Civilization Scoresheet

Article written by vlvas
Originally published on 06-12-2004 ; updated on 08-17-2014
Tags: Military Archives

Introduction

The scoresheet is made on stages, each stage complementing the result at the previous one. First and second stages - combat performance and unit cost deal with actual figures, it's all plain mathematics there, so there is little to argue about (unless of course I have made some terrible mistake in the formulae).

The third stage - adding the upgrade cost estimations may seem to you somewhat controversial at first. However, the general idea is reasonable, and, as you will find if you read on, adjustments to the additionally introduced coefficients would only make minor difference.

The results

Fourth stage is the most subjective one. It is all about adding scores that I found most appropriate (careful also not to deform the result received on the previous stages).

Most accurate, in my opinion, are the final results. However, if you do not agree with the way scores are calculated, let's say on stage 3, you can use the scores reflecting combat performance only or those adjusted with the unit cost. That is why I have given the results on all stages separately.

Stage 1

1.1. Evaluating combat performance against units:

A. Infantry, archery and cavalry

All units of the above types available in a certain civilization are matched against a fully upgraded unit of each type, called 'base' unit. For example, all civs' knights, swordsmen, etc. (including a 'base' swordsman, knight, etc.) are matched against FU paladin, FU hussar, etc. The score for the separate units is calculated in reference to the score that a 'base' unit of the same type gets.

Confronting units:

Units are matched only 1 vs. 1. This, unfortunately, excludes some factors such as the area damage of the mangonel, scorpion or demo ship. The 'distance' between the units is the longest possible distance allowing one of the units to fire/hit immediately. Then the times for each unit to kill the other are calculated. The shorter one gives the time to solve this conflict.

The time to kill includes not only the time necessary to make the necessary number of hits, but also the time for closing the range enough to hit. For example, when a swordsman is confronting a 'base' arbalest it needs first to walk the distance to the arbalest and then to start hitting. When the time in which one of the units kills the other is known, it is estimated how much damage can each unit inflict and how much HP will it have in the end. The score of each compared unit is calculated as sum of the damage the compared unit is able to inflict to the 'base' one and the HP the compared unit has left. All scores are then converted in percentages (the base unit always getting 100 for his sum of damage and HP left).

B. Siege

Siege units are matched against the units that the specific siege engine is most normally used and against siege units. Thus the mangonel is matched against ranged units and siege, the scorpion is matched against ranged units, infantry and siege, rams and bombard cannons are matched agains siege only. Trebuchets are not matched against any unit.

C. Navy

All navy units are matched against all navy units only.

1.2. Evaluating combat performance against buildings.

All units are also matched against buildings: a house, a barracks and a keep. Siege units in addition are matched against a fortified wall. The percentages for the house, barracks and wall are calculated against the time needed for a compared unit to destroy the building. The longer it takes for a unit to demolish a building, the lower its score will go.

When attacking keeps the percentages relate to the sum of damage inflicted plus HP left, except for the bombard cannon and the trebuchet. Those units, due to their long range don't die to keeps, unless they come unreasonably close. For the bombard cannon and trebuchets the percentages are related to the time it takes to demolish the keep.

When calculating the time it takes for a siege unit to destroy a house, barracks or wall, those siege units are 'positioned' 30 tiles away from the building. This was included specifically to evaluate Mongol siege units' speed bonus.

For the trebuchets the time to destroy includes the time to unpack and the time to pack as well. This was included to reveal the effect of Japanese UT. The trebuchets are given accuracy of 75%. This came out of one of the tests I have carried out in the scenarion editor. A FU trebuchet was targeting 10 other trebuchets and needed 36 shots, 27 of which went in, 9 - out. This standard accuracy gives accuracy of the Hunnic trebs of 97.5%.

1.3. After all scores are calculated they are given degrees of importance (DoI).

A. Infantry, archery and cavalry units:

All units are divided in three categories:
  • General combat (GC) units: paladin, hussar, arbalest, cavalry archer and champion.
  • Counter (C) units: camel and halberdier to mounted units; arbalest, cavalry archer and Hand cannoneernoneer to infantry units; skirmisher to archery units.
  • Trash (T) units: hussar, skirmisher and halberdier.
The score of a GC unit against other GC units has DoI 2.

The score of a C unit against units it counters has DoI 2.

The score of a countered unit against its counters has DoI 1.

The score of a T unit against other T units has DoI 1.

The DoI of the results of all units against arbalests and champions are at least 1.

The principle for choosing DoI:

For the main combat tasks of the units their results receive DoI 2, for the auxiliary tasks - 1, and for tasks those units are not used for - 0. For example, the results of a knight against other GC units are given DoI 2; against heavy camels and halberdiers - 1, and for attacking Hand cannoneernoneers and skirmishers - 0.

Camel's main targets are mounted units, so its results when fighting those get DoI 2. And so on. The result against buildings of a champion has DoI 2, of the paladin, hussar, camel and halberier - 1, of the archery units - 0.5, skirmisher - 0.

B. Siege

The results of all siege units against buildings receive DoI 5, except for scorpions' results that get DoI 1. Ram, mangonel and scorpion also are matched against other siege units and the results receive DoI 1. Furthermore, mangonels' scores against ranged non-siege units and scorpions' results against infantry are given DoI 2. Bombard cannons' results against siege units have DoI 2.

C. Navy

The scores of any navy unit among themselves are given DoI 2. For the attack at buildings the DoI for all but the cannon galleon the DoI is 1. For the cannon galleon is 3.

1.4. Calculating the final combat scores:

For each unit all scores against 'base' units/buildings are weighed with the respective DoI. Thus a unit that excells where it has to, receives a slight but completely justifiable advantage over a unit of the same type that lags behind. The formula used is for weighed geometrical average.

This method favours steady lines of results and somewhat punishes lines with big fluctuations. Actually, the formula for weighed algebrical average can also be used. I have checked it and the difference is in no case more than 4-5 points. As long as all civs are subject to one and the same rules, the exact formula is of less importance.

Some notes regarding the matching of units against other units.
  1. Those calculations involve zero micromanagement. The only movement a unit is allowed is to close the range enough to fire/shoot. Even if an archer (for example) could avoid the shot from a mangonel, it stands still firing as many arrows as possible before the rocks kill him.
  2. Also, since the confrontation is always 1 vs 1, it is not possible to show the effectiveness of a particular unit against massed enemies. For example, a demolition ship kills a fire ship 1 vs 1. However, the explosion of the demo ship will kill all adjacent fire ships (not only one of them). Similar is the situation with mangonels and scorpions. They also inflict area damage, although not 100%. My test have shown that the mangonel and scorpion inflict full damage only to the unit they are targeting. To the rest of the units the damage is very similar to the trample damage of the elite war elephants. The ram inflicts damage also to the buildings built right next to the building the ram is hitting.
Regular units compared by combat performance only

Click here to view the table

Stage 2

Evaluating the influence of unit cost.

This section is quite clear. If a unit costs regularly 100F and the same unit in your civ cost only 75F, you will be able to train 4 instead of 3 units. The cost of a unit has a definite influence on its score since the increased number of cheaper units increases he combat score of the resources 'invested'. The amounts of food, wood and gold needed to train one unit are converted in villager seconds (see the end notes) and added together to give one total. This aggregate value gives the one of your villies needs to work on various resources to afford one relevant military unit. This total value of villager seconds is then divided to the combat score of the relevant military unit. This gives vilseconds needed to get one point of the combat score of the military units. The 'base' unit of each type gets 100; all other are compared to that value. Higher values mean more expensive units, so the score drops. On the contrary, lower values mean cheaper, more affordable units, so the score increases.

For example, it takes 313 vil seconds to get the resources necessary to train one knight. This value of 313 is divided to the score each civ's knight gets. Thus one point of 'base' paladin's combat score of 100 takes 3.13 vilsecs to get. Turks also need 70F and 75G to train a knight. Their gold-mining bonus however reduces the total time from 313 secs to 291 secs. The score of their cavalier increases from 73 to 78. The gold-mining bonus has similar effect on the remaining Turkish gold-costing units. The same is the situation with Celtic units requiring wood (their combat + unit cost scores are higher then their combat scores alone). Of course, most significant is the increase for the units with reduced unit costs - Mayan archers, Gothic infantry, Byzantine camels and trash, etc. For example, the score of the Hunnic cavalry archer goes up from 88 to 115, that is whopping 27 points! The score of the Mayan archer is increased with 40 points due to the 25% reduced unit cost. The score of the Byzantine skirmisher is increased with 33, etc.

Regular units compared by combat performance and unit cost

Click here to view the table

Stage 3

Evaluating the influence of upgrade cost.

First, for all civs all technologies are reviewed - whether a technology is available and what number of units does it influence. For example, chemistry influences: archer, cavalry archer, skirmisher, galley, scorpion, mangonel, trebuchet - a total of 7 units. Then the total price of the upgrade divided to the number of units affected shall give the price of the upgrade per type of unit. For example, chemistry costs 300F and 200G and serves 7 types of units, so the cost of that technology to each of those 7 types will be ~43F and ~29G.

Then it is estimated how much food, wood and gold will it take to fully upgrade a unit. The cost of all technologies affecting the unit are divided by the total number of units those technologies affect in the given civilization. Unit upgrades (such as paladin upgrade, for example) most naturally are divided by 1 only, since they affect only the relevant unit.

Now, each civilization is given 10,000 resources. Their distribution between food, wood and gold is different for each unit. For example, for the hussar, it is 10,000 food. For the champion it is 7,500 food and 2,500 gold. For the cavalry archer thase resources are divided to 3600W and 6300G, and so on. The point is to calculate how many units can be trained with than given amount of resources. This number varies among the different types of units, reflecting the differences in their unit costs. For example 10,000 resources suffice for 74 knights. If used for scouts only they are well enough to train 125 units. Skirmishers and spearmen, being the cheapest units, can be trained in hordes (167 unit for each type).

This number is then used to calculate the price of each technology to each of the units trained with the package of resources. Thus, the price of a technology is first divided to the number of types of units it affects and the result for each type is then divided to the number of units of the type it is possible to train with 10000 resources. Actually, the important thing about this number is that it is the same for all civs. Thus all civs are under same conditions. Changing that number with +/- 50 (!!!) results in changing only some scores with mere 5-6 points.

The cost of the technologies per one 'base', fully upgraded unit is calculated through the following steps. First, a standard, non-existent civilization is introduced that has all units, all technologies, NO unique units and NO unique technologies. Then it the estimated for each technology how many units are affected. For the units of that 'base' civilization the same calculations are made as for the units of the real civilizations. Please note that in cases of real civilization it is possible the number of units to be higher than in the case of that 'base' civilization.

Such is the case with Britons and their chemistry; Saracens, Persians and Byzantines and their cavalry-related blacksmith technologies and so on. This higher number of types of units influenced in its turn decreases the price of the technology per type of unit and hence the price of the technology per unit. Thus, a knight from the 'base' civilization cost 2075F to fully upgrade, while for the same upgrades a Persian player will pay 1993.

Of course, as with the unit cost, all upgrade costs in terms of food, wood and gold are converted to villager seconds. This, apart from the opportunity to add all vil seconds in one total, allows some of the economic bonuses to be included in the calculations as well. Celtic wood-chopping bonus helps their production of units costing wood; Turkish gold-mining bonus helps them with their gold-heavy units.

Also included are:

Chinese technology cost reduction bonus - the cost of each technology is reduced as if the technology has been researched at the earliest possible moment. Turkish free Light cavalry and Hussar upgrades, half-price gunpowder technologies cost, free chemistry Spanish bonus the blacksmith upgrades cost no gold

Unique technologies are also included followings the general rules.

Thus the price of Zealotry upgrade in the Saracens is split in two (since it affects their regular camels and also the mamelukes) and one half is added to the cost of technology for the haevy camel. This value (for food and gold) is thn divided by the number of camels possible to train with 10000 res. The price of Shinkichon at the same time is divided to 1, since it affects mangonels alone. Aztecs 'garland wars' affect all four of their infantry units, so is divide to 4; etc. etc. UT not included (for self-explanatory reasons): Logistica, Bearded Axe, Anarchy, Atheism, El Dorado, Mahouts, Supremacy, Crenellations, Bersekergang.

When the technology price per one unit of each type is known and is converted to vil seconds, it is added to the unit cost, calculated on stage 2. This combined value of unit cost and upgrade cost expressed in seconds is divided to the battle score of the relevant unit. Base' units of the certain type get 100 for their vil seconds per point of the battle score and all other units are measured against the 'base' ones. Lower values mean that for every point of the battle score a civilization is working less, and vice versa. Generally, the more upgradeable the unit is, the more expensive it gets. However, the total cost in vil seconds divided to the battle score is a very appropriate criterion to see what do you get for the resources and time you have invested in a unit.

Let's take the knight line again as an example. Base' paladin needs 313 vil secs for its unit cost only and further 105 vil secs for all upgrades. This gives a total of 419 vil secs, or 4.19 vil secs for one point of the battle score. Chinese cavalier also needs 313 vil secs for its unit cost, but due to the reduced technology cost only 33 vil secs. This gives a total of 346 vil secs necessary to create and fully upgrade the Chinese knight in cavalier with combat score of 73 points. As a result of this the score of the Chinese cavalier rises from 73 to 88.

The scores received at this stage are more comprehensive and accurate than the ones received at the stage when only unit cost considerations were added to the battle scores. This stage and the way scores are calculated favours all-rounders because the more types of units a given technology affects the less its cost for any of those types will be. In this way civs that have more types of units have their technologies relatively cheaper. Civs with limited number of units, on the contrary, pay relatively more for the technologies, since the scope of the technology is limited.

Regular units compared by combat performance, unit cost and upgrade cost

Click here to view the table

Stage 4

Adding non-measurable factors.

Here all other bonuses that could not be fit into the formulae are added to give more comprehensive view of the units. Such bonuses are reduced build time, increased line of sight,etc.

All units that have any such bonus were granted additional points:
  • 10 pts for reduced BT
  • 5 pts for increased LOS
Exceptions:
  • Gothic infantry get +30 pts for their reduced BT, since the reduction is really signifficant.
  • Viking navy get +5 pts for their cheaper docks.
  • Persian navy receives +10 pts for their faster working and stronger docks.
And, finally, here is the end result:

Click here to view the table

Acknowledgements

All comments or suggestion will be more than welcome. Please send your e-mails to vlvas [at] mail [dot] bg.

In case you want to see exactly how those result were calculated you can download the complete file with all calculations from: http://www.karlssson.freeservers.com/scoresheet.xls
http://www.karlssson.freeservers.com/scoresheet.xls
Note:
The above external link is dead. If anyone has downloaded a copy of this Excel file when it was still available, please e-mail it to me at luke.gevaerts [at] heavengames [dot] com so I can upload it to the Age of Kings Heaven and make it available for download. Thanks!

This is the thread on the G&SD forum at Age of Kings Heaven which originated this scoresheet
http://aok.heavengames.com/cgi-bin/aokcgi/display.cgi?action=ct&f=3,33498,,all

Thanks to Gordon B for his appreciation of my first attempt.

Thanks to AFK_Tick for developing his own scorecard and for suggesting the evaluation method. The scoresheet can be found at: http://www.federationofkings.com.
Here I have tried to further develop AFK_Tick's general idea (although I only had vague notion about it).

Thanks to the people who created the AOK:TC Unit tables and the article about the resource gather rates, both hosted at MrFixitOnline. This scoresheet is based on the figures there.

Unit tables (through archive.org):
http://www.mrfixitonline.com/readPosting.asp?PostingId=479343
Author: KickMyButt

Gather rates (through archive.org):
http://www.mrfixitonline.com/readPosting.asp?PostingId=71
Authors: Neilkaz and phlsphr