diy wrote:
This reduced the collision rate by something like 200%
How is this possible, without going into a negative collision rate, whatever that might be.
The conventional definition is 100% * (X2 - X1) / X1, which for -200% would require a negative collision rate.
The only way I know is to use the logarithmic definition of percentages.
percentage = 100% x Natural-Log(X2 / X/1)
-200% means that X2 is 0.1353 times X1, or a reduction of 86.5% by the conventional definition.
For small changes this produces the same results as the conventional method, but is much better when large changes are being considered, such as occur in some engineering calculations
A good interim method for reasonably large changes is 200% * (X2 - X1) / (X2 + X1), which is the first term of the Taylor expansion series for the logarithmic version, but for -200% that would give the result that X2 = 0
.