The main goal behind this is to check whether White has an advantage in Chess. We will use some of the concepts learnt in IPS to test and estimate this effect.
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dat %>%mutate(white_win =ifelse(winner =="white", 1, 0)) %>%ggplot(aes(time_class, white_win)) +stat_summary(fun = mean, geom ="point") +stat_summary(fun.data = mean_cl_boot,geom ="errorbar",width =0.2) +theme(legend.position ="top") +labs(x ="", y ="Observed Probabilty of White Wins") +ggtitle("Proportions of White Wins Across Time Classes")
Methodology
We will fit 3 models of varying complexity and select the one that results in the best predictions.
First, we need to change the data format to allow us to estimate the white advantage. Basically, we want to see how much does the probability of success of player changes if he plays white instead of black.
p1_winner p1_white log_odds average_ratings time_class
0:31756 0:31813 Min. :-10.724290 Min. : 111.0 bullet:21727
1:31724 1:31667 1st Qu.: -0.224502 1st Qu.: 983.4 blitz :27665
Median : 0.000000 Median :1252.0 rapid :12256
Mean : 0.002473 Mean :1248.6 daily : 1832
3rd Qu.: 0.224502 3rd Qu.:1521.5
Max. : 11.789236 Max. :2682.5
We will fit the model of increasing complexity on the above predictors. Interaction terms between p1_white and the other variables to see how the white advantage across skill, game, and player differences.
use K-Fold Cross Validation to determine the best model and analyse and visualize those results.
Models
Hi, we are pretty much only using logistic regression models.
That means we are modeling the log odds of player 1 winning:
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dat %>%ggplot(aes(white_rating, black_rating)) +geom_point()
dat %>%sample_n(1000) %>%mutate(average_rating = (white_rating + black_rating) *0.5) %>%ggplot(aes(white_rating, black_rating)) +geom_point(alpha =0.5) +labs(x ="White Player Elo Rating",y ="Black Player Elo Rating",title ="Black vs White Ratings",subtitle ="Most People Play Against Similarly Rated" ) +geom_smooth(method ="lm", se =TRUE, color ="firebrick", linewidth =2)
`geom_smooth()` using formula = 'y ~ x'
dat %>%mutate(white_win =ifelse(winner =="white", 1, 0)) %>%ggplot(aes(time_class, white_win)) +stat_summary(fun = mean, geom ="point") +stat_summary(fun.data = mean_cl_boot,geom ="errorbar",width =0.2) +theme(legend.position ="top") +labs(x ="", y ="Observed Probabilty of White Wins") +ggtitle("Proportions of White Wins", subtitle ="Sample Average and Confidence Interval ")
dat %>%pivot_longer(cols =ends_with("rating"),names_to ="player",values_to ="rating" ) %>%ggplot(aes(rating, time_class, fill = player)) +geom_violin() +scale_fill_manual(values =c("#333", "#fff")) +coord_flip() +labs(x ="Elo Rating", title ="Distribution of Ratings") +theme(axis.title.x =element_blank())
plot_models(mods) +scale_fill_discrete(name ="Model", labels =c("1", "2", "3"))+ggtitle("Estimates and CI across 3 Models") + viridis::scale_color_viridis(discrete = T) +theme(legend.position ="top", legend.title =element_blank())
Scale for colour is already present.
Adding another scale for colour, which will replace the existing scale.
