There are nice visualizations from chess data: piece movement, piece survaviliy, square usage by player. Sadly not always the authors shows the code/data for replicate the final result. So I wrote some code to show how to do some this great visualizations entirely in R. Just for fun.

1. The Data
2. Piece Movements
3. Survival rates
4. Square usage by player
5. Distributions for the first movement
6. Who captures whom

The Data

The original data come from here which was parsed and stored in the rchess package.

library("rchess")
data(chesswc)
str(chesswc)

## Classes 'tbl_df', 'tbl' and 'data.frame':    1266 obs. of  11 variables:
##  $ event   : chr  "FIDE World Cup 2011" "FIDE World Cup 2011" "FIDE World Cup 2011" "FIDE World Cup 2011" ...
##  $ site    : chr  "Khanty-Mansiysk RUS" "Khanty-Mansiysk RUS" "Khanty-Mansiysk RUS" "Khanty-Mansiysk RUS" ...
##  $ date    : Date, format: "2011-08-28" "2011-08-28" ...
##  $ round   : num  1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 ...
##  $ white   : chr  "Kaabi, Mejdi" "Ivanchuk, Vassily" "Ibrahim, Hatim" "Ponomariov, Ruslan" ...
##  $ black   : chr  "Karjakin, Sergey" "Steel, Henry Robert" "Mamedyarov, Shakhriyar" "Gwaze, Robert" ...
##  $ result  : chr  "0-1" "1-0" "0-1" "1-0" ...
##  $ whiteelo: int  2344 2768 2402 2764 2449 2746 2477 2741 2493 2736 ...
##  $ blackelo: int  2788 2362 2765 2434 2760 2452 2744 2480 2739 2493 ...
##  $ eco     : chr  "D15" "E68" "E67" "B40" ...
##  $ pgn     : chr  "1. d4 d5 2. Nf3 Nf6 3. c4 c6 4. Nc3 dxc4 5. e3 b5 6. a4 b4 7. Nb1 Ba6 8. Ne5 e6 9. Nxc4 c5 10. b3 cxd4 11. exd4 Nc6 12. Be3 Be7"| __truncated__ "1. c4 Nf6 2. Nc3 g6 3. g3 Bg7 4. Bg2 O-O 5. d4 d6 6. Nf3 Nbd7 7. O-O e5 8. e4 c6 9. Rb1 exd4 10. Nxd4 Re8 11. h3 Nc5 12. Re1 a5"| __truncated__ "1. Nf3 Nf6 2. c4 g6 3. Nc3 Bg7 4. g3 O-O 5. Bg2 d6 6. O-O Nbd7 7. d4 e5 8. b3 exd4 9. Nxd4 Re8 10. Bb2 Nc5 11. Qc2 h5 12. Rad1 "| __truncated__ "1. e4 c5 2. Nf3 e6 3. d3 Nc6 4. g3 e5 5. Bg2 d6 6. O-O Be7 7. c3 Nf6 8. Nbd2 O-O 9. a3 b5 10. Re1 Kh8 11. d4 Bd7 12. b4 cxd4 13"| __truncated__ ...

chesswc %>% count(event)

chesswc <- chesswc %>% filter(event == "FIDE World Cup 2015")

The most important variable here is the pgn game. This pgn is a long string which represent the game. However this format is not so visualization friendly. That's why I implemented the history_detail() method for a Chess object. Let's check.

set.seed(123)
pgn <- sample(chesswc$pgn, size = 1)
str_sub(pgn, 0, 50)

## [1] "1. d4 Nf6 2. Nf3 d5 3. c4 e6 4. e3 Be7 5. Nbd2 O-O"

Compare the previous string with the first 10 rows of the history_detail()

chss <- Chess$new()
chss$load_pgn(pgn)

## [1] TRUE

chss$history_detail() %>%
  arrange(number_move) %>% 
  head(10)

The result is a dataframe where each row is a piece's movement showing explicitly the cells where the travel in a particular number move. Now we apply this function over the 433 games in the FIDE World Cup 2015.

library("foreach")
library("doParallel")
workers <- makeCluster(parallel::detectCores())
registerDoParallel(workers)

chesswc <- chesswc %>% mutate(game_id = seq(nrow(.)))

dfmoves <- adply(chesswc %>% select(pgn, game_id), .margins = 1, function(x){
  chss <- Chess$new()
  chss$load_pgn(x$pgn)
  chss$history_detail()
  }, .parallel = TRUE, .paropts = list(.packages = c("rchess")))

dfmoves <- tbl_df(dfmoves) %>% select(-pgn)
dfmoves %>% filter(game_id == 1, piece == "g1 Knight")

The dfmoves data frame will be the heart from all these plots due have a lot of information and it is easy to consume.

Piece Movements

To try replicate the result it's necessary the data to represent (and then plot) the board. In the rchess package there are some helper functions like chessboardata().

dfboard <- rchess:::.chessboarddata() %>%
  select(cell, col, row, x, y, cc)

head(dfboard)

Now we add this information to the dfmoves data frame and calculates some field to to know how to draw the curves (see here for more details).

dfpaths <- dfmoves %>%
  left_join(dfboard %>% rename(from = cell, x.from = x, y.from = y),
            by = "from") %>%
  left_join(dfboard %>% rename(to = cell, x.to = x, y.to = y) %>% select(-cc, -col, -row),
            by = "to") %>%
  mutate(x_gt_y = abs(x.to - x.from) > abs(y.to - y.from),
         xy_sign = sign((x.to - x.from)*(y.to - y.from)) == 1,
         x_gt_y_equal_xy_sign = x_gt_y == xy_sign)

The data is ready! So we need now some ggplot, geom_tile for the board, the new geom_curve to represent the piece's path and some jitter to make this more artistic. Let's plot the f1 Bishop's movements.

ggplot() +
  geom_tile(data = dfboard, aes(x, y, fill = cc)) +
  geom_curve(data = dfpaths %>% filter(piece == "f1 Bishop", x_gt_y_equal_xy_sign),
             aes(x = x.from, y = y.from, xend = x.to, yend = y.to),
             position = position_jitter(width = 0.2, height = 0.2),
             curvature = 0.50, angle = -45, alpha = 0.02, color = "white", size = 1.05) +
  geom_curve(data = dfpaths %>% filter(piece == "f1 Bishop", !x_gt_y_equal_xy_sign),
             aes(x = x.from, y = y.from, xend = x.to, yend = y.to),
             position = position_jitter(width = 0.2, height = 0.2),
             curvature = -0.50, angle = 45, alpha = 0.02, color = "white", size = 1.05) +
  scale_fill_manual(values =  c("gray10", "gray20")) +
  ggtitle("f1 Bishop") +
  coord_equal()

In the same way we can plot every piece.

I think it's look very similar to the original work made by Steve Tung.

Survival Rates

In this plot we need filter dfmoves by !is.na(status) so we can know what happend with every piece in at the end of the game: if a piece was caputered of or not. Then get summary across all the games.

dfsurvrates <- dfmoves %>%
  filter(!is.na(status)) %>%
  group_by(piece) %>%
  summarize(games = n(),
            was_captured = sum(status == "captured")) %>%
  mutate(surv_rate = 1 - was_captured/games)

dfsurvrates %>% arrange(desc(surv_rate)) %>% head()

This helps as validation because the kings are never captured. Now we use a helper function in the rchess package rchess:::.chesspiecedata() to get the start position for every piece and then plot the survival rates in the cell where the piece start in the game.

dfsurvrates <- dfsurvrates %>%
  left_join(rchess:::.chesspiecedata() %>% select(start_position, piece = name, color, unicode),
            by = "piece") %>%
  full_join(dfboard %>% rename(start_position = cell),
            by = "start_position")

# Auxiliar data to plot the board
dfboard2 <- data_frame(x = 0:8 + 0.5, y = 0 + 0.5, xend = 0:8 + 0.5, yend = 8 + 0.5)

ggplot(dfsurvrates) +
  geom_tile(data = dfsurvrates %>% filter(!is.na(surv_rate)),
            aes(x, y, fill = surv_rate)) +
  scale_fill_gradient(low = "darkred",  high = "white") +
  geom_text(data = dfsurvrates %>% filter(!is.na(surv_rate)),
            aes(x, y, label = scales::percent(surv_rate)),
            color = "gray70", size = 5) +
  scale_x_continuous(breaks = 1:8, labels = letters[1:8]) +
  scale_y_continuous(breaks = 1:8, labels = 1:8)  +
  geom_segment(data = dfboard2, aes(x, y, xend = xend, yend = yend), color = "gray70") +
  geom_segment(data = dfboard2, aes(y, x, xend = yend, yend = xend), color = "gray70") +
  ggtitle("Survival Rates for each piece") + 
  coord_equal() + 
  theme_minimal() +
  theme(legend.position = "none")

Obviously the plot show same data in text and color, and there a lot of space without information but the idea is use the chess board to represent the initial position in a chess game.

We can replace the texts with the piece's icons:

ggplot(dfsurvrates) +
  geom_tile(data = dfsurvrates %>% filter(!is.na(surv_rate)),
            aes(x, y, fill = 100*surv_rate)) +
  scale_fill_gradient(NULL, low = "darkred",  high = "white") +
  geom_text(data = dfsurvrates %>% filter(!is.na(surv_rate)),
            aes(x, y, label = unicode), size = 11, color = "gray20", alpha = 0.7) +
  scale_x_continuous(breaks = 1:8, labels = letters[1:8]) +
  scale_y_continuous(breaks = 1:8, labels = 1:8)  +
  geom_segment(data = dfboard2, aes(x, y, xend = xend, yend = yend), color = "gray70") +
  geom_segment(data = dfboard2, aes(y, x, xend = yend, yend = xend), color = "gray70") +
  ggtitle("Survival Rates for each piece") + 
  coord_equal() +
  theme_minimal() +
  theme(legend.position = "bottom")

Square Usage By Player

For this visualization we will use the to variable. First of all we select the player who have more games in the table chesswc. Then for each of them get the to counts.

players <- chesswc %>% count(white) %>% arrange(desc(n)) %>% .$white %>% head(4)
players

## [1] "Karjakin, Sergey" "Svidler, Peter"   "Wei, Yi"         
## [4] "Adams, Michael"

dfmov_players <- ldply(players, function(p){ # p <- sample(players, size = 1)
  games <- chesswc %>% filter(white == p) %>% .$game_id
  dfres <- dfmoves %>%
    filter(game_id %in% games, !is.na(to)) %>%
    count(to) %>%
    mutate(player = p,
           p = n/length(games))
  dfres
})

dfmov_players <- dfmov_players %>%
  rename(cell = to) %>%
  left_join(dfboard, by = "cell")

ggplot(dfmov_players) +
  geom_tile(aes(x, row, fill = p)) +
  scale_fill_gradient("Movements to every celln(normalized by number of games)",
                      low = "white",  high = "darkblue") +
  geom_text(aes(x, row, label = round(p, 1)), size = 3, color = "white", alpha = 0.5) +
  facet_wrap(~player) +
  scale_x_continuous(breaks = 1:8, labels = letters[1:8]) +
  scale_y_continuous(breaks = 1:8, labels = 1:8)  +
  geom_segment(data = dfboard2, aes(x, y, xend = xend, yend = yend), color = "gray70") +
  geom_segment(data = dfboard2, aes(y, x, xend = yend, yend = xend), color = "gray70") +
  coord_equal() +
  theme_minimal() +
  theme(legend.position = "bottom")

Distributions For The First Movement

Now, with the same data and using the piece_number_move and number_move we can obtain the distribution for the first movement for each piece.

piece_lvls <- rchess:::.chesspiecedata() %>%
  mutate(col = str_extract(start_position, "\w{1}"),
         row = str_extract(start_position, "\d{1}")) %>%
  arrange(desc(row), col) %>%
  .$name

dfmoves_first_mvm <- dfmoves %>%
  mutate(piece = factor(piece, levels = piece_lvls),
         number_move_2 = ifelse(number_move %% 2 == 0, number_move/2, (number_move + 1)/2 )) %>%
  filter(piece_number_move == 1)

ggplot(dfmoves_first_mvm) +
  geom_density(aes(number_move_2), fill = "#B71C1C", alpha = 0.8, color = NA) +
  scale_y_continuous(breaks = NULL) +
  facet_wrap(~piece, nrow = 4, ncol = 8, scales = "free_y")  +
  xlab("Density") + ylab("Number Move") + 
  xlim(0, 40) +
  theme_gray() +
  theme(panel.background = element_rect(fill = "gray90"))

Notice the similarities between the White King and h1 Rook due the castling, the same effect is present between the Black King and the h8 Rook.

Who Captures Whom

For this plot we'll use the igraph package and ForceAtlas2 package an R implementation by Adolfo Alvarez of the Force Atlas 2 graph layout designed for Gephi.

We get the rows with status == "captured" and summarize by piece and captured_by variables. The result data frame will be the edges in our igraph object using the graph.data.frame function.

library("igraph")
library("ForceAtlas2")

dfcaputures <- dfmoves %>%
  filter(status == "captured") %>%
  count(captured_by, piece) %>%
  ungroup() %>% 
  arrange(desc(n))

dfvertices <- rchess:::.chesspiecedata() %>%
  select(-fen, -start_position) %>%
  mutate(name2 = str_replace(name, " \w+$", unicode),
         name2 = str_replace(name2, "White|Black", ""))

g <- graph.data.frame(dfcaputures %>% select(captured_by, piece, weight = n),
                      directed = TRUE,
                      vertices = dfvertices)

set.seed(123)
# lout <- layout.kamada.kawai(g)
lout <- layout.forceatlas2(g, iterations = 10000, plotstep = 0)

dfvertices <- dfvertices %>%
  mutate(x = lout[, 1],
         y = lout[, 2])

dfedges <- as_data_frame(g, "edges") %>%
  tbl_df() %>%
  left_join(dfvertices %>% select(from = name, x, y), by = "from") %>%
  left_join(dfvertices %>% select(to = name, xend = x, yend = y), by = "to")

To plot the the network I prefer use ggplot2 instead igraph just you get more control in the style and colors.

ggplot() +
  geom_curve(data = dfedges %>%
               filter((str_extract(from, "\d+") %in% c(1, 2) |
                         str_detect(from, "White"))),
             aes(x, y, xend = xend, yend = yend, alpha = weight, size = weight),
             curvature = 0.1, color = "red") +
  geom_curve(data = dfedges %>%
               filter(!(str_extract(from, "\d+") %in% c(1, 2) |
                          str_detect(from, "White"))),
             aes(x, y, xend = xend, yend = yend, alpha = weight, size = weight),
             curvature = 0.1, color = "blue") +
  scale_alpha(range = c(0.01, 0.5)) +
  scale_size(range = c(0.01, 2)) +
  geom_point(data = dfvertices, aes(x, y, color = color), size = 15, alpha = 0.9) +
  scale_color_manual(values = c("gray10", "gray90")) +
  geom_text(data = dfvertices %>% filter(str_length(name2) != 1),
            aes(x, y, label = name2), size = 5, color = "gray50") +
  geom_text(data = dfvertices %>% filter(str_length(name2) == 1),
            aes(x, y, label = name2), size = 9, color = "gray50") +
  ggtitle("Red: white captures black | Blue: black captures white")

It's know we usually exchange pieces with the same values: queen by queen, knight by bishop, etc. The interesting fact we see here is the d2 pawn/c7 pawn/g1 knight relationship beacuse d2 pawn/c7 pawn is not so symmetrical and it's explained by the popular use the Sicilian Opening in a master level (1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4).

I hope you enjoyed this post in the same way I enjoyed doing it :D. If you notice a mistake please let me know.