Old GOTM Scoring Discussions

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Don't need the formula that was posted in another thread and I'm not sifting through 500 posts to find the one you are talking about.

We know that the early bonus points awarded are inadequate to offset milking so just increase the early bonus points awarded for the game and the gap diminishes.
 
Since I mentioned posting formulas:

Adjusted_Game_Score = Game_Score + (Game_Bonus_Points_Awarded *2)

We know that the bonus points awarded is calculated:
Years_Finished_Early*Difficulty

Simple and fairly effective.
 
Beard,

So I looked at your spreadsheet and find a number of peculiar things in your calculations. For instance, in GOTM7 there were 97 participants, only 19 finished in victory. Yet your table shows the average years left as 500+ years and used that to calculate the finish bonus (it should have been about 114). Why were the early finishers not able to have the data posted by people who had losses in the game toward the average years left in the game? Those same people had their results factored in to enhance the average score in favor of the winners to determine 'score ratio'.

In equations like those you will find that if you apply a win bonus in the years section of the equations you will have much better results (we discussed way to acheive this in that scoring thread.). If, two people that finish the game in 2050 with the same score but one won and one lost need to have a way to distinguish that fact in their final score.

And I still say that your adjusted base score premise is lame, lame, lame....

CB
 
Originally posted by Cartouche Bee
Adjusted_Game_Score = Game_Score + (Game_Bonus_Points_Awarded *2)

We know that the bonus points awarded is calculated:
Years_Finished_Early*Difficulty

Simple and fairly effective. [/B]

I like simple. The simpler a scoring formula is the more likely players will understand and accept it. The simplest scoring formula is to just use the game score but there are problems with that as stated many times.

When I developed the scoring formula, I had five basic objectives. These are stated in a previous post of mine on this page about the third post down. Take a second to read this and I think you'll agree with the objectives.

Although the formula you suggest is nice and simple, it has some problems:
  • Not comparable. Scores calculated with this formula would not be comparable from month to month. For example, a score from a large emperor game would not be comparable to a standard warlord game.
  • Not balanced. Map parameters will dictate the best way to score with this formula. On smaller maps, fast domination or conquest would be the best strategy. On large maps, milking would probably be the best strategy.

The formula I've suggested is a little more complex than the one you've suggested but I believe it meets all of the objective I’ve set out for a scoring formula. I've avoided using standard deviation or any other such witchcraft.

Scoring Formula

GOTMScore = 50 * (FinishBonus + ScoreRatio) / 2

FinishBonus = YearsLeft / AverageYearsLeft
ScoreRatio = PlayersScore / AverageScore

YearsLeft = 2050 - FinishYear
AverageYearsLeft = Average number of years left in all winning games.
PlayersScore = GameScore - (2050 - FinishYear) * DifficultyLevel
GameScore = Actual game score.
AverageScore = Average pre-bonus score of all winning games.
DificultyLevel = 1 for Chieftan through 6 for Diety.

FinishBonus is 0 when the player does not meet a victory condition

Some properties of this formula:
  • It is always better to finish a game than to milk a game for a few turns. The only exception is after an extensive period of milking.
  • Scores range from 0 to 100+ with the average of all games meeting a victory condition always around 50. Scores of 100+ are exceptional (2% of tournament and GOTM games).
  • Milking is a viable strategy and can give you one of the better scores. However, finishing faster is always the better option if your objective is score.
 
Although the formula you suggest is nice and simple, it has some problems:


Not comparable. Scores calculated with this formula would not be comparable from month to month. For example, a score from a large emperor game would not be comparable to a standard warlord game.

Not balanced. Map parameters will dictate the best way to score with this formula. On smaller maps, fast domination or conquest would be the best strategy. On large maps, milking would probably be the best strategy.




Well as for not comparable, we don't have that requirement in GOTM but Matrix does rate everyone's game based against the average result so I doubt your argument holds since you are rated against the average. Believe me most of us know when we did better or worse.

As for the 'Not balanced' of course the duct tape method allows you to add a fixed mapsize modifier with very little effort.

so:

Adjusted_Game_Score = Game_Score + (Game_Bonus_Points_Awarded * 2)

becomes:

Adjusted_Game_Score = Game_Score + (Game_Bonus_Points_Awarded * Mapsize_modifier)
 
Beard,

And if you hadn't noticed, in your proposed system your style of win is determined by the difficult that you play. On deity milk and chieftain finish quick. That's because on diety you have a high percentage of losses so averaging the year portion against only the winning games means that fast finishers lose out to milker's.

CB
 
Originally posted by Cartouche Bee
So I looked at your spreadsheet and find a number of peculiar things in your calculations. For instance, in GOTM7 there were 97 participants, only 19 finished in victory. Yet your table shows the average years left as 500+ years and used that to calculate the finish bonus (it should have been about 114). Why were the early finishers not able to have the data posted by people who had losses in the game toward the average years left in the game? Those same people had their results factored in to enhance the average score in favor of the winners to determine 'score ratio'.


GOTM 7 was the deity game. If any game is going to break a scoring formula this will be it as the results are so unusual.

The reason the average score and average years left are computed from winning games only is to improve the comparability. In general, the results from a losing game are essentially random and tend to make the end results less comparable. This is particularly true of years left. A person knocked out very early would raise the average years left not lower it, in effect lowering everyone’s score. For example, in GOTM 7 Melinder got wiped out in 470 bc with over 2500 years left in his game. BTW, the average years left in GOTM 7 if you include losing games is 712.

I think GOTM 7 is an anomaly and no scoring formula could make the results of this game comparable to others. Only some of the best players and the cheater got comparable scores to other months.

Originally posted by Cartouche Bee
In equations like those you will find that if you apply a win bonus in the years section of the equations you will have much better results (we discussed way to acheive this in that scoring thread.). If, two people that finish the game in 2050 with the same score but one won and one lost need to have a way to distinguish that fact in their final score.

I looked through the posts and I think I know what you’re talking about. This modification has more application on an early version of the scoring formula. The formula a few posts up does not favor milking and therefore does not need this modification. The only time where this may be a factor is with finishes around 2050.

When the finish is this late, the game is either a milked game or one of the lower scoring games. For milked games, finishing at 2050 with a win or a loss is just semantics, the game should have been won ages ago. Note that with this formula a milked game’s score is not limited to 33 or 50 as in previous versions of the formula. If the game is milked exceedingly well, your score can be over 100. Your worker dogpile game in GOTM 8 would receive a score of 162 with this scoring formula.

For a lower scoring game even the measly finish bonus awarded for a late victory will significantly effect the score.
Originally posted by Cartouche Bee
And I still say that your adjusted base score premise is lame, lame, lame....

And I repeat my lame premise for removing the game computed finish bonus:

The game score has an imbalance between your per turn score and finish bonus. On a tiny map the highest score is achieved by finishing fastest, on a large map the highest score is achieved by milking the game. It is kind of balanced for a standard map but that also depends on your skill level, play style and other factors. This is one of the reasons it is impossible to compare the scores between a large and small game on the same level.

Keeping the finish bonus in the game score would tip the balance of the formula to strongly favor fast finishes. This is not necessary as the formula already favors fast finishes. Leaving the finish bonus in also re-introduces an unbalancing component to it.
 
Originally posted by Beard Rinker



The reason the average score and average years left are computed from winning games only is to improve the comparability. In general, the results from a losing game are essentially random and tend to make the end results less comparable. This is particularly true of years left. A person knocked out very early would raise the average years left not lower it, in effect lowering everyone’s score. For example, in GOTM 7 Melinder got wiped out in 470 bc with over 2500 years left in his game. BTW, the average years left in GOTM 7 if you include losing games is 712.


If a player loses why would the years left not be zero? They did not win. I think years left is where you went wrong. It is really the number of years before 2050 the win occured.

As for the game bonus, you say it does not serve the purpose and skews your equation. Well I think you need to fix your equation then.

I say the game bonus is inadequate, so make it adequate.
 
Originally posted by Cartouche Bee
Well as for not comparable, we don't have that requirement in GOTM but Matrix does rate everyone's game based against the average result so I doubt your argument holds since you are rated against the average. Believe me most of us know when we did better or worse.

Yes it is not as important to have the score comparable from month to month but it is desirable. My best score is 71 and it would be nice to know if this month’s game was better. I feel as though I played better but I would like some hard numbers.

The formula essentially incorporates Matrix’s normalized score as part of the formula. In fact, that’s where I got the idea.

Originally posted by Cartouche Bee
As for the 'Not balanced' of course the duct tape method allows you to add a fixed mapsize modifier with very little effort.

You must have a magic roll of duct tape. What is this mapsize modifier?

Aeson’s original tournament scoring formula used this concept and built a modifier based on the map size, water level and I think even terrain type. The problem with this approach is it is much more complex and the results are not as good.

We have the benefit of basing our scoring system on the results of other players. A pretty reliable base and one that automatically compensates for map size, difficulty level, terrain type, starting position, etc.
 
Originally posted by Beard Rinker


You must have a magic roll of duct tape. What is this mapsize modifier?

Aeson’s original tournament scoring formula used this concept and built a modifier based on the map size, water level and I think even terrain type. The problem with this approach is it is much more complex and the results are not as good.

We have the benefit of basing our scoring system on the results of other players. A pretty reliable base and one that automatically compensates for map size, difficulty level, terrain type, starting position, etc.

You must be kidding, it could simply be the ratio between the mapsizes.

As for the averages, yes we do an average in GOTM. I think you score 10 if your game is average (but I'm not sure). I know it is not 71 or 50 but it still is a point of reference.
 
Originally posted by Cartouche Bee
If a player loses why would the years left not be zero? They did not win. I think years left is where you went wrong. It is really the number of years before 2050 the win occured.

Good point.

I re-computed the results of GOTM 7 using this suggestion but got strange results. Essentially everyone who won the game had a score of 100+. Since a score of more than 100 should only occur 2% of the time, this does not seem like a good modification.

I stand by my assessment that using losing scores when computing the averages adds a randomizing element to the formula. Losing scores should not be used for the averages.

Originally posted by Cartouche Bee
As for the game bonus, you say it does not serve the purpose and skews your equation. Well I think you need to fix your equation then.

I say the game bonus is inadequate, so make it adequate.

The game bonus is not inadequate, it is unbalanced. The best way to balance score vs. finish date is to separate them completely, rank them based on how others did and combine them with equal weighting.
 
Originally posted by Beard Rinker



The game bonus is not inadequate, it is unbalanced. The best way to balance score vs. finish date is to separate them completely, rank them based on how others did and combine them with equal weighting.

If you want to call it unbalanced fine, then I call it balancing it.

I don't think you know how to rank the finish date properly so I don't think you can combine score and finsih date equally.
 
Originally posted by Cartouche Bee
You must be kidding, it could simply be the ratio between the mapsizes.
I don’t think so. Water level is a big factor, as well as if the map is an archipelago or pangea. The more you think about it the more factors are involved in this ratio.

Originally posted by Cartouche Bee
As for the averages, yes we do an average in GOTM. I think you score 10 if your game is average (but I'm not sure). I know it is not 71 or 50 but it still is a point of reference.

But then we are back to the original problem. The normalized score produced by Matrix is based entirely on your game score, which is essentially a measurement of how well the game was milked.

I want a point of reference on how well I played the game.
 
Originally posted by Cartouche Bee
And if you hadn't noticed, in your proposed system your style of win is determined by the difficult that you play. On deity milk and chieftain finish quick. That's because on diety you have a high percentage of losses so averaging the year portion against only the winning games means that fast finishers lose out to milker's.

The scoring formula favors fast finishes over milking games in all games, regardless of difficulty, map size or other parameters. It does not favor fast finishes by a large margin meaning a milking game, space, cultural or diplomatic victory may occasionally win.

I suspect had SirPleb finished GOTM 7 with a conquest or domination victory instead of milking the scoring formula would have given him a higher score.
 
Beard,

From your last couple of posts I see that you have trouble grasping how truly flawed your concept is.

I know you will protest but as a point of reference for you, go to your spreadsheet and turn to GOTM6.

Delete all the entries except Aeson and Lucky's.

Look at the result, even though Lucky lost his game he is rated with your formula as 112.1 and Aeson is rated at 50.

That is in spite of the fact that you claim the faster victory will always have a higher score. Sorry but it is your lame score adjustment and faulty date calculations that cause the problem. This sample just magnifies the problem of the poor foundation. that you based this concept on.

I also know it is hard to believe that a mapsize adjustment could be determined without much effort but I'll leave it at that.

CB
 
Originally posted by Cartouche Bee
Beard,

From your last couple of posts I see that you have trouble grasping how truly flawed your concept is.

I know you will protest but as a point of reference for you, go to your spreadsheet and turn to GOTM6.

Delete all the entries except Aeson and Lucky's.

Look at the result, even though Lucky lost his game he is rated with your formula as 112.1 and Aeson is rated at 50.

That is in spite of the fact that you claim the faster victory will always have a higher score. Sorry but it is your lame score adjustment and faulty date calculations that cause the problem. This sample just magnifies the problem of the poor foundation. that you based this concept on.

This formula is intended for use with a bunch of scores not just two. The premise behind the formula is your score is based on the average of all games and that the average is a consistent benchmark from month to month. I also noticed that Aeson beat Lucky when all scores are included and by no small margin. 194 for Aeson and 92 for Lucky.

I do not claim that fast victory will always win, I said it would usually win. That is one of the strengths of the formula, you can win with any victory condition as long as it is a very well played game. I think most players would rather play to their strength instead of going for the victory condition that always wins. This is particularly true with the current scoring system as milking games are probably the least popular way to finish a game.
 
So, Aeson's game was more than twice as good as Lucky's using your scoring system.

My simplified score proposal would only have rated Aeson's game as being about 30% better.

Aeson's game was very good but Lucky is a very good player also and I doubt that it was more than twice as good as Lucky's game. I also doubt that it was twice as good as Sir Pleb's game.

I guess it's a matter of opinion but most milker's have the game under control pretty early and are very good player's. I think the results your system produces are not representative of a decent scoring replacement in any way.
 
After reading all of this and after spending time trying to come up with a formula a couple months ago in the tournament, I can see why Firaxis never bothered to address the flawed scoring system. My policy now is I'm not gonna touch the scoring system with a ten foot pole!!!
 
Bamspeedy,

:lol:

When you and I were working on that we made solutions for the problems that as they were identified. We just made the changes so quickly that they just couldn't comprehend the "dynamics" of it so they went back into the hole and used to 10 to 1 weighting to compensate for the mess they had finally discovered.

CB
 
As I see it, the aim is for a scoring system that gives score parity between early finishers and milkers.

Many players when milking post “estimated” scores based on the number of tiles to the domination limit, the current population etc etc. What may be a fair way of calculating a score for early finishers is to estimate a “milkers’ potential score”. Look at the number of tiles available to the domination limit, and the current population to generate a bonus score on what the final score could if it was milked properly. This bonus could be (say) 80% of the theoretical maximum to make up for the fact that the population may not grow, milking may not be completely efficient etc.

The main drawback to this is that someone who finishes early with (say) spaceship may not have been able to milk right through to 2050, due to the AI winning (culture, diplomacy etc). Therefore, to qualify for the bonus, you may have to show that you are in a position where you can do a milk-run. EG. You need to have the highest population, highest culture or be at 90% of the domination limit anyway etc. Not sure of the details, but this may be a reasonable framework for a better bonus system?


Edit: Implimentation would be quite simple too, as mapstat could be modified to calculate the bonus quite easily.
 
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