"Mx are the modifiers." To expand, M is the sum of - not necessarily addition, but the end result of whatever crazy equation you build - all static factors. This is your strength bonus, the penalty for firing through mist, injury modifiers, and, in some systems, your emotional state, or "morale." In other systems, emotional states are assigned to Y, the die roll.

Quote from: Engine;253822"Mx are the modifiers." To expand, M is the sum of - not necessarily addition, but the end result of whatever crazy equation you build - all static factors. This is your strength bonus, the penalty for firing through mist, injury modifiers, and, in some systems, your emotional state, or "morale." In other systems, emotional states are assigned to Y, the die roll.

Would it be fair than to phrase this as "The sum of explicit mechanics in the system"?

Absolutely.

Quote from: Engine;253824Absolutely.

Excellent. We're still in agreement.

So far we have X = Y + Mx

Where X equals the "range of All Possible Combat Outcomes"
And Mx equals the "The sum of explicit mechanics in the system"

At this point we have no choice as to what Y represents.

X - Mx = Y

What would you phrase as the meaning of Y?

Before the algorithm is run, Y is "the range of possible die rolls." After it's run, Y is "the result of the die roll."

Quote from: Engine;253830Before the algorithm is run, Y is "the range of possible die rolls." After it's run, Y is "the result of the die roll."

Too focused on what's rolling on the table, and not what the variables mean.

X = Y + Mx

"range of All Possible Combat Outcomes" = Y + "The sum of explicit mechanics in the system"

Y = "range of All Possible Combat Outcomes" - "The sum of explicit mechanics in the system"

Agreed?

Would another way of phrasing Y be "The sum of non-explicit mechanics in the system"?

Are there any non-explicit mechanics which are not the die roll? I know "die roll" is part of the set of non-explicit mechanics, but I'd like to know what else is in the set.

Quote from: Engine;253842Are there any non-explicit mechanics which are not the die roll? I know "die roll" is part of the set of non-explicit mechanics, but I'd like to know what else is in the set.

I would say not, your selected expression only has three variables and two of those have been defined. Everything else affecting the outcome must exist in the remaining term.


Edit: In practical terms, that means all non-explicit influences must exist in the die roll.

I can imagine other influences, GM and players over-ruling the mechanics and/or the die roll for example. But I would call those out of scope because we're concerning ourselves with only the game system here and its abstractions.

Then, those caveats in mind, it's reasonable to consider Y = die roll = "The sum of non-explicit mechanics in the system."

Excellent, then we're still in agreement.

"The Range of All Possible Combat Outcomes" = "The sum of non-explicit mechanics in the system" + "The sum of explicit mechanics in the system"

Shown as: X = Y + Mx

Y = X - Mx

Y/X = (X - Mx)/X

Y/X = X/X - Mx/X

Y/X = 1 - Mx/X

This version of the expression gives the percentage importance of the "The sum of non-explicit mechanics in the system".

Now for battles of no advantage, i.e. those were all the values of Mx taken together equals zero, this is the resulting influence of Y.

Y/X = 1 - 0/x
Y/X = 1

Or the effect of "The sum of non-explicit mechanics in the system" is 100%, i.e. completely determinative.

As advantage is gained by the explicit mechanics, this 100% will drop. At it's most extreme, Mx will will become completely determinative. In real terms, this happens when the total modifiers to the die will max the result matrix no matter the roll of the die (edit: individual systems may or may not be capable of this).

Thus one may say that either Y or Mx may be determinative in direct inverse of the other- with Y being solely determinative at equal encounters and Mx being solely determinative at vastly unequal encounters.

Agreed?

Okay, so all you're saying is if the explicit mechanics have no effect - there are either no static factors, or they end up with a net result of zero - then the result is solely determined by the die roll. And if for some reason the total sum of Mx is greater than that necessary for success, then the die roll is meaningless: if your target number is 10, but your total Mx is already 15, you succeed, no matter the die roll [unless there's some sort of penalty for rolling a one, for instance, or some sort of benefit for extraordinary success].

I agree with that. If X = Y + Mx, and Mx is 0, then X = Y. If X = Y + Mx, and Mx is greater than the threshold for success, X still equals Y + Mx, but the extra bit of Y is unnecessary. [With the exceptions for rolling 1 and for extraordinary success, of course; if those mechanics aren't present, then X can usefully equal Mx, because Y is extraneous.]

So, yes, provided I'm understanding the thrust of your argument, we're agreed.

Quote from: Engine;253952So, yes, provided I'm understanding the thrust of your argument, we're agreed.

It appears we're still on the same page.

Let's talk about the nature of Mx. I believe we can in all reason say that Mx may vary in its rate of change (and thus the significance of its change) between designs.

For example, one may use a D100 system with modifiers like 1%, or one may use a D100 system with modifiers like 5%. It would be clear that the rate of change of Mx would be higher in the latter than in the former.

Agreed?

Quote from: jhkim;253807I'd agree with this.  I'd also note that how well the abstraction works depends on whether there are established facts in the game that break the abstraction.  For example, if you don't have a hit location system, then you are breaking the abstraction if you specify unequal armor coverage and what wounds are like.  For example, someone's armor is specified as a helmet only, and you state in-game that a given wound is on the head.  

With regards to morale, it seems to me that there are plenty of factors that would affect morale that are often specified in the game.  For example, the presence or absence of leader figures.  Killing the enemy leader should have a morale effect, but could have no different effect than killing an underling.  That would be parallel to being mechanically able to specifically target the head, but then finding that a head shot is no different than a limb shot.  

Some morale effects can certainly be role-played by the GM and/or players, and one can assume that the effects average out, but it is an assumption.

To be certain, but one cannot assume (without some sort of indicator as you mention) that an aspect is part of the design. For example, if you look at Iridium (my game) I do not mention weapon speeds anywhere in the rules. They are not part of the explicit rules. However, they are represented by different weapons having different numbers of attacks in a round. There, you can then make the observation that weapon speeds are a part of the design.

The problematic issue in such analysis is whether you bring your own assumptions or merely observe the system and comment on what is there. To assume an aspect is built in as an "abstraction" may be correct or it may be incorrect since you cannot know unless you consult the designer (or there are tells as you have sited).

Bill

Quote from: gleichman;253954Let's talk about the nature of Mx. I believe we can in all reason say that Mx may vary in its rate of change (and thus the significance of its change) between designs.

Absolutely. Think of D&D 3.5e, for instance: usually it assigns a sort of generic +2 modifier for lousy conditions. A system could be identical in all ways, but offer a +4 modifier for lousy conditions. Certainly the influence of Mx can vary drastically, from wildly unrealistic ["Climbing in the rain is 3000 percent more difficult"] to vaguely realistic ["Climbing in the rain is 300 percent more difficult"]. Matching your Ms to reality's Ms is the tough part, and, as we've agreed, precise parity is not only "tough," it's "impossible."

Quote from: Engine;253958Absolutely.

Great, we're doing quite well. And I really liked total f your answer as well.


Now let's review Y and Mx just a bit more.

It would seem clear that in a ideal world with infinite processing ability and knowledge- all possible influences on the outcome could be contained in Mx and made explicit. Y in such a case would be 0.

And it would seem clear that if one was only concerned with outcomes, that all possible influences could be contained in Y, and left non-explicit. Mx in such a case would be 0.

We can also say that between these two extremes one may split the influences between Y and Mx in any way. The only requirement (per our agreements above) is that all influences must be included.

Agreed?