Combat mechanics

[Deathsinger]

In looking at your data, row 2: attacker 7.5, defender 3.28, A wins 10, D wins 0. Is that to be interpreted as
1) You fought this exchange 10 times with A winning 10 times, or
2) A did 10 points of damage to B w/o sustaining any damage in 1 combat?

[Chaos Theory]

2

[Senethro]

For the mathematically illiterate, can you tell us what your results mean? What are the consequences and how should I modify my military behaviour?

[Chaos Theory]

Originally posted by Chaos Theory
In even simpler terms, the odds are somewhat further skewed towards the stronger unit than the ratio of their strengths would indicate.

[Petek]

Chaos Theory,

Do you know about this thread:

http://apolyton.net/forums/showthread.php?s=&threadid=103023

and the two links in MariOne's first post there? If not, you might want to take a look. Seems that others have thought along the same lines as you have.

[Chaos Theory]

Originally posted by Verrucosus
Maybe it is time for a bit of comparative combat theory. SMAC has borrowed a lot of its game mechanics from Civilization II. As can be seen from the Combat thread in the Civ2 Strategy Forum (easily accessible through the Great Library Index), modern Civologists have encountered similar problems.

What is presented under the heading "On to the real calculation ..." is too puzzling for me at the moment, so I'd like to stick to the simplified formula suggested in that thread. It is as follows:

Odds = (S + (S - W)) * Shp * Sfp / (W * Whp * Wfp)

where:
S = Stronger unit's modified attack or defense value
W = Weaker unit's modified attack or defense value
Shp = Stronger unit's hit points
Sfp = Stronger unit's firepower
Whp = Weaker unit's hit points
Wfp = Weaker unit's firepower

Now, we know that the firepower (i.e. the amount of damage inflicted on the loser of a round of combat) in SMAC is always "1". The hitpoint factor seems to correspond to the hitpoint modifier that we had been discussing earlier, so there isn't anything new in that respect. What is intriguing however, is that the difference between the combatants' attack strengths is added to the stronger unit's strength. I didn't have the time to check yet, but I have a distinct feeling that such a modification might provide an explanation for MariOne's test results.

That suggestion, to add the difference of strengths to the stronger unit's strength, fits perfectly with all the data I have and so is very likely the correct formula. I had tried to search for posts like this, but didn't check the archives. I didn't even know we *had* archives.

From a mathematical perspective, the Civ 2/SMAC formula irritates me, since the second derivative of the odds function has a discontinuity at attacker's strength = defender's strength, but oh well.