GOTM-1: Closing Spoiler

[bradleyfeanor]

Here are my numbers for comparison:

2386 (327/685) Pop
1370 (601/877) Land
686 (103/300) Tech
347 (80/230) Wonders

Hendrikszoon had me beaten in every category, but it looks like population made up the biggest difference in our scores, with research being a distant second. That makes sense since I had turned research off in my game until the last few turns.

I went pretty far over the dom limit (68.5%), but Hendrickszoon went all the way to 72%. That was worth an extra 71 points of base score. I'm not sure what that 71 points translates to once the early victory multipier is applied, but I would love to find out. Does anyone know if the multiplier (or curve, whatever the heck it is), applies evenly to all factors--pop, land, tech and wonders? Or is it weighted more heavily toward one category such as population?

I also looked at the turn before victory in my game, and noted that I picked up 26 points of base score just for researching education. So, as someone in this thread already mentioned, it's probably not a good idea to turn off research unless it results in a significantly earlier victory.

 

[Gyathaar]

How the scoring system works is described in detail in a thread in the HoF forum.

 

[Grogs]

How the scoring system works is described in detail in a thread in the HoF forum.

I reread that article and I think it's finally all clicked now. You guys should consider chopping the pertinent posts out of that article and stickying it though. Even knowing exactly where to go, it still took me a couple of minutes to find the posts with the formulas laid out.


DaveMcW really laid it out with the simplest explanation IMO:

The "scoring curve" expects you to double your score every 10% of the game. So the winning strategy is to keep growing your empire until you cannot maintain the "double every 10%" rate, and then claim victory.

 

[bradleyfeanor]

How the scoring system works is described in detail in a thread in the HoF forum.

Thanks for posting that tidbit. That thread has progressed quite far since last I looked at it in early November. Wish I had read it before 4oTM 1! Now I know the answer about the population portion of the score...and all my fears about having a poor scoring system are now confirmed.

As Aeson mentioned earlier, that system definitely won't work for 4oTM competition purposes.

For those who haven't seen the scoring thread, I would recommend page 5 as a good starting point.

 

[Civgeek]

Just for the record for those making comparisons;

Entry class: Open
Game status: Spaceship Victory
Game date: 1953 AD
Firaxis score: 15794
Base score: 5538

I'm not sure how to get the detialed breakdowns of my final score (pop etc. etc.); can somebody post how to do that?

[edit to add final score breakdown]
2518 from Pop (345/685)
825 from Land (362/877)
1913 from Tech (287/300)
282 from Wond (65/230)


I did think the final victory screen was appropriate ...

 

[hendrikszoon]

I went pretty far over the dom limit (68.5%), but Hendrickszoon went all the way to 72%. That was worth an extra 71 points of base score. I'm not sure what that 71 points translates to once the early victory multipier is applied, but I would love to find out. Does anyone know if the multiplier (or curve, whatever the heck it is), applies evenly to all factors--pop, land, tech and wonders? Or is it weighted more heavily toward one category such as population?

The 31 Land tiles (or 71 Game Score points) I got more than you, are not worth a lot. At 1450AD they are equivalent to around 500 points of the Final Score. Or, to make it more clear, they are also equivalent to a little bit more than 2 citizens. More or less only Population counts.

 

[bradleyfeanor]

I'm not sure how to get the detialed breakdowns of my final score (pop etc. etc.); can somebody post how to do that?

Hover the cursor over your name in the leader list at the bottom right hand corner of the screen (when in the game).

 

[bradleyfeanor]

Pardon the double post, but I missed Hendrik's reply:

The 31 Land tiles (or 71 Game Score points) I got more than you, are not worth a lot. At 1450AD they are equivalent to around 500 points of the Final Score. Or, to make it more clear, they are also equivalent to a little bit more than 2 citizens. More or less only Population counts.

I knew the land/tech factors were less significant than pop, but I didn't realize it was by that much! I guess I am going to have to map out the curves so that I can visualize the relative score values in my head. I don't have the intuitive mathmatical genius of many people in Civdom.

 

[AlanH]

I guess I am going to have to map out the curves

I'll save you the trouble. Here's one I prepared earlier. The max scores for each score component are plotted below against turn, for this game. Your actual final score for each component is the weighting factor multipled by the ratio of your actual score to the the max score. The weighting factors are:

Pop: 5000
Land: 2000
Techs: 2000
Wonders: 1000

​

 

[Mahatmajon]

A glorious, wonderful way to make 20 hours disappear. The number of obscene scores in these GotMs is intimidating, though. At least I can console myself by saying it's the "barely won" games that make the most interesting reports.

Well, in case this is true and people are interested in the "barely won" games I'll put my story in (at least the short/brief/no picture version). This was my first game of Civ4 after playing the demo a few times. I had no idea that the GOTM was/is a scorefest and never had a plan for the game other than my normal culture build up, develop all cities, & decide what to do in the latter 1/3 of the game.

Summary: Never left my island, never built a cottage myself (I did turn on AI workers and let them destroy improvements ~1900AD because I was bored of dealing with them), had the score lead for pretty much the entire game & won a Diplomatic Victory on the last possible turn of the game! one turn before I would have finished the spaceship.

Early game: Founded Rome 1S (I think, don't have photos here to check). After scouting around and finding the stone on the West coast of the island I decided to make my second city there and try to build all of the early Stone wonders. This worked out fine and I had Stonehenge & Pyramids in Rome. Also picked up Judaism and Confucianism along the way. The only down side to the wonder building was that not expanding faster allowed Greece to make 2 cities in the middle of my empire.

First war: Greece had no religion so I converted them to mine. Did some trading and had him at happy, but 'our close borders caused tension' and he declared war on me. At the time he declared war I had exactly 1 archer in every city and my initial 2 warriors. If he would have put any effort into the battle I would have lost multiple cities but I ended up not losing any. I was pretty disappointed to see the AI perform so badly. I whipped out a few Prats and took the 2 cities in my land and killed most of his invading army before declaring peace.

No more Greece: I filled in a few city spots and rebuilt my economy up before switching to vasslage/other +experience civics (I don't even know their names yet!) to finish Greece off with catapults and Prats.

Midgame: I didn't trade many techs (maybe not even any) with the computer. China landed & attacked once with grenadiers but was repelled. Isabella came in with helicopters & better troops but was also repelled. I counter-attacked Isabella with 3-5 transports of tanks & artillery but I need A LOT more experience in managing these troop types. I burned one city but my entire force was destroyed at the next city. She had the same techs and helicopters were a pain.

Endgame: I got very concerned about losing when Isabella made the UN and was elected SG. I expected her to win Diplomatically but I'm not sure if the AI does that or not. Mao also had China ahead in the space race (I was woefully behind) and I thought I was going to lose. My only chance came when I convinced Germany to war with Isabella and I joined in one turn later. I only burned one more city with a small 12 unit force but this lead to Germany pounding on Isabella and she finished 4th in score after being second the entire game.

In the end I realized too late that I wasn't going to have enough production to finish the space ship. I quickly built ~30 workers to make all workshops around Rome but I ended up 1 turn short of being able to build the spaceship. I'll find the screenshot but it was something like I needed 166hpt for the last 2 turns and I could only get 160hpt.

1st win: To my great surprise I was elected the UN SG and with 2 turns left to play a Diplomatic victory came up for vote and I was elected on the last turn of the game.

This was a lot of fun. I know that I wasted a ton of time & production on useless buildings in all of my cities and have a long way to go toward specializing cities and maximizing scores but I enjoyed the game and it's interesting to see how others did, especially the people who didn't have to deal with Isabella at all!

 

[bradleyfeanor]

Here's one {maxScore curve} I prepared earlier...

Thank you, as usual, Alan the Great.

In addition to the curve, I was going to create a bar graph that shows how much each score component (land, pop, etc.) makes up in the total score for my game, Dynamics, Hendrikszoon's and CivGeek's (those who posted the relevant data), but I am running into a score calculation discrepancy.

In converting Dianthus's scoring formula (for land, pop and tech) to excel speak, I get:

(Factor*rawScore)/(initialScore*(maxScore/initialScore)^(curTurn/maxTurn))

For wonders I used:

(Factor*rawScore)/(initialScore+curTurn/maxTurn*(maxScore-initialScore))

For my game I used the following numbers in the formula:

	curTurn	maxTurn	iniScor	rawScor	maxScor	Factor	Score	% of Total
Pop	203	430	1	327	685	5000	74,956	82
Land	203	430	21	601	877	2000	9,829	11
Tech	203	430	6	103	300	2000	5,416	6
Wonder	203	430	0	80	230	1000	737	1
Total							90,938

Unfortunately, the actual game total was 91,022, so my calculation is off by -84. Are there any "Civ4 Score Masters" out there who know what the problem might be?

 

[AlanH]

There are some subtle rounding corrections you need to apply to the sub-totals. At least one of the calculations is rounded down. Also remember that the victory date, and raw score, are taken at the point of victory, not from the save you have to submit for the GOTM entry.

 

[bradleyfeanor]

I have now rounded down (using Int) every iScore component. iScore appears to be the function used to return each of the four score elements--pop, land, tech, wonders. I assume that is what you were referring to regarding rounding.

I think I am also using the correct victory date and rawScore: victory date should be 1430 (turn 203). For the rawScore values I am using the values from turn 1440, although it may be that not all the values accrue on the interturn. I can't find any posts and/or code to confirm that.

In any case, taking the rawScore values from the previous turn would make my "Total Score" calculation even lower--which is the wrong direction.

I must be missing something else.

 

[Grogs]

I'll save you the trouble. Here's one I prepared earlier. The max scores for each score component are plotted below against turn, for this game.

I must be in the slow group. I can't for the life of me figure out what you've graphed here. From reading Dianthus's post over in the HOF forum, it seems that as soon as the game is started, initial and max scores are set. If I pop open my 4000 BC save, my max. population (for example) is 685, the same as what Bradleyfeanor has in his table for turn 203, which is the same thing I had on turn 331 when I finally won.

If I could trouble you, what's the formula you're using for your y-axis?

 

[Fardaza]

This was my first ever GOTM. What a treat!

I finished in 1945 with a domination victory. My final score was 18,176!

I feel pretty good about that score. It's my personal high score in Civ4 by about 10,000 points.

I look forward to more GOTMs!

Fardaza

 

[AlanH]

Sorry I confused you. Let's take population:

Your normalised pop score is equal to:

5000 * (actual_pop - initial pop) / (max_pop - min_pop)

The other components have lower normalisation factors making their effect on final score lower.

During the game you are absolutely correct. the only number that varies is actual pop. The other factors remain constant. So this value is your Base Score for pop. Your value of 685 for max_pop is the value at the right hand end of the dark line on my previous graph.

At the end of the game, however, if you win then the value of max_pop is reduced as a function of the number of turns you played to victory. The effect of this is to increase your Final Score, because the denominator in the above expression decreases as you finish earlier. This provides your victory bonus, and it explains how it's possible to get total scores considerably above 10K. The graph I posted above simply plots the relationship of max_pop (and of the other max_values) to the victory turn.

As an exercise I plotted the Final Score that could be achieved at any victory turn if you played a game where each raw score component increased along a straight line from min_score to max_score. Here is the resulting curve. You can see that if you could score linearly and achieve victory between turns 50 and 100 you could get a final score around 200K


I've also plotted the scatter graph of actual scores in this game vs victory turn, and the distribution centers on the second half of this curve remarkably well. I'll publish that plot when the game is over.

 

[Grogs]

Sorry I confused you. Let's take population:

Thanks, that helps. I had surmised from reading Dianthus's post (several times) that the victory bonus was a decaying exponential, so seeing a graph of exponential growth threw me. Since what you plotted is essentially the denominator in the final score calculations, that makes sense.

At the end of the game, however, if you win then the value of max_pop is reduced as a function of the number of turns you played to victory. The effect of this is to increase your Final Score, because the denominator in the above expression decreases as you finish earlier. This provides your victory bonus, and it explains how it's possible to get total scores considerably above 10K. The graph I posted above simply plots the relationship of max_pop (and of the other max_values) to the victory turn.

I think we just look at it 2 different ways. Taking this equation from Bradleyfeanor's post:

(Factor*rawScore)/(initialScore*(maxScore/initialScore)^(curTurn/maxTurn))

I like to rearrange it as follows:

[(Factor*rawScore)/Initial Score] * [(maxScore/InitialScore)^-(curTurn/maxTurn)]

It's the same equation (after a little algebraic manipulation,) it just has 2 distinct parts: A linear growth term where rawScore is the only variable, and an exponential decay term where curTurn is the only variable. This, to me, gives the clearest picture of the 2 opposing forces that go into determining overall final score. It's also very clearly visible in your graph as the linear growth term dominates early, but gets overwhelmed by the decaying exponential after the peak.

As an exercise I plotted the Final Score that could be achieved at any victory turn if you played a game where each raw score component increased along a straight line from min_score to max_score. Here is the resulting curve. You can see that if you could score linearly and achieve victory between turns 50 and 100 you could get a final score around 200K

I've also plotted the scatter graph of actual scores in this game vs victory turn, and the distribution centers on the second half of this curve remarkably well. I'll publish that plot when the game is over.

I really like the graph - game scores in a nutshell. If you increase your score faster than linear, the peak should shift to the right and go up. I strongly suspect though, that no realistic rate of growth would be enough to move the peak into the timeframe of our fastest finishers.

 

[hendrikszoon]

Unfortunately, the actual game total was 91,022, so my calculation is off by -84. Are there any "Civ4 Score Masters" out there who know what the problem might be?

I believe that I know the origin of the difference: It seems that they are rounding down (maxScore/initialScore). For Pop (685/1) and Technology (230/6) it makes no difference. But for Land you have to use 41 instead of 41.7619...

Also all the final results are rounded down. So it seems that we have to modify Dianthus formulas a little bit. My proposal is:

trunc((Factor*rawScore)/(initialScore*(trunc(maxScore/initialScore))^(curTurn/maxTurn)))

trunc((Factor*rawScore)/(initialScore+curTurn/maxTurn*(maxScore-initialScore)))

Using these formulas to modify your table leads to

	curTurn	maxTurn	iniScor	rawScor	maxScor	Factor	Score	% of Total
Pop	203	430	1	327	685	5000	74,956	82
Land	203	430	21	601	877	2000	9,915	11
Tech	203	430	6	103	300	2000	5,415	6
Wonder	203	430	0	80	230	1000	736	1
Total							91,022

 

[Olmo]

Victory: Time
Game Score: ~5400

My first GOTM and I barely managed not to loose it.
Started my war against Alexander a bit late waiting for praets and catapults.
The war did not go that well because the Greek managed twice to land a couple of units near my iron and to capture and destroy the mine.
So first lesson learnt: Always protect your assets.
I conquered the last Greek city at about 1600 AD.
Then I decided to go for Diplomatic victory which proved to be the wrong decision. I tried to bribe the other AI's giving them techs and resources.
But after building the UN and having been elected as GS, only Gemany voted for me, the others abstained or voted for Saladin.
When I tried to send Judaic missionaries to the other continents the AIs soon started to switch to Theocracy, so no more converting was possible.
When I realized that I was having problems getting more UN votes it was too late to change to the Starship race.
Got attacked by Monty once (shortly after greek war) and very surprisingly by Mao in the late game.
Enjoyed the game very much and will try to improve my tactics in the next GOTM.

 

[Civgeek]

Also all the final results are rounded down. So it seems that we have to modify Dianthus formulas a little bit. My proposal is:

trunc((Factor*rawScore)/(initialScore*(trunc(maxScore/initialScore))^(curTurn/maxTurn)))

trunc((Factor*rawScore)/(initialScore+curTurn/maxTurn*(maxScore-initialScore)))

Using these formulas to modify your table leads to

Seems to work for me. Here's my orginal scores ...

Entry class: Open
Game status: Spaceship Victory
Game date: 1953 AD
Firaxis score: 15794
Base score: 5538

2518 from Pop (345/685)
825 from Land (362/877)
1913 from Tech (287/300)
282 from Wond (65/230)

and from your formulas ....

	curTurn	maxTurn	iniScorerawScoremaxScoreFactor	Score	%Total
Pop	343	430	1	345	685	5000	 9,436 	60%
Land	343	430	21	362	877	2000	 1,782  11%
Tech	343	430	6	287	300	2000	 4,222  27%
Wonder	343	430	0	65	230	1000	 354 	 2%
Total							[B] 15,794[/B]