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Twilight Imperium (Third Edition)» Forums » Sessions

Subject: Preparation for the GenCon Tourney yields valuable statistical data rss

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Christopher Halbower
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I'll send it out tomorrow when I'm in the office.
 
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Christopher Halbower
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Wow! It's been a month since I promised this. Of course, we did play two games since then (one was the Scenario).

The following is from
Shawn Garbett
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who is always available to lend his statistical wizardry. This is his analysis and his words...


Quote:
Not much changed from previous run. However, the effects of race are diminishing and player skill is dominating the results (which is what people want out of a game usually).

Notably the Yin aren't that bad, but Ghosts of Creuss is really sucking eggs.


> summary(model)

Call:
lm(formula = Raw.Score - Deviation.from.winning ~ Player + Race +
Strategy.Card, data = data)

Residuals:
Min 1Q Median 3Q Max
-12.766 -1.991 0.000 2.222 6.609

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.09597 2.64753 1.925 0.05596 .
PlayerBen Burkholder 0.36583 2.61145 0.140 0.88876
PlayerBill Haynes -7.23257 4.26499 -1.696 0.09180 .
PlayerBruce Bullion -1.00187 4.26737 -0.235 0.81467
PlayerBubba Bartels -11.97953 4.20531 -2.849 0.00495 **
PlayerCasey Bousho -11.42051 4.08320 -2.797 0.00577 **
PlayerCharles Fletcher -6.14896 3.42073 -1.798 0.07406 .
PlayerChris Halbower -0.79365 2.49028 -0.319 0.75035
PlayerDan Shanty -3.99256 4.19939 -0.951 0.34311
PlayerDavid Mitchell -2.20654 3.35941 -0.657 0.51220
PlayerDugas -1.57949 4.08320 -0.387 0.69938
PlayerDusty Shunta 0.93067 2.50988 0.371 0.71126
PlayerJake Iams -5.57062 3.17981 -1.752 0.08164 .
PlayerJeremy Durga -0.31537 4.20827 -0.075 0.94035
PlayerJeremy Scott Pyne 0.35191 3.44349 0.102 0.91873
PlayerJill Veldhuis -2.92782 2.93528 -0.997 0.31999
PlayerJoe Morse 0.72650 3.42613 0.212 0.83233
PlayerJon Horne -0.02962 2.57122 -0.012 0.99082
PlayerJoshua Hannebohn -5.39162 4.28738 -1.258 0.21032
PlayerKelly -8.46233 4.16825 -2.030 0.04393 *
PlayerKevin Raleigh -1.71940 2.51637 -0.683 0.49538
PlayerLauren Calkin 2.10327 4.25404 0.494 0.62166
PlayerMatt Bigham -4.54348 2.97219 -1.529 0.12825
PlayerMatt Spencer 0.57252 2.51911 0.227 0.82049
PlayerMongo Closz -0.71107 2.52720 -0.281 0.77878
PlayerNick Sima -1.97917 2.62469 -0.754 0.45188
PlayerProfessor Mike -6.70830 3.15588 -2.126 0.03501 *
PlayerRocky Thompson -0.58993 2.64705 -0.223 0.82391
PlayerSteve Wilson -1.39162 4.28738 -0.325 0.74590
PlayerZack Anderson -3.01311 3.08943 -0.975 0.33083
RaceBarony of Letnev -1.62156 1.54243 -1.051 0.29465
RaceBrotherhood of Yin -0.78035 1.57678 -0.495 0.62132
RaceClan of Saar -0.56498 1.42076 -0.398 0.69139
RaceEmbers of Muatt -0.51649 1.44347 -0.358 0.72094
RaceEmirates of Hacan -1.11645 1.44959 -0.770 0.44229
RaceFederation of Sol -0.10342 1.43905 -0.072 0.94280
RaceGhosts of Creuss -3.11055 1.49450 -2.081 0.03894 *
RaceL1Z1X Mindnet -0.69651 1.36162 -0.512 0.60966
RaceMentak Coalition 0.47561 1.42060 0.335 0.73820
RaceNaalu Collective 1.36636 1.32783 1.029 0.30497
RaceNekro Virus -1.01130 1.42766 -0.708 0.47971
RaceSardakk N'orr -0.75099 1.43157 -0.525 0.60057
RaceUniversities of Jol Nar 1.32454 1.45462 0.911 0.36384
RaceWinnu -1.78061 1.44422 -1.233 0.21935
RaceXxcha Kingdom -0.26038 1.38480 -0.188 0.85108
RaceYssaril Tribes 1.32275 1.52221 0.869 0.38612
Strategy.CardImperial II -0.08280 0.60283 -0.137 0.89092
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.285 on 166 degrees of freedom
(21 observations deleted due to missingness)
Multiple R-squared: 0.3822, Adjusted R-squared: 0.211
F-statistic: 2.233 on 46 and 166 DF, p-value: 0.0001163

> summary(aov(model))
Df Sum Sq Mean Sq F value Pr(>F)
Player 29 871.3 30.043 2.784 2.29e-05 ***
Race 16 236.8 14.797 1.371 0.162
Strategy.Card 1 0.2 0.204 0.019 0.891
Residuals 166 1791.3 10.791
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
21 observations deleted due to missingness
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Christopher Halbower
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Our group cannot seem to win with the Brotherhood of Yin or the Ghosts of Creuss. I think this is largely due to our group-think and slightly due to racial inequities.

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Shawn Garbett
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I posted on this in another thread. It's bad statistical practice to keep running the same model as you continue to collect data. The p-values are all over optimistic in when you do this. However, we're just looking at games and it's not a clinical trial or anything, so we'll run with it.

That said, this is the 3rd time the model is run. Each run has shown less effect for race, to the point now that Ghosts of Creuss is the only one with issues in Halbower's group. The effect of player skill has increased over time. One can conjecture that the more a group plays TI3 the less race matters and the more that skill is important. The big debates about which races are good or bad, in this group mostly boil down to how hard a race is to learn to play well and how much one enjoys playing them--at least in Halbower's group.

P.S., can you put the above model post inside a "bracket-c". Just edit, highlight and click the C button on the upper right of the editor.
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Starkiller
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Thanks so much!
This is fascinating....but I only understand it so much.

I don't suppose we could get a couple graphs on how often the races have won/lost, etc?


 
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Christopher Halbower
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Yes I can.
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Shawn Garbett
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akinfantryman wrote:
Thanks so much!
This is fascinating....but I only understand it so much.


Hopefully I can help a bit with more explanation. The essential viewpoint of statistics is estimating an effect. There are two parts to that, the actual measurement which is commonly reported in the press--but this is terrible as it lacks the precision. When I measure something how big are the division on my ruler? If my ruler is marked in meters and I'm measuring something that I want to compare with centimeter resolution then it's not a useful measure. Random variance, e.g.. dice rolls, card flops, all introduce random noise around some desired measure. Statistics determines how much one can measure in the presence of that noise. The model denotes what we want to measure.


> summary(model)
Call:
lm(formula = Raw.Score - Deviation.from.winning ~ Player + Race +
Strategy.Card, data = data)


This says, how much is the raw score with the deviation from the winning score in the game predicted by the player, the race, and the strategy card?
ANOVA looks directly at the question do any of these have an effect at all without getting into specifics.


> summary(aov(model))
Df Sum Sq Mean Sq F value Pr(>F)
Player 29 871.3 30.043 2.784 2.29e-05 ***
Race 16 236.8 14.797 1.371 0.162
Strategy.Card 1 0.2 0.204 0.019 0.891
Residuals 166 1791.3 10.791
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
21 observations deleted due to missingness


The ANOVA model says that the only measurable effect in this data is the Player skill, p=2.293-05. This mysterious p is probability that the effect observed occurred by random chance. Statistics looks at the noise in the data and considers if this noise happened in every pattern possible at that level, what is the chance the effect the observation was just noise? I.e., the measurement capability of the ruler in terms of probability. The standard interpretation here is that the effect of race cannot be discerned from this data. Not that it doesn't have an effect--just that we can't measure it without a lot more data.

I mentioned the model has been run twice before. All those random considerations to compute the p-value assumed I didn't do that, so all these numbers are actually a bit fuzzier. Abusing the statistics a bit and taking these runs at face value the effect of race has been declining in Halbower's group and the effect of player skill has increased.

This big pile of numbers is the breakdown in a more detailed model. The intercept is just the average overall different when accounting for all the other factors. ANOVA told us that the effect of race isn't significant, so even the problems with the Ghosts of Creuss (the Pr(>|t|) column is the p-value here) shown in this model can't be trusted. Note the asterisks on the right draw your eye to the discernable measures. Halbower can rank order his players by the estimate, but realize there's still some randomness to it. Looks like Lauren Calkin is the one to beat. The significant estimates are all for really outstandingly poor performance which leads to a conjecture that the effect of skill noticed here is splitting the players into two groups. This is where those plots you requested are really needed.



Residuals:
Min 1Q Median 3Q Max
-12.766 -1.991 0.000 2.222 6.609

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.09597 2.64753 1.925 0.05596 .
PlayerBen Burkholder 0.36583 2.61145 0.140 0.88876
PlayerBill Haynes -7.23257 4.26499 -1.696 0.09180 .
PlayerBruce Bullion -1.00187 4.26737 -0.235 0.81467
PlayerBubba Bartels -11.97953 4.20531 -2.849 0.00495 **
PlayerCasey Bousho -11.42051 4.08320 -2.797 0.00577 **
PlayerCharles Fletcher -6.14896 3.42073 -1.798 0.07406 .
PlayerChris Halbower -0.79365 2.49028 -0.319 0.75035
PlayerDan Shanty -3.99256 4.19939 -0.951 0.34311
PlayerDavid Mitchell -2.20654 3.35941 -0.657 0.51220
PlayerDugas -1.57949 4.08320 -0.387 0.69938
PlayerDusty Shunta 0.93067 2.50988 0.371 0.71126
PlayerJake Iams -5.57062 3.17981 -1.752 0.08164 .
PlayerJeremy Durga -0.31537 4.20827 -0.075 0.94035
PlayerJeremy Scott Pyne 0.35191 3.44349 0.102 0.91873
PlayerJill Veldhuis -2.92782 2.93528 -0.997 0.31999
PlayerJoe Morse 0.72650 3.42613 0.212 0.83233
PlayerJon Horne -0.02962 2.57122 -0.012 0.99082
PlayerJoshua Hannebohn -5.39162 4.28738 -1.258 0.21032
PlayerKelly -8.46233 4.16825 -2.030 0.04393 *
PlayerKevin Raleigh -1.71940 2.51637 -0.683 0.49538
PlayerLauren Calkin 2.10327 4.25404 0.494 0.62166
PlayerMatt Bigham -4.54348 2.97219 -1.529 0.12825
PlayerMatt Spencer 0.57252 2.51911 0.227 0.82049
PlayerMongo Closz -0.71107 2.52720 -0.281 0.77878
PlayerNick Sima -1.97917 2.62469 -0.754 0.45188
PlayerProfessor Mike -6.70830 3.15588 -2.126 0.03501 *
PlayerRocky Thompson -0.58993 2.64705 -0.223 0.82391
PlayerSteve Wilson -1.39162 4.28738 -0.325 0.74590
PlayerZack Anderson -3.01311 3.08943 -0.975 0.33083
RaceBarony of Letnev -1.62156 1.54243 -1.051 0.29465
RaceBrotherhood of Yin -0.78035 1.57678 -0.495 0.62132
RaceClan of Saar -0.56498 1.42076 -0.398 0.69139
RaceEmbers of Muatt -0.51649 1.44347 -0.358 0.72094
RaceEmirates of Hacan -1.11645 1.44959 -0.770 0.44229
RaceFederation of Sol -0.10342 1.43905 -0.072 0.94280
RaceGhosts of Creuss -3.11055 1.49450 -2.081 0.03894 *
RaceL1Z1X Mindnet -0.69651 1.36162 -0.512 0.60966
RaceMentak Coalition 0.47561 1.42060 0.335 0.73820
RaceNaalu Collective 1.36636 1.32783 1.029 0.30497
RaceNekro Virus -1.01130 1.42766 -0.708 0.47971
RaceSardakk N'orr -0.75099 1.43157 -0.525 0.60057
RaceUniversities of Jol Nar 1.32454 1.45462 0.911 0.36384
RaceWinnu -1.78061 1.44422 -1.233 0.21935
RaceXxcha Kingdom -0.26038 1.38480 -0.188 0.85108
RaceYssaril Tribes 1.32275 1.52221 0.869 0.38612
Strategy.CardImperial II -0.08280 0.60283 -0.137 0.89092
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.285 on 166 degrees of freedom
(21 observations deleted due to missingness)
Multiple R-squared: 0.3822, Adjusted R-squared: 0.211
F-statistic: 2.233 on 46 and 166 DF, p-value: 0.0001163


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Alwin Derijck
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Absolutely love it!

And yes, a graph would be nice to show to our TI3 group. Especially to those who think that some races are better then others

Thanks a lot an keep the data coming.

I am now down to playing TI3 once a year or so, so by the time we have any statistically reliable data we will all be playing TI3 in a geriatric facility.
 
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