Terminology: "Randomness"

[Vaxalon]

Let's say that you have a system where you roll 1d100+skill against "difficulty ratings" that run from 10 to 150, and skill ratings run from 0 to 100.

Also, you have a system where you roll 1d20+skill against "difficulty ratings" that run from 2 to 30, and skill ratings run from 0 to 20.

Is the first system "more random" than the second?  I would argue that even though the first system has more individual values that can be rolled, it's no more random than the second; in practice they're nearly identical.

[beingfrank]

The implication is that any concept of "randomness" should include (a) range, (b) variance, and (c, borrowing from an earlier post) degrees of freedom, which here is used to indicate how many different possible rules conditions there are that affect the resolution.  So, for example, a system described as "Have the skill, roll 2d6 plus your skill; don't have it, automatically fail" would have (1) range 11, variance 6 (standard deviation about 2.5), (2) range 0, variance 0, and 2 degrees of freedom.

Note that this use of degrees of freedom is slightly different than I've seen it used in statistics.  But I'm not a statistician, so I may be in error.

Yup it is different.  In statistics degrees of freedom refers to how many of the numbers we can change while the mean remains the same.  So if you're taking the mean of 3 numbers, you can change 2 to whatever you like, but if you want the overall mean to remain constant then how you change those two will determine how the 3rd must change.  So you have 2 degrees of freedom.  Quite a different idea from the one used above.  Not that that has to be a problem, but if degrees of freedom starts getting used in that sense too frequently it might do my head in.

[ErrathofKosh]

Let's say that you have a system where you roll 1d100+skill against "difficulty ratings" that run from 10 to 150, and skill ratings run from 0 to 100.

Also, you have a system where you roll 1d20+skill against "difficulty ratings" that run from 2 to 30, and skill ratings run from 0 to 20.

Is the first system "more random" than the second?  I would argue that even though the first system has more individual values that can be rolled, it's no more random than the second; in practice they're nearly identical.

You're right, in this given instance.  The only difference between the two systems you've described is granularity.  If rolling a 60 is little different than rolling a 65, the first system's finer granularity is of little value because it doesn't affect the randomness of the in-game results.

However, if each value has a distinct meaning, (in a overblown Rolemaster kind of way...) then the first system is inherently more "random" because it has more in-game possiblities.

Cheers
Jonathan

[Doug Ruff]

Bill,

I used 'degrees of freedom' to describe what you refer to as 'range' - but I think your terms are much better, so I'll change!

And thanks for the reminder about std. deviation... that exactly explains why 1d11 'feels' more random to me than 2d6-1.

I agree that range & variance both affect randomness. But does the existence of a separate mechanic (such as automatically failing if you don't have the skill) affect randomness? Or does it simply increase the number of possible resolution methods, each of which may have a different randomness?

- Tetsuki

[Bill_White]

I agree that range & variance both affect randomness. But does the existence of a separate mechanic (such as automatically failing if you don't have the skill) affect randomness? Or does it simply increase the number of possible resolution methods, each of which may have a different randomness?

That's something we may have to defer to a statistician or a game theorist; I was just trying to incorporate the idea that it mattered how many outside parameters one had to account for before one could get a sense of the predictability of an event's outcome.  But I think it's probably fair to suggest as you do that "randomness" be associated with particular mechanics, rather than with entire sets of mechanics.

Yah, and granularity matters too.  If the possible outcomes are only "success/failure," that leads to a different calculus than if there are also critical successes and critical failures.  

But the larger point is, I think, this:  Coming up with a single "randomness" number to describe a mechanic is hard, and one may actually need to consider the subordinate features (range, deviation, granularity) in making a decision about what kind of mechanic to employ.

[Vaxalon]

Take a look at the dice mechanic in Skein to see how I use randomness directly in the game.