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I'm running an adventure that centers around a race, and I want to use the overland speed between scenes as a scoring mechanism. What is the best way to determine overland speed in D&D 4e? The players are likely to be outfitted with either light riding horses or warhorses, and the terrain is desert. Thanks in advance!

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The D&D 4th Edition rules for Overland Speed essentially breaks down to this:

1 unit of speed = 5 mi/day, 0.5 MPH, or 50 ft/min.

The D&DI Compendium references PHB page 283, with the following chart:

\begin{array}{ccrc} \text{Speed} & \text{Per Day} & \text{Per Hour} & \text{Per Minute} \\ \hline 5 & 25\ \text{miles} & 2½\ \text{miles} & 250\ \text{ft.} \\ 6 & 30\ \text{miles} & 3\ \text{miles} & 300\ \text{ft.} \\ 7 & 35\ \text{miles} & 3½\ \text{miles} & 350\ \text{ft.} \\ \end{array}

Also, see the related question, How does character movement translate to real-world speed?

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You have to check the slowest creature's speed (or mount, if the party is mounted). In your case is the war horse with a speed of 8.

Your group can travel 40 miles per day at 4 miles per hour.

Watch out for elves with the Light StepDDI feat: they add +1 to the base overland speed of all group.

By rules terrain does not affect overland speed, but feel free to adjust the base speed value according to the specific landscape.

Sandy zone of desert could be reasonably be regarded as difficult terrain. On planet Earth desert are for the most rocky, however.

Deserts pose environmental dangers and should probably call for Endurance check every 8 hours.
DC should be set according to your party level (see the fundamental Difficult Class and Damage by Level table). Guidelines say a DC 22 for heat environment or DC 26 for stifling heat).
Failed Endurance checks make characters lose one healing surge or an amount of hp equal to their level (if no healing surge remains). These healing surges cannot be recovered until characters take appropriate shelter against the environmental danger.

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If you're doing a race in 4E, I say forget thinking about overland speed altogether. Static numbers are pretty boring, and if each leg of the race is determined by the same number, then the outcome will be essentially predetermined. Instead, run it as a skill challenge of sorts. Only track relative position between the PCs and their competition. For example: far ahead, ahead, even, behind, far behind. Then have the characters encounter challenges along the way: having to consult their map, crossing a rough patch of terrain, sabotage from opposing teams, etc.

Make skill checks. If the PCs fail at the task at hand, their relative position moves back one step. If they succeed by a small margin, their relative position stays the same. If they succeed by a good margin, their relative position moves up by one step.

If you want another exciting challenge, have them attacked by wandering monsters of some sort. If they defeat the enemies quickly, they move up, but if they take too long, they move back.

And to make it even more interesting, allow the PCs to proactively interfere with the opposing teams. For example, if one PC gets the idea to cause a landslide, thereby blocking a pass, let them try it, and if their skill check is high enough, give them the bonus to their position.

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The best way to determine overland speed is personal experience.

During my Duke of Edinburgh gold award my group travelled 50 miles over 4 days doing little else but rest for food and sleep. We each carried about 40 Kilos (?) including Food, Tents, first aid kit, cooking equipment. Water was collected at the sites we stopped at. We travelled about 10-12 hours a day. I'd say it was a fairly reasonable travel time for amateur/enthusiast walkers. No one had spent a feat to make extended travel easier.

Maths time:

\$50\,\text{mi}/4\,\text{days} = 12.5\,\text{mi}/\text{day}\$
Which is equivilent to ~45ft/min or 0.5 MPH.

at 45ft/min that's 9 squares every minute. Assuming a round is 6 seconds, that's 0.9 squares/round. Lets call it 1 square per round. I am (last time I checked) human, so my base speed is 6 squares per round, or 60 feet per round.

This means to convert from combat speed to overland speed you divide by 6. To get your overland speed in Mi/day you multiply your sqrs/round by 2 (roughly).

That war horse is travelling at about 16 Mi/Day.

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