**Amateur Statistician Moment**

For the sake of argument, I took a sample of 179 games of classic that I'd previously collected from PlayDip. Not a huge sample, but enough to run a primary experiment. These games were full-press, no variants, et cetera.

Keep in mind that all rated games on PlayDip currently use Draw-Sized-Scoring.

I used the SC counts at end-of-game to come up with these variables:

- Did the game end in a solo?
- What was the board-topper's Sum-of-Squares score for the game?
- How many powers were eliminated by end of game?
- What was a surviving player's DSS score assuming the game ended in DIAS?

I fed these values into R and produced a few different logistic regressions.

In a logistic regression, the dependent variable is assumed to be a binary or boolean value. A game that actually ended in a solo has a Solo value of 1, and a game that actually ended in a draw has a Solo value of 0.

I found the following:

- There was no evidence of a correlation between hypothetical DSS score and the game ending in a solo. The coefficient for this was actually negative, but the p-value was absurdly high.
- Likewise, there was no evidence of a correlation between powers eliminated and the game ending in a solo. This is effectively the same test as what was done for (A), just with the independent variable scaling linearly.
- There was significant evidence of positive correlation between the hypothetical SOS score and the game ending in a solo. I tried two different regressions for this value, and the p-values were 7.23e-11 and 0.00692 for regressions with nonzero or zero intercepts, respectively.

*very*good measure for closeness-to-the-solo, while draw size was not, even in an environment

*where draw size is the only system used*.

This doesn't necessarily mean that Sum-of-Squares is a perfect scoring system, but it does provide evidence for some of what has already been discussed in this thread.

Code: Select all

```
> head(games,10)
Solo Elims GPI SOS.p.GPI Delta.SC SOSR Delta.SOSR DSS.Score
1 0 4 131.33 1.29 1 0.429 0.063 0.3333333
2 1 4 150.67 2.15 10 0.717 0.575 0.3333333
3 0 2 61.60 1.96 0 0.393 0.000 0.2000000
4 1 3 115.00 3.14 12 0.785 0.678 0.2500000
5 0 2 62.00 1.61 0 0.323 0.000 0.2000000
6 1 2 84.00 4.30 14 0.860 0.800 0.2000000
7 0 1 38.33 2.61 3 0.435 0.222 0.1666667
8 0 4 136.67 1.65 4 0.549 0.254 0.3333333
9 1 2 91.60 4.37 14 0.873 0.795 0.2000000
10 0 4 132.67 1.48 3 0.492 0.188 0.3333333
> games.dss.glm <- glm(Solo ~ DSS.Score, data = games, family = binomial)
> summary(games.dss.glm)
Call:
glm(formula = Solo ~ DSS.Score, family = binomial, data = games)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.202 -1.190 1.156 1.165 1.192
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.09439 0.54201 0.174 0.862
DSS.Score -0.25661 1.85836 -0.138 0.890
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 246.74 on 177 degrees of freedom
Residual deviance: 246.72 on 176 degrees of freedom
AIC: 250.72
Number of Fisher Scoring iterations: 3
> games.sos.glm <- glm(Solo ~ SOSR, data = games, family = binomial)
> summary(games.sos.glm)
Call:
glm(formula = Solo ~ SOSR, family = binomial, data = games)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.3274 -0.2509 0.0368 0.3240 1.9783
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -16.399 2.517 -6.516 7.23e-11 ***
SOSR 26.108 3.931 6.641 3.11e-11 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 246.74 on 177 degrees of freedom
Residual deviance: 82.99 on 176 degrees of freedom
AIC: 86.99
Number of Fisher Scoring iterations: 6
> games.elim.glm <- glm(Solo ~ Elims, data = games, family = binomial)
> summary(games.elim.glm)
Call:
glm(formula = Solo ~ Elims, family = binomial, data = games)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.300 -1.179 1.060 1.176 1.297
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.4173 0.4613 -0.905 0.366
Elims 0.1400 0.1388 1.009 0.313
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 246.74 on 177 degrees of freedom
Residual deviance: 245.71 on 176 degrees of freedom
AIC: 249.71
Number of Fisher Scoring iterations: 3
> games.sos.zero.glm <- glm(Solo ~ SOSR + 0, data = games, family = binomial)
> summary(games.sos.zero.glm)
Call:
glm(formula = Solo ~ SOSR + 0, family = binomial, data = games)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.4166 -1.3173 0.9383 0.9809 1.0273
Coefficients:
Estimate Std. Error z value Pr(>|z|)
SOSR 0.6507 0.2409 2.701 0.00692 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 246.76 on 178 degrees of freedom
Residual deviance: 239.28 on 177 degrees of freedom
AIC: 241.28
Number of Fisher Scoring iterations: 4
```