News: GOTM 39 Results and Congratulations

[dr_s]

You're right Alan, the final score is a complicated function of both raw score and finish date. I had always sort of assumed that final score was something of the form:

final score = (raw score) x (factor that depends on finish date)

But that's not true. To check this, I took my last save from this game and just hit shift-return until I got to 1514, Gosha190's finish date. At that date my raw score was 3310, and my final score was 58163. So the ratio of my raw score compared to Gosha190's is 2.09, but the ratio of final scores is 2.68.

I also noticed something else, which is that you don't get credit for all your tiles in your land score. I'm not sure what the difference is, exactly, but in looking at my game at 1514, it lists the score from land as coming from 503 out of 952, while I actually control 667 out of 952 tiles.

edit: xposted with Niklas ...

 

[Niklas]

I also noticed something else, which is that you don't get credit for all your tiles in your land score. I'm not sure what the difference is, exactly, but in looking at my game at 1514, it lists the score from land as coming from 503 out of 952, while I actually control 667 out of 952 tiles.

This one is easier. You only get score for tiles that you have owned for 20 turns (normal speed, not sure if that changes with speed).

 

[Gosha190]

and one thing more: real number of tiles covered with your culture you can see in "victory condition" screen. Its pictogram looks like fist.

 

[pnp_dredd]

I feel very lucky that I got 2nd and not 4th - my final score was bouncing around all over the place between about 102k and 107k for the last few turns, as population increased and the date multiplier decreased.

Congrats to CP and JK who dominated much earlier than I was able to. I only finished America in 1370AD (after a fairly early removal of France and England).

Here's when the top scorers discovered biology:

[B]Player		Date	Score	Biology[/B]
Gosha190	1514AD	155873	1055AD
pnp_dredd	1559AD	106932	1328AD
Cactus Pete	1292AD	106450	nil
Jovan Kukic	1118AD	105548	nil
SuperHead	1700AD	88507	1430AD
Lagashvili	1616AD	87170	1520AD
ShannonCT	1667AD	84771	1562AD

The year of discovery of biology correlates fairly well with final score (except for the two early wins).

This helps to illustrate that population still plays a major role in the final score, perhaps more so than finish date. e.g. SuperHead finished later than Lagashvili or ShannonCT but had earlier biology and a higher score.

 

[jesusin]

To give a simple answer to the original question: The reason two people with the exact same in-game score and end date can still get vastly different victory scores is that the final victory score is non-linear separately for each component, and that each component is weighted differently in the final reckoning.

As a very simplified example disregarding two of the factors (land and wonders), if you have 2000 base score of which 1000 is pop (200/1000 * 5000) and 1000 is tech (180/360 * 2000), your victory score on turn 330 (of 660) would be

PopScore = PopFactor*FinalPop/(MaxPop ^ (CurrentTurn/MaxTurn)) = 5000*200/(1000^(330/660)) = 31622
TechScore = TechFactor*FinalTech/(MaxTech ^ (CurrentTurn/MaxTurn)) = 2000*180/(360^(330/660)) = 18973

Total score = PopScore + TechScore = 50595

Note that despite having the same ingame base score in both components, they contribute very differently to the final score. Now compare this with a player with same base score of 2000, of which 1500 is pop (300/1000 * 5000) and 500 is tech (90/360 * 2000). Doing the same calculations again, for winning on the same turn, we get

PopScore = PopFactor*FinalPop/(MaxPop ^ (CurrentTurn/MaxTurn)) = 5000*300/(1000^(330/660)) = 47434
TechScore = TechFactor*FinalTech/(MaxTech ^ (CurrentTurn/MaxTurn)) = 2000*90/(360^(330/660)) = 9486

Total score = PopScore + TechScore = 56920

Quite a significant difference, with the emphasis being on the fact that population is more worth, more more worth than it is in the base ingame score.

Wow, I never knew this!

What's the practical application of all this?


Imagine I want to win a 1500AD game, which of the 4 factors should I stress?

Now imagine the game is going slower than expected and I expect to win 1750AD, which factor should I stress now?

What if the victory date is 2000AD?

 

[Adonias]

Whoopdydoop! My first award!

Congrats to all other winners!

 

[Gosha190]

Wow, I never knew this!

What's the practical application of all this?


Imagine I want to win a 1500AD game, which of the 4 factors should I stress?

Now imagine the game is going slower than expected and I expect to win 1750AD, which factor should I stress now?

What if the victory date is 2000AD?

pop is always the definitive part of your score.

 

[Niklas]

The simple answer is what Gosha said - pop is always the factor to focus on, it will always pay off the most. But if you want more detail than that, read on.

The reason why the relative contribution of the components differs from in-game score to post-victory score is the exponential term in the denominator: X = maxX^(winTurn/maxTurn). To answer the question of how much more a component contributes to post-victory score than it contributes to in-game score, the interesting value is maxX/X, i.e. the ratio between the denominator for in-game score and the denominator for post-victory score. Plotting this ratio by winTurn for various values for maxX, we get the expected negative exponential graphs. As an example, for maxX = 1000, we have

maxX/X (winTurn=0) = maxX = 1000
maxX/X (winTurn=100) = 401.8
maxX/X (winTurn=250) = 100.9
maxX/X (winTurn=500) = 10.09
maxX/X (winTurn=750) = X/X = 1

The way to interpret this is that if your maxPop value is 1000, your winTurn is 250 and your in-game pop score at that point is 1000, your post-victory pop score would be ~100900.

Now, the really interesting calculation is how these negative exponential graphs compare to each other, for different values of maxX. It should be easy to see from the above that on turn 750 (final turn), the relative contribution will be restored to 1, since the values will be 1 for both of them. At turn 0, the relative contribution will be identical to the relative values of maxX. If you have maxTech = 360 (fixed) and maxPop = 720, then 720/360 = 2, meaning that at turn 0 the population score will be magnified twice as much as the tech score.

Here is a graph plotting the value of (maxA/A)/(maxB/B), for maxA = 1500 and maxB = 310:

The way to interpret this graph is that if you have a maxPop value of 1500 and a maxWonders value of 310 (fixed), and you have the same in-game score for both, then the graph shows you how much more the population component will contribute to the post-victory score compared to the wonders component.

Summary: A component with a higher maxX value will be magnified more than a component with a lower maxX value, and the relative boost to the component with the higher value will be higher the earlier you win. So boosting your population early pays off big-time.

As an aside, the maxX value for the land component, maxLand, can on some low-food maps be higher than the maxPop value for that map. You should still focus on population. The reason is that the score factor for pop, PopFactor in the calculations in my previous post, is 5000 compared to the lousy 1000 for LandFactor. So the in-game score will already favor population by a factor 5, which will be impossible for land to catch up to even with a lower denominator.

 

[Erkon]

Congratulations all, especially Gosha, Jeffa, and Eric - see you've finally got your cow, only domino to go. We have a chance to see 3 new eptathletes next tour

Yes, finally. And I got it with challenger on jesusin's map, which is a weird coincidence since jesusin won his cow on challenger as well in GOTM33.

Congrats to all! Thanx jesusin! Special congrats to Erkon - God love you!

Thanks. I've probably used up all my luck for this year

 

[Grifftavian]

Shazaam My first award
Lowest scoring Cultural Victory
(keep those low culture jokes to yourself, thank you very much )

Congrats to all the other winners

And a big to the GOTM staff for all the great games!

 

[jesusin]

Now, the really interesting calculation is how these negative exponential graphs compare to each other, for different values of maxX.

Thank you! That was exactly my question.