Leon Marrick
Chieftain
- Joined
- Jun 27, 2002
- Messages
- 6
This essay takes the traditional explanation of CivII combat, demolishes it, and supplies a couple of rules of thumb that every scenario designer should know by heart. Along the way, the true effects of veteran status, terrain, improved positions, and of hitpoints and firepower are laid out in some detail.
(rough draft)
Base Combat Odds
The starting point of combat is the comparison between attack and defence strength. The CivII manual is very confident about this subject. If an Elephant (strength 4) attacks a Phalanx (strength 2), and no modifiers apply to either side, the Elephant will hit its opponent about 4 times in 6, and get hit about 2 times in 6.
If the rest of this discussion is to make any sense to you, you need to throw this claim out the window.
In actual fact, when an Elephant (strength 4) attacks a phalanx (strength 2), it loses about 3 times in 11, and the phalanx 8 times in 11. In other words, the elephant loses not 50 HPs, but about 34 for every 100 HPs the phalanx does. If, however, a unit of strength 2 were to attack one of strength 4, it inflicts not 50, nor even 34, but only about 28 damage for every 100 HPs it loses! Strong attacks are favored. Weak attacks are severely penalized.
Experiments over a range of combat odds give enough data to clearly show the difference between theoretical and actual values.
(chart goes here. see attached image at end of post)
* Note that all values from testing are approximate. See the "methodology" section for more details.
Adjustments to Combat Odds
The basic rule for adjustments to combat odds is that the effects of veteran status, terrain, and improved positions are multiplied one after another. Fractions are retained. For example: Warriors have a base defence of 1. Unit is veteran, which gives it a strength of 1.5. Unit is on hill terrain; hills have a defence value of 4 * 50% = 200%, which means that they double defence. Unit now has a strength of 3. Unit is also behind city walls, and city walls triple defence against most attackers. Final defensive strength is 9.
Things to remember:
- Rivers add 50% to the base terrain value: forests + river = 100% defence bonus.
- Units that ignore city walls also ignore fortresses. No unit ignores fortified positions. A unit cannot get a bonus for both being fortified and for being protected by fortresses or city walls.
- Air units do not ignore terrain effects, whether attacking or defending. They do ignore City Walls and fortresses.
- Naval units do not ignore terrain effects.
Consequences of the rules governing combat odds:
- Veteran units are not just 50% more effective than ordinary troops, but often 100% more.
- Dug-in units can be up to twice as effective as units in the open.
- Units defending along rivers can be up to twice as effective as units in open terrain.
- Units in mountain squares or behind city walls kick butt.
Hitpoints and firepower
Hitpoints and firepower are more important than most scenario designers realize. A unit with 20 hitpoints is twice as effective as one with 10. A unit with a firepower of 2 is twice as effective as one with 1. If this essay convinces authors of scenarios to stop supposing that infantry with 10 or 20 hitpoints and one firepower belong on the same battlefield as mechanized unit with 20 hitpoints, 2 or 3 firepower, and better combat factors, then - and only then - will we see realistic simulations of warfare.
Things to remember:
- Units with the submarine/hidden ability always defend with one firepower. This is something you'll need to remember if you give it to most naval units in order to prevent shore bombardments.
- Shore bombardments reduce the firepower of attacker and defender to 1. Hitpoints become the key to success.
Suggestions:
- Units that you think should be tough to destroy should have high hitpoints. This isn't the same as the unit being hard to hurt (evasive or well-protected), it's how hard the unit is to actually destroy. Normal infantry, for example, tend to come in large numbers; this gives them staying power.
- Units that do a lot of destroying should get higher FP values. Artillery and unguided missiles may not be particularly accurate, but they can be devastating.
- Units with 10 HPs and 2 FP are not quite as effective as those with 20 HPs and 1 FP. They do just as much damage on average, but a few unlucky combat rolls can get them killed.
- Incremental advances in unit technology are best handled by adjustments to attack and defence strengths. Adjustments to hitpoints and firepower should often reflect quantum leaps in technology, unit mass and organization, or ways of destroying one's foes.
Conclusions
At this point, having covered odds, modifiers, and HPs/FP, we are able to replace the old method of calculating combat results.
Determining Combat Results: Marrick's Rules of Thumb
A. If the modified combat odds are between 1 to 2 and 2 to 1 (neither unit has a clear advantage) then: 1) take the modified combat factor. 2) multiply it by itself*. 3) Multiply by the unit's hitpoints. 4) Multiply by the unit's firepower. 5) perform steps 1-4 for the other unit, and compare the two values.
B. If the modified combat odds are 1 to 2 or less, or 2 to 1 or greater (attacker or defender has a clear advantage) then: 1) take the modified combat factor. 2) if it is higher than that of the opposing unit, multiply it by 2*. 3) Multiply by the unit's hitpoints. 4) Multiply by the unit's firepower. 5) perform steps 1-4 for the other unit, and compare the two values.
* Special case: Multiply by 1.5 instead if attacking at about 2 to 1 odds.
Methodology: How the testing was done
The manual claims that combats are resolved in rounds; each round, the loser loses a number of hitpoints equal to the firepower of the winner. This appears to be correct. Therefore, by setting units to have 100 HPs (10x normal), and 1 firepower, one can readily get large enough sample sizes to support analysis. Most of the time, I gathered data on 20 combats at a time (sets of >2000 internal rolls). In some cases - when the data suggested unusual conclusions, I needed a solid baseline to support a series of tests, the difference between two sets of figures was not large, or when I tested units with more than 1 firepower - I did not feel safe drawing conclusions until I had data from 40 or even 80 combats.
Most testing was done using CivII Fantastic Worlds. I also performed some spot checks in MGE and TOT, but did not see any clear difference in combat results.
Most testing was done at King level. I also performed a number of tests on Prince and Deity mode, but again did not see any clear difference in combat results. I ignored Chieftain mode. No testing was done with barbarian units.
Land battles were fought in sets of 10 attacking Warriors and 10 defending Phalanxes, with combat strengths and terrain adjustments as determined in rules.txt. A good way of checking on a number of the claims I make in one test is to make a city on mountains, give it city walls, pack it full of veteran Warriors, and try to take it with veteran Riflemen. Warriors rule!
If you believe portions of this essay may be incorrect, I encourage you to send me the results of your own testing. Please: 1) have a large enough sample size and 2) tell me exactly how to copy your tests.
And a last word
There are a number of curious results and seeming inconsistencies that are not covered in this essay. To take but one example: attacks at odds of 30 to 60 do not yield exactly the same results as attacks at 1 to 2. If any reader of this work is ever in a position to let me take a look at the actual CivII combat code, I would be forever grateful.
(rough draft)
Base Combat Odds
The starting point of combat is the comparison between attack and defence strength. The CivII manual is very confident about this subject. If an Elephant (strength 4) attacks a Phalanx (strength 2), and no modifiers apply to either side, the Elephant will hit its opponent about 4 times in 6, and get hit about 2 times in 6.
If the rest of this discussion is to make any sense to you, you need to throw this claim out the window.
In actual fact, when an Elephant (strength 4) attacks a phalanx (strength 2), it loses about 3 times in 11, and the phalanx 8 times in 11. In other words, the elephant loses not 50 HPs, but about 34 for every 100 HPs the phalanx does. If, however, a unit of strength 2 were to attack one of strength 4, it inflicts not 50, nor even 34, but only about 28 damage for every 100 HPs it loses! Strong attacks are favored. Weak attacks are severely penalized.
Experiments over a range of combat odds give enough data to clearly show the difference between theoretical and actual values.
(chart goes here. see attached image at end of post)
* Note that all values from testing are approximate. See the "methodology" section for more details.
Adjustments to Combat Odds
The basic rule for adjustments to combat odds is that the effects of veteran status, terrain, and improved positions are multiplied one after another. Fractions are retained. For example: Warriors have a base defence of 1. Unit is veteran, which gives it a strength of 1.5. Unit is on hill terrain; hills have a defence value of 4 * 50% = 200%, which means that they double defence. Unit now has a strength of 3. Unit is also behind city walls, and city walls triple defence against most attackers. Final defensive strength is 9.
Things to remember:
- Rivers add 50% to the base terrain value: forests + river = 100% defence bonus.
- Units that ignore city walls also ignore fortresses. No unit ignores fortified positions. A unit cannot get a bonus for both being fortified and for being protected by fortresses or city walls.
- Air units do not ignore terrain effects, whether attacking or defending. They do ignore City Walls and fortresses.
- Naval units do not ignore terrain effects.
Consequences of the rules governing combat odds:
- Veteran units are not just 50% more effective than ordinary troops, but often 100% more.
- Dug-in units can be up to twice as effective as units in the open.
- Units defending along rivers can be up to twice as effective as units in open terrain.
- Units in mountain squares or behind city walls kick butt.
Hitpoints and firepower
Hitpoints and firepower are more important than most scenario designers realize. A unit with 20 hitpoints is twice as effective as one with 10. A unit with a firepower of 2 is twice as effective as one with 1. If this essay convinces authors of scenarios to stop supposing that infantry with 10 or 20 hitpoints and one firepower belong on the same battlefield as mechanized unit with 20 hitpoints, 2 or 3 firepower, and better combat factors, then - and only then - will we see realistic simulations of warfare.
Things to remember:
- Units with the submarine/hidden ability always defend with one firepower. This is something you'll need to remember if you give it to most naval units in order to prevent shore bombardments.
- Shore bombardments reduce the firepower of attacker and defender to 1. Hitpoints become the key to success.
Suggestions:
- Units that you think should be tough to destroy should have high hitpoints. This isn't the same as the unit being hard to hurt (evasive or well-protected), it's how hard the unit is to actually destroy. Normal infantry, for example, tend to come in large numbers; this gives them staying power.
- Units that do a lot of destroying should get higher FP values. Artillery and unguided missiles may not be particularly accurate, but they can be devastating.
- Units with 10 HPs and 2 FP are not quite as effective as those with 20 HPs and 1 FP. They do just as much damage on average, but a few unlucky combat rolls can get them killed.
- Incremental advances in unit technology are best handled by adjustments to attack and defence strengths. Adjustments to hitpoints and firepower should often reflect quantum leaps in technology, unit mass and organization, or ways of destroying one's foes.
Conclusions
At this point, having covered odds, modifiers, and HPs/FP, we are able to replace the old method of calculating combat results.
Determining Combat Results: Marrick's Rules of Thumb
A. If the modified combat odds are between 1 to 2 and 2 to 1 (neither unit has a clear advantage) then: 1) take the modified combat factor. 2) multiply it by itself*. 3) Multiply by the unit's hitpoints. 4) Multiply by the unit's firepower. 5) perform steps 1-4 for the other unit, and compare the two values.
B. If the modified combat odds are 1 to 2 or less, or 2 to 1 or greater (attacker or defender has a clear advantage) then: 1) take the modified combat factor. 2) if it is higher than that of the opposing unit, multiply it by 2*. 3) Multiply by the unit's hitpoints. 4) Multiply by the unit's firepower. 5) perform steps 1-4 for the other unit, and compare the two values.
* Special case: Multiply by 1.5 instead if attacking at about 2 to 1 odds.
Methodology: How the testing was done
The manual claims that combats are resolved in rounds; each round, the loser loses a number of hitpoints equal to the firepower of the winner. This appears to be correct. Therefore, by setting units to have 100 HPs (10x normal), and 1 firepower, one can readily get large enough sample sizes to support analysis. Most of the time, I gathered data on 20 combats at a time (sets of >2000 internal rolls). In some cases - when the data suggested unusual conclusions, I needed a solid baseline to support a series of tests, the difference between two sets of figures was not large, or when I tested units with more than 1 firepower - I did not feel safe drawing conclusions until I had data from 40 or even 80 combats.
Most testing was done using CivII Fantastic Worlds. I also performed some spot checks in MGE and TOT, but did not see any clear difference in combat results.
Most testing was done at King level. I also performed a number of tests on Prince and Deity mode, but again did not see any clear difference in combat results. I ignored Chieftain mode. No testing was done with barbarian units.
Land battles were fought in sets of 10 attacking Warriors and 10 defending Phalanxes, with combat strengths and terrain adjustments as determined in rules.txt. A good way of checking on a number of the claims I make in one test is to make a city on mountains, give it city walls, pack it full of veteran Warriors, and try to take it with veteran Riflemen. Warriors rule!
If you believe portions of this essay may be incorrect, I encourage you to send me the results of your own testing. Please: 1) have a large enough sample size and 2) tell me exactly how to copy your tests.
And a last word
There are a number of curious results and seeming inconsistencies that are not covered in this essay. To take but one example: attacks at odds of 30 to 60 do not yield exactly the same results as attacks at 1 to 2. If any reader of this work is ever in a position to let me take a look at the actual CivII combat code, I would be forever grateful.
Actually, more hitpoints, while it has the effect of broadening the sample size of individual hit points, does not increase the sample size of units. The same 60 of 100 hp victories can mean anything from 6 wins in 6 combats (win 10, lose 6 or 7) to 6 wins in 10 combats (win all or lose all HPs each time). For actual units (which are a certain limited number of HPs), one must test with a heap of units.
I can see how it would be easier to follow an equation with one unit's numbers all on one side of the equation. Just a different preference.
