Anything that can record a player's movements?

Perhaps. You could make a value that is increased every time a player jumps; for example

local player = game:GetService("Players").LocalPlayer
local char = player.Character
local jumped = 0
local jumpval = Instance.new("NumberValue",script)
jumpval.Name = "JumpValue"
print(jumped)

while true do wait(.1)
    if char.Humanoid.Jump == true then
        wait(1)
        jumped = jumped+1
        jumpval.Value = jumped
    end
end

For moving, you could record the changes in the position of the character like

A = char.Torso.Position

char.Torso.Changed:connect(function()
B= A-char.Torso.Position --Edited; typo :P
end)

Then, of course, you could insert the value of B into a Vector Value.

Hope this helps!