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Twilight Imperium (Third Edition)» Forums » Sessions

Subject: Twilight Imperium: Our leader board rss

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Shawn Garbett
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I went ahead an ordered the results. They don't exactly match the previous bar charts in this thread. The statistical model assigns effects across the factors of Race and Player. A player's overall average score may be higher due to Races that happened to be played. So this adjusts for the observed factor of race.


Average Score 5.9

Effects of Race on Final Score

Federation of Sol 3.0
Yssaril Tribes 2.2
L1Z1X Mindnet 1.7
Brotherhood of Yin 1.5
Xxcha Kingdom 1.4
Univ. of Jol Nar 1.3
Emirates of Hacan 1.2
Mentak Coalition 1.0
Embers of Muatt 0.9
Sardakk N'orr 0.6
Nekro Virus 0.5
Barony of Letnev 0.2
Ghosts of Creuss 0.1
Clan of Saar 0.0
Arborec 0.0
Winnu 0.0


Effects of Player on Final Score

Ben Burkholder 0.3
Rocky Thomspon 0.1
Dusty Shunta 0.0
Adam Mitchell 0.0
Matt Spencer -0.5
Jon Horne -0.7
Mongo Closz -0.7
Jeremy Scott Pyne -0.8
Kevin Ralieght -1.9
Matt Bighan -2.0
Chris Halbower -2.1
Joe Veldhuis -2.2
Joshua Hannebohn -3.0
Zack Anderson -3.0
Casey Bousho -6.2
Bubba Bartels -7.1

Effect of Imperial II on final score +0.8
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Christopher Halbower
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Shawn: I see you used average score. Wouldn't deviation from winning score be more suitable?
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Shawn Garbett
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I used raw score. I could use difference from winning score and rerun the models.
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Christopher Halbower
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When I first started analyzing the data, I too used raw or "adjusted" score. (Adjusted score was to compensate for the score differences between Bureaucracy and Imperial II).

However, I think deviation from winning score is the true test. For example, it's possible that when the Sardakk N'orr is in the game, the games are much lower scoring; does this mean the N'orr are weaker? No.

When I'm in a game, score on average might be overall higher. Does this mean I'm a good player? Not necessarily.

How strong a player is, by my reckoning, is how far the player is from winning. Mathematically this is equal to:
Player strength = Σ (Player's raw score - Winning Score)

Players who win or come close to winning more often will have deviations from winning closer to zero than players who do not.
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Shawn Garbett
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> summary(aov(m))
Df Sum Sq Mean Sq F value Pr(>F)
Player 16 123.1 7.70 3.758 5.14e-05 ***
Race 17 205.4 12.08 5.900 3.20e-08 ***
Strategy.Card 2 382.7 191.35 93.447 ≺ 2e-16 ***
Residuals 73 149.5 2.05
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
1 observation deleted due to missingness

> summary(m)

Call:
lm(formula = Deviation ~ Player + Race + Strategy.Card, data = d)

Residuals:
Min 1Q Median 3Q Max
-4.3733 -0.7045 0.0684 0.7463 2.4590

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.457963 1.314841 -1.109 0.2711
PlayerBen Burkholder -0.087996 1.166783 -0.075 0.9401
PlayerBubba Bartels -3.851706 1.558403 -2.472 0.0158 *
PlayerCasey Bousho -4.637119 1.793692 -2.585 0.0117 *
PlayerChris Halbower -0.329358 1.156387 -0.285 0.7766
PlayerDavid Mitchell -1.799648 1.492558 -1.206 0.2318
PlayerDusty Shunta -0.026622 1.161339 -0.023 0.9818
PlayerJeremy Scott Pyne -0.659259 1.596985 -0.413 0.6810
PlayerJoe Veldhuis -2.228801 1.316764 -1.693 0.0948 .
PlayerJon Horne -0.165839 1.262840 -0.131 0.8959
PlayerJoshua Hannebohn -3.369184 1.997841 -1.686 0.0960 .
PlayerKevin Raliegh -1.517177 1.181284 -1.284 0.2031
PlayerMatt Bigham -2.901559 1.334672 -2.174 0.0329 *
PlayerMatt Spencer -0.296626 1.161255 -0.255 0.7991
PlayerMongo Closz -0.724173 1.152576 -0.628 0.5318
PlayerRocky Thompson -0.051455 1.244795 -0.041 0.9671
PlayerZack Anderson -1.188668 1.374951 -0.865 0.3901
RaceBarony of Letnev -0.406121 0.988363 -0.411 0.6823
RaceBrotherhood of Yin 1.473770 1.113770 1.323 0.1899
RaceClan of Saar -0.909490 0.952468 -0.955 0.3428
RaceEmbers of Muatt -0.179156 0.942028 -0.190 0.8497
RaceEmirates of Hacan -0.771112 0.961992 -0.802 0.4254
RaceFederation of Sol 1.420141 0.958943 1.481 0.1429
RaceGhosts of Creuss -0.474832 1.043783 -0.455 0.6505
RaceL1Z1X Mindnet 0.772288 0.974175 0.793 0.4305
RaceLazax -0.001947 1.393443 -0.001 0.9989
RaceMentak Coalition -0.076933 1.002705 -0.077 0.9391
RaceNaalu Collective 0.279327 0.898736 0.311 0.7568
RaceNekro Virus -0.444599 0.912499 -0.487 0.6276
RaceSardakk N'orr 0.376482 0.949711 0.396 0.6930
RaceUniversities of Jol Nar 0.095082 0.902391 0.105 0.9164
RaceWinnu -1.292565 1.045882 -1.236 0.2205
RaceXxcha Kingdom 0.691770 0.894010 0.774 0.4416
RaceYssaril Tribes 0.788482 0.973290 0.810 0.4205
Strategy.CardImperial II -0.766732 0.533783 -1.436 0.1552
Strategy.CardIndustry -7.029690 0.514413 -13.665 ≺2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.431 on 73 degrees of freedom
(1 observation deleted due to missingness)
Multiple R-squared: 0.8263, Adjusted R-squared: 0.7431
F-statistic: 9.924 on 35 and 73 DF, p-value: ≺ 2.2e-16


Wow! You were right. This is a far better statistical model. The R^2 is 83%, meaning that this model explains 83% of the differences in scoring. Less luck than I thought (other than race you receive).

My previous comments about the game being half luck were hasty and incorrect. This model shows that the game score is 83% explained by player skill, race chosen and the strategy card. Each of these factors are statistically significant.

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Shawn Garbett
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In further looking over the results, the analysis of variance says that Race is statistically significant, but not a single race stood had enough variance to show it was different. I.e., one could not trust the race rankings from this model, but race is having an effect. The fluctuations in final score on race are around +/- a point. The Brotherhood of Yin is top in this model, but Federation of Sol still comes in a close second.

With enough data, one could start handicapping based on race. I would do something like this:

Brotherhood of Yin and Federation of Sol, start with -1 VP.

Winnu starts with +1 VP.

However, it would take more data to make this a convincing handicapping scheme.
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Christopher Halbower
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CyberGarp wrote:
In further looking over the results, the analysis of variance says that Race is statistically significant, but not a single race stood had enough variance to show it was different. I.e., one could not trust the race rankings from this model, but race is having an effect. The fluctuations in final score on race are around +/- a point. The Brotherhood of Yin is top in this model, but Federation of Sol still comes in a close second.

With enough data, one could start handicapping based on race. I would do something like this:

Brotherhood of Yin and Federation of Sol, start with -1 VP.

Winnu starts with +1 VP.

However, it would take more data to make this a convincing handicapping scheme.


Awesome work, Shawn. Thanks a bunch. We are going to play again around Christmas time. If you ever come to Michigan, you should play with us.
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Alwin Derijck
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Keep those statistics coming.

Really interesting to check out how it progresses over time with more data points.

cheers,
Alwin
 
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Jon Horne
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Can we Nekro this thread, Chris? I wanna see my name in lights.
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Christopher Halbower
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Write a session report. I'll give the leaderboard data to CyberGarp. I'm sure he would break it down.
 
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Jon Horne
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halbower wrote:
Write a session report. I'll give the leaderboard data to CyberGarp. I'm sure he would break it down.

Ruthless! Very well, if you're going to the trouble to collect the data, I guess the least I can do is give you copy for the blog.
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Christopher Halbower
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Don't forget to report about all the Space Dokken that you did

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