For some years now, I've been using a "standard" method of computation for determining the winner of a melee. By standard, I don't mean its the standard of the wargaming world... far from it.
But it's the standerd at the Simon gaming table, and that, to me, is what counts.
The method consists of first, assigning a number of points to each side in the combat after the casualty phase is completed. These points come from the available force, its strength, the hits it put on the opposition, and any other factor that might be pertinent to the combat in question.
If we call the total of these points, "T", then each side has its own total... for Side A, we have A(T), and for Side B, we have B(T). Nothing exciting thus far.
What we have at the end of melee, therefore, is a number, an "index," for each side which is an indication of its capability, its advantage in melee (high ground, flank attack, etc.) And its standing. What we could do is simply compare these numbers and state that the "ice with the highest index is the winner of the melee.
To me, however, a simple comparison doesn't go far enough. It's too deterministic. For example, in a combat between heavily armored mounted knights and half-armored foot, the mounted horsemen are bound to knock down more footmen than the footmen will knights. And the number of surviving knights will, most probably, be greater than the footmen.
Which means that the index for the mounted knights will always (always?) total more than that of the footmen, hence the poor foot will never win at all.
Enter the random factor. Not too random, of course. But its introduction should give the footmen some chance, perhaps a teenyweeny chance, but some chance, of coming out on top.
Now we return to the totals, the indices, I spoke of above, A(T) and B(T). And to introduce a random factor, we'll use a 10-sided die.
Each side takes its total, T, and multiplies it by the toss of a 10-sided die. We compare the products that each side gets, and the winner of the melee is the side with the higher product.
You may disagree with the why's and wherefor's, you can argue that a 6-sided die should be used, you can dispute the way the index is obtained, but the method is "clean," it's easy to implement, and its quick.
Recently, I noted that Brian Dewitt used a similar method. Similar, but different. Enough to make me wonder about the variation in outcome between the method I'd been using and his.
As an example, assume that we have two units, A and B, each valued at 3 Combat Point. (T - 3). Suppose that Unit A has an advantage; it's slightly uphill, standing on high ground, so we give it a "+1".
The issue here concerns what we do with the "+1". The Simon usage differs from the Dewitt usage.
1. From the Book of Simon
- a. We'll add the +1 to A's points, giving Unit A a total of +4 against B's original, unchanged +3.
b. Both A and B will now take a 10-sided die, toss it and multiply the result by the total points available.
c. If A multiplies its die by 4 and B multiplies its die by 3, the statistics say that A should win the melee, i.e., get a higher product, 63.26 percent of the time.
2. From the Chronicle of Dewitt
- a. Here we start again with both units valued at 3, but this time, instead of adding A's advantage of +1 to its total, we'll add it to A's die roll. This is the big distinction
between the two methods... one (mine) adds the modifier to the value itself, while the other (Dewitt's) adds it to the die roll.
b. Now we multiply A's value of 3 by the sum of a die roll +1.
c. Here, statistics say that A will win the melee 60.44 percent of the time.
In equation form, the two methods look like:
- Simon: Result = Die Roll x (A's Value + 1)
Dewitt: Result = (Die Roll + 1) x A's Value
Now, admit it, you guys... this is, indeed, exciting stuff! Why, those of you that are still awake are probably sitting on the edge of your chairs, muttering: "What,s next?? What's next??"
And, of course, those of you that are not awake... well, it don't much matter, no how...
In looking at the two methods, I was curious to see if there was a difference in outcomes.
I took two units, A and B, each starting with a representative value of 3, and determined the outcome using both methods. I left B's value alone, i.e, it remained at 3, while A's value was the one that was affected.
I gave A a range of modifiers, from -2 to +3, and calculated the probability that A would win. The results are:
| Modifier Given To Side A | Probability That Side A Wins Using The... | |
|---|---|---|
| Simon Method | Dewitt Method | |
| -2 | 27.55% | 30.44% |
| -1 | 30.93 | 39.56 |
| 0 | 50.00 | 50.00 |
| +1 | 63.26 | 60.44 |
| +2 | 72.45 | 69.56 |
| +3 | 78.95 | 77.42 |
The above listing of modifiers represents a wide range of situations.
For example, with a modifier of +3, A's value, starting out at 3, is effectively doubled. This could be due, perhaps, to A's superiority in numbers, attacking from high ground into B's flank while B is still undeployed, etc., etc.
Similarly, a -2 modifier means that A is severely disadvantaged.
The listed outcomes indicate there's not a great deal of difference between the two methods.
The Dewitt method has one advantage, however, because of the way Brian scales the melee outcome.
According to the Dewitt scheme of things, if the final product of one side is twice that of the other, not only does the lesser side lose the melee, but additional bad things happen (the unit routs, it loses another stand, its status goes down, the men lose their PX privileges, there's no off-base leave for the week, etc).
By adding its modifier to the die, a unit with an advantage will never be cursed with a multiplier of "1", since, if a "1" is tossed, the modifier adds to it. Hence the multiplier will always be more than "1," and there will be less of a chance that the advantaged side's product is doubled by its opponent.
In the Simon scheme of things, the "degree" of loss is not important: if you lose, you lose and that's that.
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© Copyright 1995 Wally Simon
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