"System Delta" Scoring Simulator v1.0
by Taren N.

This program simulates what kind of scores you can expect to get from the scoring method I proposed on Aaron In Japan's message board. It's mainly based on how close to the beat you are.

Assuming each judging window is '1 unit' long, your steps are judged as follows:

0-0.25 units off : Marvelous
0.25-1 unit off: Perfect
1-2 units off: Great
2-3 units off: Good
3-4 units off: Boo
>4 units off: Miss

For the in-game scoring, jumps are counted as one step, and freezes are also worth one step. This program only focuses on steps for the time being.

Input:
Number of songs (iterations). The program will return this many results. A good number to use is between 10000 and 100,000.
Number of steps (in the song). This is normally between 100 and 600, but any number is fine.
Perfect Ratio: This number is how many perfects you get compared to all steps. This number must be BETWEEN zero and one- neither extreme. For the remainder of steps that are not perfects (or better), the program uses natural distribution to simulate the timing of a player's steps.

Output:
First column: This number is the score obtained out of a possible 1000. Unlike in MAX/MAX2/EX where a AAA meant a perfect score, this system allows for AAA's with different scores. The reason? Perfects are worth different amounts depending on the timing. Only Marvelous steps return maximum score.

An All-Marvelous run returns 1000 in the first column.

The second column is the number of times the program encountered that result. Third is highest number of Marvelous steps the program had for that particular scoring range. Likewise, the fourth column is the lowest number of Marvelous steps.

Finally, #5 is the number of all-Perfect-or-better runs the program encountered in that scoring range. #6 is the ratio between #5 and #2.

This program, source code, and algorithms are all (c) March 2003 Taren Nauxen.