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How scoring works, with graphs!

Discussion in 'Civ4 - Game of the Month' started by carterba, Jan 27, 2006.

  1. bshumbera

    bshumbera Warlord

    Joined:
    Jul 16, 2006
    Messages:
    210
    This was my original thinking as well. However, it should be mentioned that cultural victories require Wonders and space victories require Techs. Each of these are also weighted in score, so perhaps each victory does yield statistically insignificant results. I think that we see the highest scores from conquest and domination simply because they are easier to accomplish earlier and time is the largest component of the final score.
     
  2. da_Vinci

    da_Vinci Gypsy Prince

    Joined:
    Jun 13, 2004
    Messages:
    4,182
    Location:
    Maryland, USA
    If we look at the scores for a given turn (along a particular vertical line in AlanH’s plot) after turn 300, an “eyeball” analysis suggests that domination victories have the least variance (the vertical dispersion), and their mean (at least its point estimate) is clearly higher than the means for spaceship and cultural (but per StevenJoyce, not statistically different). Probably higher than the mean for diplomatic as well, but that is less clear from the plot.

    For turns 250 to 300, differences are less clear, except perhaps that cultural is lower for a given turn (the non-linearity issue I mentioned earlier).

    Before turn 250, not enough data to say anything.

    Looks like perhaps as turn number increases (at least beyond turn 300), domination separates itself from the other victory types in terms of score for a given turn number. This may be because at some point, the cultural, space and diplomatic victories are perhaps a coast to the end (in terms of pop and land) but domination requires active expansion of both to the end.

    But a space victory at turn 350 is better than a domination victory at turn 400.

    @ StevenJoyce: I’m betting that the influence points are all before turn 300, and maybe all before turn 250. If you run the regression for only turns 300 and above (where the data appear to “behave” better for a linear model), are there any statistically significant differences in slope or intercept? Can we say something definitive about this turn interval?

    dV
     
  3. StevenJoyce

    StevenJoyce Chieftain

    Joined:
    May 11, 2004
    Messages:
    31
    This is mostly correct, with the exception of the influence points for the cultural victories (which are all after turn 350) and for one influence point for the conquest victories (at turn 428).
     
  4. StevenJoyce

    StevenJoyce Chieftain

    Joined:
    May 11, 2004
    Messages:
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    Even limiting the regression to turn300+, we still get significant differences.

    Significantly different intercepts
    Conquest v. Diplomatic
    Conquest v. Domination
    Cultural v. Diplomatic
    Cultural v. Domination
    Diplomatic v. Domination
    Diplomatic v. Space
    Diplomatic v. Time
    Domination v. Space
    Domination v. Time

    Significantly different slopes
    Conquest v. Diplomatic
    Conquest v. Domination
    Domination v. Space

    Conclusion: Even though there are influential outliers, they aren't driving the differences in the estimated lines.
     
  5. da_Vinci

    da_Vinci Gypsy Prince

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    Maryland, USA
    @ StevenJoyce: It looks like compared to your first Oct 19 post (quoted above), the 300+ regression gives us a different set of significant slope contrasts. Or am I missing something?

    BTW, appreciate the number crunching effort!

    dV
     
  6. StevenJoyce

    StevenJoyce Chieftain

    Joined:
    May 11, 2004
    Messages:
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    You're right. The 300+ regression has a different set of significantly different slopes. Here's the full results from the 300+ regression.

    [pre]
    | Robust
    | Coef. Std. Err. t
    ----------------------------------------------------
    Conquest intercept | 8.477041 .0592616 143.04
    Cultural intercept | 8.274827 .1920754 43.08
    Diplomatic intercept | 8.68217 .0545812 159.07
    Domination intercept | 8.909265 .0299758 297.22
    Spaceship intercept | 8.530005 .0198961 428.73
    Time intercept | 8.486896 .0229012 370.59
    Conquest slope | -.0139136 .0012578 -11.06
    Cultural slope | -.0126783 .0021032 -6.03
    Diplomatic slope | -.0106283 .0007301 -14.56
    Domination slope | -.0106144 .0003714 -28.58
    Spaceship slope | -.0116568 .0003202 -36.40
    -----------------------------------------------------
    [/pre]
     

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