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11-03-2014, 10:15 AM #1
 Class 2M Laser Join Date: Nov 2012 Location: Ohio, USA Posts: 604 Rep Power: 174
Marco Polo
Class 2M Laser

Join Date: Nov 2012
Location: Ohio, USA
Posts: 604
Rep Power: 174
"Weapon dice" distribution curve given arbitrary min, max, and mean.

An online game I sometimes play uses a complicated formula to calculate the amount of damage dealt to a monster when you hit it. One component of this formula is the "weapon damage". In this game, the "weapon damage" is defined in terms of three parameters: an arbitrary minimum value, an arbitrary maximum value, and an arbitrary average (mean) value. All three parameters are constants (for a given weapon) and are set arbitrarily and independently of each other whenever a builder creates or modifies a weapon.

For example, one powerful weapon has the following damage values: Min=201, Max=1205, Average=603. (This weapon was formerly 201d5, and the distribution is approximately gaussian. I'm assuming the new function closely duplicates the old in this case.)

Another weapon has the damage values Min=20, Max=300, Average=61. This weapon did not exist when the game used XdY. Although it has a low average damage, occasionally you do get a good hit with it.

The game converts the three parameters into a "skewed gaussian" (the game admin's description, not mine) probability function. Every time you attack a monster, the game selects a random number (call it W) for the weapon damage such that Min =< W =< Max such that a good sample of such numbers will have the arbitrarily set average.

It is unknown if the game selects only integers from the range, or if the range is continuous from Min to Max.

Do I even need to know the probability function itself? If I take multiple distributions of damage values, holding everything constant except which weapon I use, shouldn't I be able to calculate the average of each data set, and then plot them on a graph? That should reveal the weapon damage's overall effect on the final amount dealt, correct? At that point I can try a regression and define the average damage = weapon average + everything else, correct? The "everything else" consists of the resultant of heck knows how many functions of various constants (strength, bonus damage roll, the monster's armor value, etc.)

Reading up on gaussian functions in general, I see that the general normal distribution is defined in terms of the expected value (the average), the value of a given x, and the variance. The variance is simply standard deviation squared.

I'm really curious to find out what formula they're using in determining the probability curve for a given weapon. The average is probably the highest point on the curve. Maybe the areas under the curve are equal to the left and to the right of the average? In the case of the second weapon above that would result in a curve that is "taller" on the left and has a long, low tail to the right - a skewed gaussian which is cut off at either end instead of going to infinity. I assume it is some sort of skewed normal using parametric equations to represent its usual variables in terms of the min, max, and average. I could be wrong.

Is anyone familiar with this sort of thing? Would greatly appreciate some direction on this, I am just not familiar enough with the relevant statistics. Clearly there is some way to convert the three parameters into a probability function. Does anyone have any ideas?

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Last edited by Marco Polo; 11-03-2014 at 10:33 AM.

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