Scrabble

Overview

Scrabble scores vs. games played

How do our scrabble scores change as we play more games?

## 
## Call:
## lm(formula = Score ~ Game, data = subset(dat, Player == "Lizzy"))
## 
## Coefficients:
## (Intercept)         Game  
##       243.5          2.4

##             2.5 % 97.5 %
## (Intercept) 199.5  287.6
## Game         -2.8    7.6

## 
## Call:
## lm(formula = Score ~ Game, data = subset(dat, Player == "Jesse"))
## 
## Coefficients:
## (Intercept)         Game  
##       251.3          1.4

##             2.5 % 97.5 %
## (Intercept) 212.0    290
## Game         -3.2      6

With every game, Lizzy’s score is improving by about 2.4 points.

With every game, Jesse’s score is improving by about 1.4 points

We are 95% confident that Lizzy’s score is improving between -2.77 and 7.58 points per game.

We are 95% confident that Lizzy’s score is improving between -3.2 and 6.01 points per game.

## Analysis of Variance Table
## 
## Response: Score
##           Df Sum Sq Mean Sq F value Pr(>F)
## Player     1      0       0       0   0.99
## Residuals 26  29382    1130

## Analysis of Variance Table
## 
## Response: Score
##           Df Sum Sq Mean Sq F value Pr(>F)
## Game       1   1315    1315    1.02   0.33
## Residuals 12  15416    1285

## Analysis of Variance Table
## 
## Response: Score
##           Df Sum Sq Mean Sq F value Pr(>F)
## Game       1    449     449    0.44   0.52
## Residuals 12  12202    1017

We cannot reject the null hypothesis that Lizzy and Jesse are the same in their growth as scrabble players

We cannot reject the null hypothesis that Lizzy score does not change as she plays more games.

We cannot reject the null hypothesis that Jesse’s score does not change as he plays more games.

## [1] 0.0018

## [1] -0.045

The linear models also have adjusted r squared values of -0.09 for Lizzy and 0.08 for Jesse. As a result, we have very low confidence in these models as Lizzy’s model explains basically none of the variation and Jesse’s model explains only about 8% of the variation.

First turn advantage?

Does getting the first turn help predict whether a player wins?

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  dat$FirstTurn and dat$Win
## X-squared = 1, df = 1, p-value = 0.3

There is no statistically significant association between getting the first turn and winning the game, assuming I understand how the Chisquare test works