Chess.com: Exploratory Data Analysis

Manipulating & Visualizing chess.com Game Data

Author

Reece Iriye

Introduction

Chess.com is a website where players can match-make against one another to play games of chess. Players are typically matched against one another based on their skill level, and the website’s welcoming interface has caused it to boost in popularity in recent years. Ordinary people are making the decision to learn chess because of chess.com’s convenience, and it’s even become popular to watch high-rated players matchmake against random stranger similarly ranked to them on streaming sites like Twitch.

Because of the newfound hype around chess.com, I have decided to make a analyze a dataset of high-rated players’ games and how well they performed. Throughout my analysis, I focuses on the performance of the highest rated players of the dataset, and I also measured how players performed overall depending on whether they were playing as white or black.

Data Overview

Issues with the Data

The original dataset converted win indicators from 1-0 to a date-time variable Jan-00, so I cleaned those elements of the dataset by converting wins back to 1-0. Additionally, for the specific player of interest in each row for the game data, I added a column to indicate the outcome of the game from the perspective of the player of interest. Below is a table of the players in the dataset who won the most amount of games.

Player Results

While the original dataset is intuitive on its own with the stories that the columns already have the potential to tell, I believe a Result column will be essential displaying the outcome of the game from the perspective of the player of interest.

With this information, I compiled a list of the top 10 players with the most wins in our dataset.

Name	Win Count
Hikaru Nakamura	234
Baadur Jobava	145
Christopher Woojin Yoo	136
Arjun Erigaisi	131
Alexey Vasilyevich Sarana	118
Denis Lazavik	115
Sergei Zhigalko	115
Nodirbek Abdusattorov	112
Levon Aronian	111
Wesley So	111

Hikaru Nakamura outperforms all other players by a longshot with 234 wins, outperforming the 2nd best performer in our dataset (Baadur Jodava) who has 145 wins. Nakamura could likely have this win count, because he is frequently active on chess.com.

I believe we should now explore chess.com’s internal rating system, so that we can understand how the website ranks players based on metrics that they believe evaluate them to the best of their ability. Observing whether or not Nakamura has one of the higher ratings may help us determine whether or not he may be one of the best players in our dataset.

ELO Ratings

Each player is assigned an “ELO Rating”. In short, an ELO rating is meant to estimate a player’s skill-level, and the higher a player’s rating is, the better they are estimated to be at playing chess. Chess.com uses multiple variables to calculate ELO, but to explain the ranking system simply, a player’s ELO increases as players win and draw other players who are ranked higher than them in most cases, and it decreases otherwise. More information about Chess ELO and how chess.com specifically calculates player ELO for giving players a rating can be found here.

Here is a distribution of each individual player’s average rating within the dataset.

It shows that most players’ average ratings were at least above 2000, meaning that most players highlighted are at least at the Master level or higher. It appears as if around half of the players have a rating of 2400 or higher, which shows that our dataset consists of games primarily from GrandMasters. Players with these ELO’s are exceptional at playing chess, so it may be interesting to observe whether or not the ELO system in chess.com is accurate in determining strength for players at this skill level and above.

Game Outcomes

Within our data, a total of 10336 unique matches have been played, 1920 unique players are included in the whole dataset, and 2964 games have resulted in draws. Here is a barplot indicating the results summary in our dataset.

This barplot shows that most games resulted in White winning the game. There is a chance that our dataset may be restricted because all players rated as Masters and above may not be included. Because of that, it may not necessarily tell a full story of high-rated raters, but from what I am able to see so far, I am making an assumption that because of the small inherent advantage that players have when making the first move in the game as White, playing as White may give high-rated players a better chance of winning the game than playing as Black. This claim makes sense in some capacity, especially when understanding that high-ranking players rarely play huge blunders (major mistakes) when they play games.

Results

Player Summary

To understand factors like Player ELO and player outcomes, it is important to observe overall results from the perspective of players themselves. More specifically, I believe that creating a player summary table and observing how top players performed on an overall scale can help us understand this data on a more individual level. Below is a summary table from the player perspective, in descending order of Total Wins.

Name	Games Played	Average Moves per Game	Total Wins	Win Percentage (%)	Average ELO Score	Average Opponent ELO Score
Hikaru Nakamura	408	48.0	234	57.35	2853	2650
Baadur Jobava	253	45.0	145	57.31	2697	2553
Christopher Woojin Yoo	253	46.6	136	53.75	2152	2505
Arjun Erigaisi	284	47.5	131	46.13	2573	2580
Alexey Vasilyevich Sarana	208	50.5	118	56.73	2659	2484
Denis Lazavik	214	51.7	115	53.74	2437	2466
Sergei Zhigalko	181	45.4	115	63.54	2663	2422
Nodirbek Abdusattorov	196	49.8	112	57.14	2631	2482
Levon Aronian	318	49.7	111	34.91	2768	2709
Wesley So	274	44.9	111	40.51	2781	2745
Sanan Sjugirov	197	45.3	109	55.33	2573	2515
Aleksandar Indjic	184	46.3	108	58.70	2631	2469
Dmitry Vladimirovich Andreikin	157	42.7	108	68.79	2762	2508
Andrew Tang	185	45.5	105	56.76	2586	2457
Parham Maghsoodloo	197	46.6	105	53.30	2610	2529
Magnus Carlsen	263	48.7	103	39.16	2865	2742
Vladislav Artemiev	235	48.5	101	42.98	2745	2674
Volodar Murzin	194	46.3	96	49.48	2509	2417
Awonder Liang	194	47.2	95	48.97	2399	2479
Vincent Keymer	203	50.6	94	46.31	2540	2464

In this table, we can see that Hikaru Makamura won the most games in part because he played more games than the rest of the top players in the dataset. Nevertheless, he still has a pretty high win percentage, which leads us to believe that he consistently performs extremely well against high-ranking players. His average opponent’s rating is less than his average rating, but the average rating of players he competes against is still extremely high at 2650.

Observing the players with the top 5 wins in our dataset, let’s use a Violin Plot to visualize exactly what rated players our top competitors tend to play against.

The vast majority of players these people are ranked between 2400 - 2900. We can see that Nakamura is playing the highest-rated competitors on average than the rest of these players. Griscuk is playing against opponents of similary ranked ELO’s to Nakamura, and the other players are competing against players with a little bit lower ratings—still extremely high and competitive nevertheless.

Individual Highest ELO

Observing exactly who had the highest ELO is important as well in determining whether or not the ELO system accurately ranks players at the GrandMaster level and above. Here is a table of players’ highest single-moment ELO’s.

Game ID	Player with Max ELO	Maximum Player ELO
16076986	Hikaru Nakamura	3223
16117900	Alexander Grischuk	3075
16165329	David Paravyan	3029
16130874	Dmitry Vladimirovich Andreikin	3027
16076010	David Wei Liang Howell	3012
16130748	Nodirbek Abdusattorov	3004
16093258	Samuel Sevian	3000
16062436	Grigoriy Alekseyevich Oparin	2992
16124234	Sanan Sjugirov	2988
16123090	Andrew Tang	2986
16124424	Anton Korobov	2984
16164551	Nodirbek Yakubboev	2972
16130768	Baadur Jobava	2969
16123062	Sergei Zhigalko	2968
16131586	Christopher Woojin Yoo	2968

Nakamura once again makes it to the top of our dataset. He had a maximum high rating of 3223, showcasing that it may be accurate to justify win count as a measure of competitiveness and skill in playing chess on chess.com.

Lowest Move Count

Chess games typically have around <a href-“https://www.alexcrompton.com/blog/time-thoughts-chess”>40 moves in the game, however some games last much longer or much shorter. Below is a summary tale of the games with the lowest number of moves in a game.

Game ID	Date	Move Count
16064010	2021.06.21	5
16118788	2021.09.18	5
16153863	2021.11.08	5
16129536	2021.10.02	6
16152763	2021.11.08	6
16025283	Mon Mar 15 2021	6
16044044	Sun May 23 2021	6
16093332	2021.08.11	7
16160339	2021.11.16	7
16162079	2021.12.04	7
15793131	Sun Feb 14 2021	7
16050844	Sun May 30 2021	7
16046924	Thu May 27 2021	7
16063154	2021.06.19	8
16072304	2021.07.06	8

Here, we can see clearly that some of these games with grandmasters in our dataset lasted exceedingly short. Some opening traps exist in chess where players checkmate other players within the first couple of moves, however that is not likely the case here. In chess.com, players have the option to resign a game at all points, so these games may have ended quickly because one of these players had to leave. We can see, however, that there are not many of these games, showcasing that players with high ratings are reluctant to leave games early because it could negatively impact their ELO, thus impacting their reputation.

Biggest Upsets

It is pretty rare for players to defeat players exceedingly higher rated than them, because ELO is an indicator of skill. However, it still happens at some points. Here is a table of the biggest upsets that have occurred on chess.com for these grandmasters.

Game ID	Date	Underdog	Player ELO	Opponent ELO	ELO Difference
15790435	Sat Jan 09 2021	Sanan Sjugirov	26	2649	2623
15791483	Sat Jan 09 2021	Sanan Sjugirov	26	2649	2623
15791957	Thu Jan 07 2021	Julien Song	23	2619	2596
15791981	Wed Jan 06 2021	Max Warmerdam	25	2552	2527
15792057	Wed Jan 06 2021	Max Warmerdam	25	2386	2361
15791955	Fri Jan 15 2021	Atulya Shetty	24	2357	2333
16137734	2021.10.15	Leon Luke Mendonca	1391	2542	1151
16060066	2021.06.10	Leon Luke Mendonca	1391	2497	1106
16127070	2021.09.25	L M S T De Silva	1621	2581	960
16126672	2021.09.25	Enkh-Amgalan Amgalantengis	1716	2662	946

For a player to have a double-digit ranking, they have to be pretty terrible at the game, especially considering that each player starts at a rating of 800 immediately upon creating an account. Players with highly differentiating ELO’s aren’t matched with each other either, meaning that these players willingly chose to play each other, or they faced each other in a chess.com tournament. I believe that the double-digit rating players defeating GrandMasters was just an experiment between these two players, and therefore, they are outliers. These games may have either been accidentally played, or they were coordinated as a potential experiment between the two players. Either way, these games should not be factored into our overall analysis of ELO’s impact on game outcomes, as the games likely did not occur under normal circumstances.

Game Outcome Classification Based on Ratings

I think we have enough data to observe how the ratings of White and Black directly impact the chances of whether or not they will win. I plotted White ELO versus Black ELO to determine exactly how ratings as White and Black effect who may win and who may lose. I excluded major outliers.

Based on our data, we can see that ELO is a pretty good measure of whether or not White or Black will win. We can see that our plot is overwhelmingly green, because white just wins more often. However, higher ranking Black players do tend to defeat lower-rated White players. The opposite is true as well. There are a lot of drawing games and games where White wins in points on the scatterplot where White and Black are similarly ranked.

Conclusion

I can conclude that ELO is a decently good measure of skill for determining how good players are good. White, however, tends to defeat Black when high-rated players are playing against one another. There are clear limitations to this dataset. For example, we only have a subset of game data for players in these rating categories. Nevertheless, I do believe my conclusions are pretty solid.

--- title: " **Chess.com: Exploratory Data Analysis** " subtitle: "Manipulating & Visualizing chess.com Game Data" author: "Reece Iriye" format: html: link-citations: true toc: true embed-resources: true code-fold: false code-line-numbers: true code-summary: "SHOW ME THE CODE!" code-tools: true theme: solar editor: visual --- ```{r} #| echo: false #| message: false #| warning: false library(reshape2) library(tidyverse) library(ggplot2) library(plotly) library(DT) library(formattable) library(reactable) library(lubridate) library(patchwork) ``` ## **Introduction** ![](chess_image.png){width="600"} ```{r} #| echo: false #| message: false #| warning: false chess.data.raw <- read.csv("chess_data.csv") ``` Chess.com is a website where players can match-make against one another to play games of chess. Players are typically matched against one another based on their skill level, and the website's welcoming interface has caused it to boost in popularity in recent years. Ordinary people are making the decision to learn chess because of <a href="https://www.chess.com">chess.com</a>'s convenience, and it's even become popular to watch high-rated players matchmake against random stranger similarly ranked to them on streaming sites like Twitch. Because of the newfound hype around chess.com, I have decided to make a analyze a dataset of high-rated players' games and how well they performed. Throughout my analysis, I focuses on the performance of the highest rated players of the dataset, and I also measured how players performed overall depending on whether they were playing as white or black. ## **Data Overview** ### **Issues with the Data** The original dataset converted win indicators from `1-0` to a date-time variable `Jan-00`, so I cleaned those elements of the dataset by converting wins back to `1-0`. Additionally, for the specific player of interest in each row for the game data, I added a column to indicate the outcome of the game from the perspective of the player of interest. Below is a table of the players in the dataset who won the most amount of games. ### **Player Results** While the original dataset is intuitive on its own with the stories that the columns already have the potential to tell, I believe a `Result` column will be essential displaying the outcome of the game from the perspective of the player of interest. ```{r} #| echo: false #| message: false #| warning: false # Replace "Jan-00" with "1-0" chess.data.raw$Result[chess.data.raw$Result == "Jan-00"] <- "1-0" # Add column indicating if a player won or drew chess.data <- chess.data.raw %>% mutate(Outcome = if_else(Player == "WhitePlayerName", if_else(Result == "1-0", "Win", if_else(Result == "0-1", "Loss", "Draw")), if_else(Result == "1-0", "Loss", if_else(Result == "0-1", "Win", "Draw")))) # Report table of 10 players with most wins in the entire dataset most.wins <- chess.data %>% group_by(Name) %>% summarize("Win Count" = sum(if_else(Outcome == "Win", 1, 0))) %>% arrange(desc(.data$"Win Count")) most.wins.10 <- most.wins[1:10,] ``` With this information, I compiled a list of the top 10 players with the most wins in our dataset. ```{r} #| echo: false #| message: false #| warning: false # Output the players with the most wins formattable::formattable(most.wins.10, align = c("l","r"), list( "Win Count" = color_bar("cyan"))) ``` Hikaru Nakamura outperforms all other players by a longshot with 234 wins, outperforming the 2nd best performer in our dataset (Baadur Jodava) who has 145 wins. Nakamura could likely have this win count, because he is frequently active on chess.com. I believe we should now explore chess.com's internal rating system, so that we can understand how the website ranks players based on metrics that they believe evaluate them to the best of their ability. Observing whether or not Nakamura has one of the higher ratings may help us determine whether or not he may be one of the best players in our dataset. ### **ELO Ratings** Each player is assigned an "ELO Rating". In short, an ELO rating is meant to estimate a player's skill-level, and the higher a player's rating is, the better they are estimated to be at playing chess. Chess.com uses multiple variables to calculate ELO, but to explain the ranking system simply, a player's ELO increases as players win and draw other players who are ranked higher than them in most cases, and it decreases otherwise. More information about Chess ELO and how chess.com specifically calculates player ELO for giving players a rating can be found <a href="https://www.chess.com/terms/elo-rating-chess">here</a>. ```{r} #| echo: false #| message: false #| warning: false # Create Player & Opponent ELO Columns chess.data <- chess.data %>% mutate(PlayerElo = if_else(Player == "WhitePlayerName", WhiteElo, BlackElo)) %>% mutate(OpponentElo = if_else(Player == "BlackPlayerName", WhiteElo, BlackElo)) ``` Here is a distribution of each individual player's average rating within the dataset. ```{r} #| echo: false #| message: false #| warning: false # Player average ratings avg.ratings <- chess.data %>% group_by(Name) %>% summarize("Player Ratings" = mean(PlayerElo, na.rm = TRUE)) # Plot a histogram of ratings p1 <- ggplot(avg.ratings, aes(x = .data$"Player Ratings")) + geom_histogram(bins = 100, color = "black", fill = "#A161D9") + labs(title = "Distribution of Average Player Ratings", x = "Player Ratings", y = "# of Players") + theme_bw() ggplotly(p1) ``` It shows that most players' average ratings were at least above 2000, meaning that most players highlighted are at least at the Master level or higher. It appears as if around half of the players have a rating of 2400 or higher, which shows that our dataset consists of games primarily from GrandMasters. Players with these ELO's are exceptional at playing chess, so it may be interesting to observe whether or not the ELO system in chess.com is accurate in determining strength for players at this skill level and above. ### **Game Outcomes** ```{r} #| echo: false #| message: false #| warning: false # Determine number of unique matches unique.matches <- length(unique(chess.data$game_id)) # Determine number of unique players in the dataset unique.players <- length(unique(chess.data$Name)) # Total Draws chess.data.inivgame <- chess.data %>% distinct(game_id, .keep_all = TRUE) unique.draws <- chess.data.inivgame %>% group_by(Outcome) %>% summarize(draw.count = sum(if_else(Outcome == "Draw", 1, 0))) %>% pull(draw.count) unique.draws <- unique.draws[1] ``` Within our data, a total of `r unique.matches` unique matches have been played, `r unique.players` unique players are included in the whole dataset, and `r unique.draws` games have resulted in draws. Here is a barplot indicating the results summary in our dataset. ```{r} #| echo: false #| message: false #| warning: false p4 <- ggplot(chess.data.inivgame, aes(x=Result)) + geom_bar(color = "black", fill=c("0-1" = "red", "1-0" = "#15C825", "1/2-1/2" = "#EFEF22")) + labs(x = "Game Results", y = "Frequency", title = "Frequency of Wins, Draws, and Losses") + theme_bw() ggplotly(p4) ``` This barplot shows that most games resulted in White winning the game. There is a chance that our dataset may be restricted because all players rated as Masters and above may not be included. Because of that, it may not necessarily tell a full story of high-rated raters, but from what I am able to see so far, I am making an assumption that because of the small inherent advantage that players have when making the first move in the game as White, playing as White may give high-rated players a better chance of winning the game than playing as Black. This claim makes sense in some capacity, especially when understanding that high-ranking players rarely play huge blunders (major mistakes) when they play games. ## **Results** ### **Player Summary** To understand factors like Player ELO and player outcomes, it is important to observe overall results from the perspective of players themselves. More specifically, I believe that creating a player summary table and observing how top players performed on an overall scale can help us understand this data on a more individual level. Below is a summary table from the player perspective, in descending order of `Total Wins`. ```{r} #| echo: false #| message: false #| warning: false summary.table <- chess.data %>% group_by(Name) %>% summarize("Games Played" = n(), "Average Moves per Game" = round(sum(NMoves) / n(), 1), "Total Wins" = sum(if_else(Outcome == "Win", 1, 0)), "Win Percentage (%)" = round((sum(if_else(Outcome == "Win", 1, 0)) / n()) * 100, 2), "Average ELO Score" = round(mean(PlayerElo, na.rm = TRUE), 0), "Average Opponent ELO Score" = round(mean(OpponentElo, na.rm = TRUE), 0)) %>% arrange(desc(.data$"Total Wins")) %>% slice(1:20) # only get the top 20 players to display ``` ```{r} #| echo: false #| message: false #| warning: false # https://www.littlemissdata.com/blog/prettytables improvement_formatter1 <- formatter("span", style = x ~ style(font.weight = "bold", color = if_else(summary.table$"Average ELO Score" > summary.table$"Average Opponent ELO Score", "#47AA44", if_else(summary.table$"Average ELO Score" < summary.table$"Average Opponent ELO Score", "#FF4D4D", "black"))), x ~ icontext(if_else(summary.table$"Average ELO Score" > summary.table$"Average Opponent ELO Score", "arrow-up", "arrow-down"), x) ) improvement_formatter2 <- formatter("span", style = x ~ style(font.weight = "bold", color = if_else(summary.table$"Average ELO Score" < summary.table$"Average Opponent ELO Score", "#47AA44", if_else(summary.table$"Average ELO Score" > summary.table$"Average Opponent ELO Score", "#FF4D4D", "black"))), x ~ icontext(if_else(summary.table$"Average ELO Score" < summary.table$"Average Opponent ELO Score", "arrow-up", "arrow-down"), x) ) # Create formattable object formattable::formattable(summary.table, align = c("l", "c", "c", "c", "r", "c", "c"), list( "Games Played" = color_tile("#012A35", "#00ADFD"), "Win Percentage (%)" = color_bar("#FDFF9F"), "Average ELO Score" = improvement_formatter1, "Average Opponent ELO Score" = improvement_formatter2 )) ``` In this table, we can see that Hikaru Makamura won the most games in part because he played more games than the rest of the top players in the dataset. Nevertheless, he still has a pretty high win percentage, which leads us to believe that he consistently performs extremely well against high-ranking players. His average opponent's rating is less than his average rating, but the average rating of players he competes against is still extremely high at 2650. Observing the players with the top 5 wins in our dataset, let's use a Violin Plot to visualize exactly what rated players our top competitors tend to play against. ```{r} #| echo: false #| message: false #| warning: false # Box and whiskers plot of 5 top rated players with their top.players <- list("Hikaru Nakamura", "Alexander Grischuk", "David Paravyan", "Dmitry Vladimirovich Andreikin", "David Wei Liang Howell") # Data is already in long form top.data <- chess.data %>% filter(Name %in% top.players) %>% filter(OpponentElo > 1500) # Remove double-digit rating outlier p3 <- ggplot(top.data, aes(x=Name, y=OpponentElo, color=Outcome)) + geom_violin(color="black", fill="cyan") + geom_point(alpha = 0.2) + theme(legend.position = "top") + theme_bw() + labs(title="Opponent Ratings & Game Outcomes for Top-Rated Players") + scale_color_manual(values = c("Win" = "#15C825", "Draw" = "#EFEF22", "Loss" = "red")) ggplotly(p3) ``` The vast majority of players these people are ranked between 2400 - 2900. We can see that Nakamura is playing the highest-rated competitors on average than the rest of these players. Griscuk is playing against opponents of similary ranked ELO's to Nakamura, and the other players are competing against players with a little bit lower ratings---still extremely high and competitive nevertheless. ### **Individual Highest ELO** Observing exactly who had the highest ELO is important as well in determining whether or not the ELO system accurately ranks players at the GrandMaster level and above. Here is a table of players' highest single-moment ELO's. ```{r} #| echo: false #| message: false #| warning: false # Highest ELO score: max.Elo.index <- which.max(chess.data$PlayerElo) # Pull necessary information max.Elo.data <- chess.data %>% distinct(game_id, .keep_all = TRUE) %>% arrange(desc(PlayerElo)) %>% distinct(Name, .keep_all = TRUE) %>% slice(1:15) %>% select(PlayerElo, game_id, Name) %>% summarize("Game ID" = game_id, "Player with Max ELO" = Name, "Maximum Player ELO" = PlayerElo) # Change index row.names(max.Elo.data) <- NULL # Output table formattable(max.Elo.data, align = c("c", "c", "c"), list( "Maximum Player ELO" = color_tile("#A161D9", "#BB0AFA") )) ``` Nakamura once again makes it to the top of our dataset. He had a maximum high rating of 3223, showcasing that it may be accurate to justify win count as a measure of competitiveness and skill in playing chess on chess.com. ### **Lowest Move Count** Chess games typically have around \<a href-"https://www.alexcrompton.com/blog/time-thoughts-chess"\>40</a> moves in the game, however some games last much longer or much shorter. Below is a summary tale of the games with the lowest number of moves in a game. ```{r} #| echo: false #| message: false #| warning: false lowest.moves <- chess.data %>% distinct(game_id, .keep_all = TRUE) %>% arrange(NMoves) %>% slice(1:15) %>% summarize("Game ID" = game_id, "Date" = Date, "Move Count" = NMoves) # Output Table formattable(lowest.moves, align = c("c", "c", "r"), list( "Move Count" = color_bar("#9AEDEB") ) ) ``` Here, we can see clearly that some of these games with grandmasters in our dataset lasted exceedingly short. Some opening traps exist in chess where players checkmate other players within the first couple of moves, however that is not likely the case here. In chess.com, players have the option to resign a game at all points, so these games may have ended quickly because one of these players had to leave. We can see, however, that there are not many of these games, showcasing that players with high ratings are reluctant to leave games early because it could negatively impact their ELO, thus impacting their reputation. ### **Biggest Upsets** It is pretty rare for players to defeat players exceedingly higher rated than them, because ELO is an indicator of skill. However, it still happens at some points. Here is a table of the biggest upsets that have occurred on chess.com for these grandmasters. ```{r} #| echo: false #| message: false #| warning: false # Upset: a match when the player with the lower Elo score wins biggest.upset <- chess.data %>% mutate("ELO Difference" = OpponentElo - PlayerElo) %>% filter(.data$"ELO Difference" > 0) %>% arrange(desc(.data$"ELO Difference")) %>% mutate(Upset = if_else(Outcome == "Win", 1, 0)) %>% filter(Upset == 1) %>% slice(1:10) %>% summarize("Game ID" = game_id, "Date" = Date, "Underdog" = Name, "Player ELO" = PlayerElo, "Opponent ELO" = OpponentElo, "ELO Difference" = .data$"ELO Difference") # Output table formattable(biggest.upset, align = c("c", "c", "c", "c", "c", "c"), list( "ELO Difference" = color_tile("#E36615", "red") )) ``` For a player to have a double-digit ranking, they have to be pretty terrible at the game, especially considering that each player starts at a rating of 800 immediately upon creating an account. Players with highly differentiating ELO's aren't matched with each other either, meaning that these players willingly chose to play each other, or they faced each other in a chess.com tournament. I believe that the double-digit rating players defeating GrandMasters was just an experiment between these two players, and therefore, they are outliers. These games may have either been accidentally played, or they were coordinated as a potential experiment between the two players. Either way, these games should not be factored into our overall analysis of ELO's impact on game outcomes, as the games likely did not occur under normal circumstances. ### **Game Outcome Classification Based on Ratings** I think we have enough data to observe how the ratings of White and Black directly impact the chances of whether or not they will win. I plotted `White ELO` versus `Black ELO` to determine exactly how ratings as White and Black effect who may win and who may lose. I excluded major outliers. ```{r} #| echo: false #| message: false #| warning: false # Violin p2 <- ggplot(chess.data.inivgame, aes(x=WhiteElo, y=BlackElo, color=Result)) + geom_point(alpha = 0.2) + theme_bw() + scale_color_manual(values = c("1-0" = "#15C825", "1/2-1/2" = "#EFEF22", "0-1" = "red")) + xlim(2400, 2900) + ylim(2400, 2900) + labs(title = "Scatterplot of White and Black ELO's Grouped by Game Result") ggplotly(p2) ``` Based on our data, we can see that ELO is a pretty good measure of whether or not White or Black will win. We can see that our plot is overwhelmingly green, because white just wins more often. However, higher ranking Black players do tend to defeat lower-rated White players. The opposite is true as well. There are a lot of drawing games and games where White wins in points on the scatterplot where White and Black are similarly ranked. ## **Conclusion** I can conclude that ELO is a decently good measure of skill for determining how good players are good. White, however, tends to defeat Black when high-rated players are playing against one another. There are clear limitations to this dataset. For example, we only have a subset of game data for players in these rating categories. Nevertheless, I do believe my conclusions are pretty solid.