3 mph is an average human walking speed, cited in numerous places. That comes to 26.4 feet per round (which is interesting, because Pathfinder 2 put human's base speed at 25; that system has a 3 action system, so a base run speed of like 9 mph, but no sprint action). This is taken from just observing people, so it's a mix of healthy and less healthy, various levels of carrying stuff, different shoes. I'm fine with D&D characters having 30 speed.
Jogging is 4 to 6 mph, so this is move+dash
12 mph run for short distances isn't ridiculous, but there's a lot less agreement on "average human sprinting speed", because average people don't really sprint a whole lot.
So, then I grabbed a bunch of records.
Records (
List of world records in athletics - Wikipedia )
Distance | time | MPH | Feet per Round
(MPH x 8.8) | Multiplier
(40 speed) |
100 m |
9.58 |
23.35
|
205
|
5.1
|
200 m
|
19.19
|
23.31
|
205
|
5.1
|
400 m
|
43.03
|
20.79
|
183
|
4.6
|
800 m
|
1:40.91
|
17.73
|
156
|
3.9
|
1000 m
|
2:11.96
|
16.95
|
149
|
3.7
|
1500 m
|
3:26.00
|
16.29
|
143
|
3.6
|
mile (1609 m)
|
3:43.13
|
16.13
|
142
|
3.5
|
2000 m
|
4:44.79
|
15.71
|
138
|
3.5
|
3000 m
|
7:20.67
|
15.22
|
134
|
3.3
|
5 km track
|
12:37.35
|
14.77
|
130
|
3.2
|
5 km road
|
12:51
|
14.51
|
128
|
3.2
|
10 km
|
26:24
|
14.12
|
124
|
3.1
|
1/2 marathon (21.1 km)
|
58:01
|
13.55
|
119
|
3.0
|
Marathon (42.2 km)
|
1:59:40.2
|
13.14
|
115
|
2.9
|
100 km
|
6:09:14
|
10.1
|
89
|
2.2
|
So, Usain Bolt holds the record for the 100 m and 200 m, and the 200 m is done in just over 3 rounds. I'm having a hard time finding it again, but I did find a graph of his acceleration, and it did take him a bit to reach his top speed of 28 mph, which he only held for a short while.
A 400 m isn't run at the same pace as the shorter sprints. You pace yourself and don't run as hard, but looking at the times it's only slightly more than double the time of the 200. The drop to the 800 isn't even as bad when you consider it's a full 400 m longer, but there is a drop.
It's also interesting to note the difference between the 5 km track and 5 km road is small; people are only seconds faster on the track than the road.
That speed is held for quite a while. The difference between 800 and 1500 are pretty small, and the difference between 2 km and 5 km, or between 5 km and 10 km are minor too. Certainly far less than would be a multiplier.
That 100 km ultramarathon allows stops to eat and drink, included in the time I believe, but that's someone holding a "double move" pace for hours. This is why I disagree with the chase system having such limited dashes.
We can probably assume that these folks all have the Mobile feat, so they have a base speed of 40. I also think we could assume the short distance sprinters could have a different feat compared to the long distance joggers.
3E had a run action for x4 speed, and a run feat for x5 speed. That actually gets us shockingly close.
So, since we're dealing with heroic characters who delve dungeons and fight dragons, not run races, where does this get us? What would an adventurer need sprinting for? I'd say it could go into a (better) charge feat. What would an adventurer need long distance running for? That could go into a (better) endurance feat (replacing the terribly worded Durable).
We could then allow for Monks and Rogues to keep their double dash/x3 movement, then have a run action (full round action, requires some athletics check), and then some kind of constitution save to fight off fatigue when going long distances.