This is just an example of my brain trying to work out the mechanical formula to find what it would take to make a true "speedster" base class. I put two benchmarks. First would be "Can it move the speed of sound by level 10?" The second was "Can it move the speed of light by L10?"
My three formula ended up being:
Base speed + speedster level
Base speed x speedster level
Base speed x (speedster level x 100)
The base speed for a creatures in D&D & Pathfinder is about 30 feet per turn. That works out to 30 feet every 6 sec. (Or about 3.5 mph)
I am using 761.207051 mph for the speed of sound (which is the speed of sound at 60*F and 670,616,629 mph for the speed of light.
30 ft per turn (6 sec) + speedster level (L10)About 15 mph
30 ft per turn (6 sec) x speedster level (L10)About 35mph
30 ft per turn (6 sec) x 100 per speedster level (L10) [1,000 x 30 = 30,000]About 3,400 mph
So... it looks like the 3rd formula worked out (It BLEW by the speed of sound though...)
I have to ask myself. What would the speed by at 20th level? What would happen if I tried to get closer to the speed of sound at 10th level? Say... trying "Base Speed x (speedster level x 50)" or even "Base Speed x (speedster level x 10)".
"Base Speed x (speedster level x 100)" (20th Level)" = About 6,818 mphThis is not past the speed of light.
"Base Speed x (speedster level x 50)" (10th Level)" = About 1705 mphThis is not close to the speed of sound.
"Base Speed x (speedster level x 10)" (10th Level)" = About 341 mphThis is not close to the speed of sound.... however I noticed something. This is a little more than half the speed of sound... hmmm (Speed of Sound is about 761 mph at sea level...)
So... lets see where that goes at L20.
"Base Speed x (speedster level x 10)" (20th Level)" = About 682 mph
This is VERY close to our first benchmark of 761. I bet if I just play with it a BIT I can get something that lands just north of the speed of sound.
This is where it gets tricky though. If I pulled out a number like "17" and inserted it into the formula (so "Base Speed x (speedster level x 17)" (20th Level)") players would just find the math wonky and odd. As a mechanics designer, I attempt to keep number nice and friendly for people. Numbers that end in 5 or 0 make people happy. Makes math easy. 0 is better than 5 mostly too. Espically
So let's give "Base Speed x (speedster level x 20)" (20th Level)" and "Base Speed x (speedster level x 15)" (20th Level)" a shot.
x20 gives us a result of 1362 mph... hmmm close.
x15 gives us a result of 1023 mph.
While the x20 is HIGHER, I don't really mind. This is going to be SO FAR past anything other characters can do, it's gonna be a game maker. I would chose the x20 over x15. However... I am going to try to look at this a different way. A static gain per level in movement speed. I will work BACKWARDS to see if I can get something around the speed of sound.
Goal 761 (speed of sound at 60 degrees Fahrenheit)
Feet per sec: 1117.469
Feet per 6 sec: 6704.814
Square = 5 feet
Turn = 6 sec
Movement speed of: 1340.9628 squares per turn
Round up: 1340 sq/turn
-30 for avrg base speed
/20 character levels
65.5 sq/turn per level gained in movement speed
So every level a speedster increases it's speed by 65 squares (or 325 ft).
That would be to low...
So every level a speedster increases it's speed by 70 squares (or 350 ft).
(That puts the speed OVER the speed of sound)
The total speed at L20 would be: 30 + 350*20 = 7,030 ft/6 sec
or... 1171 ft/sec.
The speed of sound is 1117.469 ft/sec.
To make a D&D base class with the ability to go OVER the speed of sound- it needs to get +70 squares of movement every level. Wow....