No subject

In fact there are two definitions for these properties. They have a different meaning in the "groove graph" (in song selection) and on the scoreboard. The latter differs. By the way, these stats were taken from the stepmania sourcecode [and translated twice!-FF].
In groove graph they signify:

Stream: Average number of steps over the whole dance.
Voltage: Average number of steps per second over the eight bars with the most steps.
Air: Average number of jumps per second over the whole number.
Chaos: Average number of triplets/16th/32nd per second taken over the whole number.
Freeze: Average number of freezes per second over the whole number.


On the scorebord:

Stream: The ratio of your number of Perfects to getting all Perfects
Voltage: The ratio of your maximum combo to getting a Full Combo
Air: The ratio of your number of Perfects on all your jumps (R+L, R+D, etc) to getting all Perfects on all Jumps
Chaos: The ratio of your dance level compared to that of AAA (all Perfect) level
Freeze: The ratio of your total number of "OK"s on all the Freeze arrows to getting all "OK" on all the Freeze arrows

These ratios give bonusses to your score when full.
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I don't get much of what he wrote after "on the scorebord". However, one can clearly learn a lot about a dance by numerical analysis. I once followed a course on scaling up processes, and I thought a bit about the subject; for now I'm not sure the groove definitions are the best parameters one could think up. On the other hand the user/player has to understand the numbers too.

Further

Something to keep in mind (and at the very least not make hard to implement):