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The current 5e campaign I'm running uses the encumbrance variance rules and demands a lot of travel and resource management on the part of the players.

This brought up questions about penalties when exploring and traveling while encumbered/heavily encumbered (especially from players of characters with lower strength scores)...

It is stated in the PHB that being encumbered reduces a character's movement in combat, while being heavily encumbered drops movement further, and negatively affects attack rolls, ability checks, as well as certain saving rolls. That is clear enough!

The DMG adds:

The difference between walking speeds can be significant during combat, but during an overland journey, the difference vanishes as travelers pause to catch their breath, the faster ones wait for the slower ones, and one traveler’s quickness is matched by another traveler’s endurance.

So, it appears, according to RAW, that even a heavily encumbered party's travel speed is not affected when exploring or traveling, nor do they suffer any other penalties associated with exploring and/or travel (e.g. reduced distance covered/marching time, increased risk of exhaustion, etc.).

We aren't missing anything obvious?

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Generally speaking, Encumbrance rules do not apply in overland travel.

There are rules for faster and slower travel overland, but they aren't affected by how much weight an individual character is carrying—because they aren't affected by a character's movement speed at all.

For example, it's not uncommon to have a party who, through various means, has lots of characters with higher-than-usual movement speeds, like Monks and Barbarians who gain progressively faster movement speeds, Druids with their swift beast forms, Rogues with their ability to Dash multiple times in a turn, Paladins and the Steed they can summon, and so on, and so forth.

However, no matter how fast these characters get, they still travel at 2-4 Miles per hour (depending on which pace they choose), which unless the party chooses to suffer potential Exhaustion effects in order to move farther in a day (Forced March, PHB, pg. 181), covers 16-32 miles in a day.

Every character and monster has a speed, which is the distance in feet that the character or monster can walk in 1 round. This number assumes short bursts of energetic movement in the midst of a life-threatening situation.
The following rules determine how far a character or monster can move in a minute, an hour, or a day.

Travel Pace

While traveling, a group of adventurers can move at a normal, fast, or slow pace, as shown on the Travel Pace table. The table states how far the party can move in a period of time and whether the pace has any effect. A fast pace makes characters less perceptive, while a slow pace makes it possible to sneak around and to search an area more carefully (see the "Activity While Traveling" section later in this chapter for more information).

Movement, Player's Handbook, pg. 181

It's not uncommon (I do this at my table) for a DM to modify the normal travel paces though by taking the circumstances of the party into consideration. For example, I generally allow a faster travel pace proportional to the lowest movement speed of the party, taking for granted that 30 feet per round is approximately 3 miles per hours (within ~12%), so whatever the lowest movement speed is, you'd divide it by 30 and then multiply it by whatever travel pace the party chooses, establishing their new travel pace. I find that it helps players feel more empowered by their character creation decisions: if the party is full of speedsters, chances are good they're sacrificing potential in other venues, so I'd rather let them have benefits from the feature they do have.

Whether or not I'd apply Encumbrance penalties (which I do use at my table) to travel pace depends on the circumstances of the character's Encumbrance. If a character is narratively carrying a heavy object because it's important and needs to be transported, I'll usually apply an overland speed penalty proportional to their encumbered movement speed, but if a player is just carrying their normal equipment and encumbered because the default equipment that players are issued is actually surprisingly heavy guys, oh wow, then I usually just elide it and let them travel at normal speed. In my experience having Encumbrance apply to Travel Pace just tends to frustrate players, upset that (in their perception) you're punishing them for all the sweet loot you gave them.

So while there is a very easy way to rig together a method to apply the Encumbrance Rules to overland travel, I generally don't do that unless I think it's needed, and the Rules-As-Written in 5e don't say you should anyways, so it's probably better in most circumstances to just let it be.

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