A Scoring System

[Aeson]

Over at CivFanatics GOTM Forum there is a discussion going on about the scoring system for the GOTM. This is my initial proposal. As this is a scoring system that could be used for individual games, I thought it might be interesting for those not playing the GOTM as well.

I was hoping for some input on it from the fine minds here at the Poly Strat forum. Especially on the map/difficulty modifiers!

The attachment shows how the formula affects the GOTM 6-9 submissions. It is an Excel file, with a html version for those without an xls viewer. The map specifics were obtained by using MapStat on the 4000BC files.

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For game to game comparison, the map could be analyzed to figure out 'best' scores and dates, and player's results adjusted accordingly. This could be done before the game was released. All that is needed is a utility to extract the basic information (behind the scenes so the administrator can still participate) and make the calculations. The results would be released with the game.

Score

Score would be determined by the efficiency the player showed in obtaining the 'max' milking score. A bonus for early victory would then be added to keep milking and early victories both as viable options.

Objectives

- To determine the max milking score possible for the map
- To use that figure to modify the players score

AverageFoodPerTile = Food / FoodTiles
ClaimableFood = DominationLimit * AverageFoodPerTile
WorkingCitizens = DominationLimit
SpecialistCitizens = ((AverageFoodPerTile - 2) * DominationLimit) / 2)
MaxTurnScore = ((WorkingCitizens * 2) + SpecialistCitizens + DominationLimit) * Difficulty
MaxMilkedScore = MaxTurnScore * Landform

PlayerScore = ((GameScore - GameBonus) / MaxMilkedScore) * ScoreAdjustment

GameBonus = (2050 - PlayersDate) * Difficulty

Landform

Archipelago = ?.45?
Continent = ?.55?
Pangaea = .65

ScoreAdjustment = 10000 (arbitrary number to set a score in score form instead of %, this would result in a 'max' score [theoretically possible to exceed] of 10,000 for example)

Depending on the Landform (archipelago, continent, pangaea), another % of that is max 'milked' score. I'm pretty sure on the pangaea number already (65%) because of HOF attempts, and the others could be deduced from the plethora of well milked games that have been played in the GOTM's so far (excluding the dogpile game of course). It would give us a pretty decent max score to judge the games by, and would be a score that is available to the player as soon as they finish the game.

I think removing the territory portion of the score could also help to bring building back towards parity with early conquest then build. This way a size 6 city would be worth as much as 6 size 1 cities, though eventually more cities will win out (as they should). Population is dependant on territory, and so territory is counted twice (once directly, once indirectly through population) in the current scoring system.

Date

Date is a bit more difficult, but we can still come up with good estimates of a well played victory condition from map settings and difficulty level. Again, this is information that is available to the player before the game is played, and they can play accordingly. Instead of having to guess at what the adjustments will be once all is said and done.

Objectives

- To balance scoring by finish date
- To give a date bonus which is comparable between victory conditions
- To allow for comparison between maps and difficulty levels

Each victory condition would get a 'best' date for each map setting/difficulty combination.

Base victory condition 'best' dates: (standard continents map, monarch)

Conquest       : 10AD
Culture (100k) : 1500AD
Culture (20k)  : 1700AD
Diplomatic     : 1300AD
Domination     : 500AD
Spaceship      : 1600AD

Difficulty        Chi   War   Reg   Mon   Emp   Dei

Conquest       : -300, -200, -100,    0, +400, +600
Culture (100k) : -100,  -50,  -25,    0, +100, +200
Culture (20k)  :  -50,  -25,    0,    0,  +75, +100
Diplomatic     : +150, +100,  +50,    0, -200, -100
Domination     : -300, -200, -100,    0, +100, +400
Spaceship      : +100,  +50,  +25,    0, -100, -300

Map Modifiers    Tiny Small Stand Large  Huge    Arch  Cont  Pang

Conquest       : -200, -100,    0, +300, +400    +200,    0, -200
Culture (100k) : +300, +200,    0, -100, -200    +100,    0, -100
Culture (20k)  :    0,    0,    0,    0,    0       0,    0,    0
Diplomatic     :    0,    0,    0,    0,    0       0,    0,    0
Domination     : -200, -100,    0, +300, +400    +200,    0, -200
Spaceship      :    0,    0,    0,  -50, -100    +100,    0, -100

EXAMPLE: Conquest/Emperor/Small/Cont

ConditionBestDate = 10 + 400 - 100 + 0 = 310AD

Of course all these numbers could use some refinement! (suggestions welcome) Also, it might be best to convert entirely into turns.

After all the modification to the 'best' date for each victory conditions is done, a bonus (in score form, comparible to the ScoreAdjustment) is added based on how quickly the player was able to achieve the victory condition. With a decent balance in the modifiers, it should award a comparable bonus for a 'good' conquest as a 'good' spaceship victory, even on different maps or difficulty levels. Taking out the difficulty level comparison could be done if it was desired.

Bonus = ((2050 - PlayerDate) / (2050 - ConditionBestDate)) * ScoreAdjustment

ScoreAdjustment = same as in the scoring section, to equally weight score and date.

FinalScore = PlayerScore + Bonus

Conclusion

I know there is a lot of tweaking to do in a system like this, but even as it is, it should give a reasonable basis for comparison of different victory types within the same game, and even from game to game. There could always be more modifiers added (wonders, future tech, ect) as well. A utility to determine the score would definitely be needed. I could write one if necessary, though mapstat is already pretty much there if Chiefpaco would care to allow for it.

Each GOTM would be released with the following info: (example)

MaxMilkingScore = (would depend on the map generated)

Condition 'Best' Dates (Emperor/Small/Continents)

- Conquest = 310AD
- Culture (100k) = 1800AD
- Culture (20k) = 1825AD
- Diplomatic = 1400AD
- Domination = 500AD
- Spaceship = 1500AD

[alexman]

Re: A Scoring System

In 1.29f, the tech rate was changed so that now it is the same for the AI (but not the human) on all levels. Do your values for 'best date' take this into account, or are they based on games before the latest patch? If they are based on experience with 1.29f, it's too bad Firaxis' fix didn't work as expected.

[Aeson]

Tech rate type modifiers are from pre 1.29f experience for the most part. Diplomatic and Spaceship Difficulty modifiers may need to be toned down a bit. Tech rate doesn't seem to have changed too much overall though.

[alexman]

Also, you have a typo in the formula for PlayerScore.
It should be
PlayerScore = ((GameScore - GameBonus) / MaxMilkedScore) * ScoreAdjustment
(otherwise PlayerScore can easily be more than ScoreAdjustment)

[Aeson]

I think I need to add a Archipelago 60%/Continents 80% and Continents 60%/Pangaea 80% modifier as well. Both to the score portion (currently .45, .55, .65) and date.

[Aeson]

Thanks for pointing that out. It's got the right formula now.

[Aeson]

Here is a slightly modified modifier list. Added the 60/80 categories, and updated some others:

- base conquest to 200AD from 10AD
- deity diplomatic to -300 from -100
- emperor diplomatic to -100 from -200
- emperor domination to +200 from +400
- deity domination to +300 from +400
- large conquest and domination to +200 from +300
- low difficulty domination factors increase
- some domination land form modifiers softened.
- all 'tech' modifiers for diplo and space removed for < Monarch

- Spaceship base date was lowered by 20 turns to make for a better comparison with Diplomatic (40 turn spread instead of 60)

Updated the GOTM6-9 examples with the new values.

Base victory condition 'best' dates: (standard continents map, monarch)

Conquest       : 200AD
Culture (100k) : 1500AD
Culture (20k)  : 1700AD
Diplomatic     : 1300AD
Domination     : 500AD
Spaceship      : 1500AD

Difficulty        Chi   War   Reg   Mon   Emp   Dei

Conquest       : -300, -200, -100,    0, +400, +600
Culture (100k) : -100,  -50,  -25,    0, +100, +200
Culture (20k)  :  -50,  -25,    0,    0,  +75, +100
Diplomatic     :    0,    0,    0,    0, -100, -300
Domination     : -400, -300, -150,    0, +200, +300
Spaceship      :    0,    0,    0,    0, -100, -300

Map Modifiers    Tiny Small Stand Large  Huge    Arch 60/80  Cont 60/80  Pang

Conquest       : -200, -100,    0, +200, +400    +200, +100,    0, -100, -200
Culture (100k) : +300, +200,    0, -100, -200    +100,  +50,    0,  -50, -100
Culture (20k)  :    0,    0,    0,    0,    0       0,    0,    0,    0,    0
Diplomatic     :    0,    0,    0,  -50, -100       0,    0,    0,    0,    0
Domination     : -200, -100,    0, +200, +400    +100,  +50,    0, -100, -200
Spaceship      :    0,    0,    0,  -50, -100    +100,  +50,    0,  -50, -100

[alexman]

Shouldn't there be a modifier for the number of civs in the game? Conquest with 16 civs on a huge map is more difficult than conquest with only two civs.

Also, it's well known that the map generator has a good deal of variability for the same settings.

Why not smooth the map modifiers by taking the actual number of continents and number of civs into account? (A continent would be defined as a landmass that contains at least one civ starting location). This shouldn't be too much work for the MapStat utility to calculate.

We could come up with a formula for each victory type. For example, for Domination:

MapModifier = (NumberCivs-8)*50 + (1-2/NumberContinents)*100

[Aeson]

I hadn't really thought of that. The GOTM tends to use the default number of opponents for map sizes. For general use there would need to be some sort of modifier for number of civs.

As for the continent count modifiers, I don't know if they'd add anything really. The number of continents could end up having a different effect from game to game, even with the same number. On one you might end up on a small isolated landmass, while on another large landmass all the AI are racing ahead. The opposite scenario would change things considerably, even though in both there would be 2 landmasses. Add in the orders of seperation (ie. Galley crossings, Collosus/Astronomy crossings, Navigation/Magnetism crossings)... The range of possibilities on this is too much to account for I think, regardless of the scoring system implemented.

[seraphin]

as an former occ-player i ask you:
are you sure about this:

Culture (20k) : 0, 0, 0, 0, 0 0, 0, 0, 0, 0
?

i believe landmass and map size have a huge impact on global research speed ... dif.-level as well - it makes the whole tactic completely change (deity would be much more like a culture-occ then regent...).

the biggest thing is: 20kculture nearly always wins on archipel , bould could be prevented by the AI on pangae...(and landform changes global research speed too ...and you know: the worst things about 20k is waiting for wonders becomming available)

[Aeson]

20k culture is something I haven't played much, so I wasn't sure what to put. My thinking was that faster research rates allow for culture improvements earlier, but also allow for more 'spillover' builds from the AI, which cut down on the number of wonders that the player can build. I'm not sure how balanced these effects are, so just left it at even.

What modifiers would you suggest for difficulty?

[seraphin]

hmm....
its all a question of risk: on pangea ,deity ,small map you will be fastest but nearly always lose cause 1200 is AI domination...

for map size i would say:
-100,-50,0,+100,+200

for landform i would say:
-100 pangea
+50 archipel
but that does not make sence: archipel is of course much easier...
youre right about that balance...

if difficulty would be somehow transformed to time (in addition to its direkt effect) i would say(otherwise deity would of course be fastest):
and...
deity +100
emp. +25
mon. -50
reg. -100
chieftain -200...or....-a trillion? cant tell you anything about how easy it might be - very easy ?!?

i would give a big landmass a bonus....about +50 (60%) . -20 (80%)

but in the end it is all a about whee the 20k city is build:
how good the land is ,whether it is with or without ariver or a coast is even more important than the settings...