Movement Speed Tests

Mercurial armor is expensive, but I realized that if I was vendoring Almirian Seal items for crowns, I might as well get Ancient Plate and test with it before I vendor it.
So I ran laps in the advanced training hall in my normal gear and in full Ancient Plate (movement speed reduced: medium). I chose a rectangular circuit that was 44 tiles in circumference. There will be some random errors from me not cornering at exactly the same point on every lap, but they should mostly cancel out.
15 laps (660 tiles) in my normal gear took 2:15 (speed: 4.89 tiles/sec)
15 laps (660 tiles) in full Ancient Plate took 2:26 (speed: 4.52 tiles/sec)
Conclusion: Movement Speed Reduced: Medium lowers movement speed by around 7.5%. That's close enough to attack speed abilities that they probably use the same scale.

I'd be happy to, if you'll give me around 2400 ce for expenses.

I don't buy CE with real moneys and therefore don't have access to test servers, but feel free to conduct your own tests and report back.

I think this is close to what needs to happen, but we need to get more scientific. I'd recommend using a macro program to hold down a direction key for a set number of milliseconds and then comparing that with a number of floor tiles traveled.
I'll do a similar thing, run some tests and then take a look at the data.

I think you'll be hard-pressed to match my precision with your suggested methods. Keep in mind that short tests suffer a greater loss of accuracy both due to measurement limitations (I doubt you can reliably tell the difference between 24.3 tiles and 24.4 tiles traveled without enormous effort) and due to lag (you can't possibly determine the true amount of time you spent moving down to the millisecond unless your code is running on the game server). So unless you can find some place where you can run 660 tiles in a straight line without stopping...
If you're not satisfied with the accuracy of my tests, I think you're better off repeating them with methods similar to mine, but with a more accurate stopwatch, and possibly with longer trials.
Also, I don't think you know what "scientific" means.

I did a slightly different route around the check-in desk which was 36 squares. Did 15 laps with:
Proto 540 tiles in 1:49.8 or 4.9 tiles/s
Mercurial Set 540 tiles in 1:40.7 or 5.4 tiles/s an increase of about 10%
I did the Mercurial Set several times because I thought it odd that the increase was 10% instead of 7.5%, but I got the same result each time.

Is this 10% per piece or 10% for both pieces combined? :(

I believe 109.8 seconds / 100.7 seconds is closer to a 9% increase, but yes, it's curious.
I repeated my tests, and got 2:14 for normal and 2:25 for ancient plate (compared to 2:15 and 2:26 originally). That's a -7.6% difference. If you compare my faster normal time to my slower ancient plate time, it's a -8.2% difference.
And I tried a run with 1 Ancient piece (decreased: low) and timed 2:19, a 3.6% decrease.
I also got a friend with 1 Mercurial piece (increased: low) to participate, and timed him at 2:08, which is a 4.7% speed increase over my 2:14 time.
So...your tests and my tests both show movement increases making a bigger difference than movement decreases, with multiple trials. That's suggestive. But if you assume there's about a 1% uncertainty in our tests (which doesn't seem outlandish), all the data points could form a straight line.
You say you did the mercurial set test several times. How many trials, and how consistent were your times?

Interesting data.
Something the think about: Since you are running in circles the exact size of the circle may vary (as the OP already noted). However, since this depends screen-eye-hand coordination, the amount by which the corners are cut might depend on the speed at which a knight is running. This could lead to systematic error. For example, you might tend to cut more corners if the knight is running faster, which would give a slightly bigger speed increase.
This could be circumvented using straight line trials, but (as noted) those would introduce different errors. (Although, (depending on the exact implementation of the netcode) holding down a key for x millisecond should make the knight walk for exactly x milliseconds, independent of the lag. More troublesome is the possibility of acceleration effects.)
Some other interesting data to gather would the amount of speed decrease caused by charging various weapons. Possibly even the amount of speed decrees caused by firing/reloading a gun. (Although the latter may prove troublesome.)

I tried three trials with full Mercurial Set (Medium Speed Increase total). First two trials were 1:40.7, third trial was 1:40.9. I was using my phone as a digital stopwatch so was concerned what error the device's use might cause, but the results were pretty similar. I lagged for a split second in the first two trials when cornering, but it didn't seem to affect the outcome since the lag-free trial was around the same time to finish.
next step:try with mercurial, see if it scales in the opposite direction