the group is not concerned with game abstractions there is no need for narrative justifications either).

DM effort: Medium (or none) / System changes: None

At-wills and Encounters instead of Daily resources

The module should give guidelines to convert dailies into encounters and/or at-wills, decreasing their outcome to balance the higher frequency of use.

This solution is neat in terms of balancing, but sacrifices the tactical aspect of resource management.

DM effort: Low / System changes: High

Charging instead of depleting resources  

Instead of starting the day with a full array of resources, the ‘dailies’ need to be charged up before becoming available. The charging up is triggered by performing gameplay activities across the 3 pillars (combat, exploration, roleplay) during the day. After an extended rest all ‘daily’ resources reset and will need to be re-charged.

This method requires a mathematical balancing of the charging system so that the outcome is balanced across different classes.

DM effort: None/ System changes: Medium

I very, very, very much like the idea of using "milestone" and "adventure" to trigger resource recovery--so long as milestones and adventures are linked to the narrative rather than in-game time. For those who feel differently, the modular nature of Next could allow different modes--"simulationist" using in-game time, "narrativist" using story beats, and perhaps "gamist" following something similar to AEDU.
Sorry for my misunderstanding, what do you propose characters get for a milestone.
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