Introduction

In project 1, we were given a text file with chess tournament results. The goal of the project was to tidy the data in r, calculate the average pre chess rating of opponents, and generate a .CSV file. In this extra credit assignment, we identify the top 5 over performers and under performers by comparing the player’s actual score and their calculated expected score.

Project 1

Load Text File into R

In project 1, I loaded the text file into R. Below is the table of the text file. The table has the following issues:

1. There are dashes and empty rows and column.

2. Each player’s information are within every two rows.

2. The ‘Player names’, ‘USCF ID’, ‘Pre-Rating’ and ‘Post-Rating’ are in every 2 rows of the 2nd column.

3. There are no header.

4. Every cell contains both numeric and non-meric values.

#library(dplyr)
library(tidyverse)
library(tidyr)
library(DT)
# I used the following links to see how to read txt file http://rfunction.com/archives/1441 and 
txtfile <- readLines('https://raw.githubusercontent.com/suswong/DATA-607-Project-1/main/tournamentinfo.txt')
table1<-read.delim(textConnection(txtfile),header=FALSE,sep="|")
datatable(table1)

Tidy Data

Below is a table of the tidied data. Below are the steps I took to tidy the data:

  1. Remove the empty rows that were between each player information and the last empty column.
  2. Remove the “header” row and created a header row for the columns.
  3. Create a column for the ‘Player names’, ‘USCF ID’, ‘Pre-Rating’ and ‘Post-Rating’
new <-table1 %>% 
  filter(row_number() %% 3 != 1) ## Delete every 3rd row starting from 1
#I searched how to fitler certain rows that I do not want to keep in my datatable. <https://stackoverflow.com/questions/24440258/selecting-multiple-odd-or-even-columns-rows-for-dataframe>

colnames(new) <- c("Pair_Num", "Player_Name", "Total_Points", "Round_1", "Round_2", "Round_3", "Round_4", "Round_5", "Round_6", "Round_7", "n/a")


new <- new[-1,] #Remove the 1st row
new <- new[-1,] #Remove the 2nd row
new <- new[,-11] #Remove the last column

#I searched how to select and extract even and odd rows using the following link. <https://datacarpentry.org/R-genomics/03-data-frames.html>
odd <- seq(1,nrow(new),2)
even <- seq(2,nrow(new),2)
players <-new[odd,]
player_state <- select(new[even,],1,2) #I used this link to see how to select certain columns https://sparkbyexamples.com/r-programming/r-select-function-from-dplyr/

colnames(player_state) <- c("State", "USCF_ID.Rating")

# I used the following link to split a column into multiple columns. https://www.statology.org/split-column-in-r/
library(stringr)
player_state[c('USCF_ID', 'Rating')] <- str_split_fixed(player_state$USCF_ID.Rating, '/ ', 2) 
df1 <- player_state[c('State','USCF_ID', 'Rating')]

df1[c('Prerating', 'Postrating')] <- str_split_fixed(df1$Rating, '->', 2) 
df2 <- df1[c('State','USCF_ID','Prerating','Postrating')]
df2$Prerating<-gsub("R:","",as.character(df2$Prerating)) # I used this link to help me remove "R:" in the Prerating column. https://www.tutorialspoint.com/how-to-remove-a-character-in-an-r-data-frame-column#:~:text=Side%20ProgrammingProgramming-,To%20remove%20a%20character%20in%20an%20R%20data%20frame%20column,%22%2C%22%22%2Cas.

# I search and used the following link to help me combine two tables. <https://statisticsglobe.com/cbind-r-command-example/>
df3 <- cbind(players,df2)
#df3 <- df3[,-1] #Remove the first column

#http://www.sthda.com/english/wiki/reordering-data-frame-columns-in-r
col_order <- c("Pair_Num","Player_Name", "State","USCF_ID","Prerating","Postrating","Total_Points", "Round_1", "Round_2", "Round_3", "Round_4", "Round_5", "Round_6", "Round_7")
df4 <- df3[, col_order]

# I search how to remove any letter from each round https://datascience.stackexchange.com/questions/15589/remove-part-of-string-in-r
df5 <- df4[c('Pair_Num', 'Player_Name','State','Prerating','Total_Points','Round_1','Round_2','Round_3','Round_4','Round_5','Round_6','Round_7')]
df5$Round_1<-gsub("[a-zA-Z ]","",as.character(df5$Round_1))
df5$Round_2<-gsub("[a-zA-Z ]","",as.character(df5$Round_2))
df5$Round_3<-gsub("[a-zA-Z ]","",as.character(df5$Round_3))
df5$Round_4<-gsub("[a-zA-Z ]","",as.character(df5$Round_4))
df5$Round_5<-gsub("[a-zA-Z ]","",as.character(df5$Round_5))
df5$Round_6<-gsub("[a-zA-Z ]","",as.character(df5$Round_6))
df5$Round_7<-gsub("[a-zA-Z ]","",as.character(df5$Round_7))
df5$Prerating<-as.numeric(unlist(str_extract(df5$Prerating,"\\d+\\d")))
df5$Pair_Num<-as.numeric(df5$Pair_Num)

Final <- df5


Tidied_Table <- df4
Tidied_Table$Prerating<-as.numeric(unlist(str_extract(df5$Prerating,"\\d+\\d")))
Tidied_Table$Postrating<-as.numeric(unlist(str_extract(df5$Prerating,"\\d+\\d")))

colnames(Tidied_Table) <- c("Player Number", "Player Name", "State","USCF_ID", "Pre-Rating","Post-Rating","Total Points", "Round 1", "Round 2", "Round 3", "Round 4", "Round 5", "Round 6", "Round 7")

rownames(Tidied_Table) <- NULL

library(kableExtra)
kbl(Tidied_Table) %>%
  kable_classic() %>%
  add_header_above(c("Player Information" = 7 , "Opponent Player Number for Each Round" = 7))
Player Information
Opponent Player Number for Each Round
Player Number Player Name State USCF_ID Pre-Rating Post-Rating Total Points Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 Round 7
1 GARY HUA ON 15445895 1794 1794 6.0 W 39 W 21 W 18 W 14 W 7 D 12 D 4
2 DAKSHESH DARURI MI 14598900 1553 1553 6.0 W 63 W 58 L 4 W 17 W 16 W 20 W 7
3 ADITYA BAJAJ MI 14959604 1384 1384 6.0 L 8 W 61 W 25 W 21 W 11 W 13 W 12
4 PATRICK H SCHILLING MI 12616049 1716 1716 5.5 W 23 D 28 W 2 W 26 D 5 W 19 D 1
5 HANSHI ZUO MI 14601533 1655 1655 5.5 W 45 W 37 D 12 D 13 D 4 W 14 W 17
6 HANSEN SONG OH 15055204 1686 1686 5.0 W 34 D 29 L 11 W 35 D 10 W 27 W 21
7 GARY DEE SWATHELL MI 11146376 1649 1649 5.0 W 57 W 46 W 13 W 11 L 1 W 9 L 2
8 EZEKIEL HOUGHTON MI 15142253 1641 1641 5.0 W 3 W 32 L 14 L 9 W 47 W 28 W 19
9 STEFANO LEE ON 14954524 1411 1411 5.0 W 25 L 18 W 59 W 8 W 26 L 7 W 20
10 ANVIT RAO MI 14150362 1365 1365 5.0 D 16 L 19 W 55 W 31 D 6 W 25 W 18
11 CAMERON WILLIAM MC LEMAN MI 12581589 1712 1712 4.5 D 38 W 56 W 6 L 7 L 3 W 34 W 26
12 KENNETH J TACK MI 12681257 1663 1663 4.5 W 42 W 33 D 5 W 38 H D 1 L 3
13 TORRANCE HENRY JR MI 15082995 1666 1666 4.5 W 36 W 27 L 7 D 5 W 33 L 3 W 32
14 BRADLEY SHAW MI 10131499 1610 1610 4.5 W 54 W 44 W 8 L 1 D 27 L 5 W 31
15 ZACHARY JAMES HOUGHTON MI 15619130 1220 1220 4.5 D 19 L 16 W 30 L 22 W 54 W 33 W 38
16 MIKE NIKITIN MI 10295068 1604 1604 4.0 D 10 W 15 H W 39 L 2 W 36 U
17 RONALD GRZEGORCZYK MI 10297702 1629 1629 4.0 W 48 W 41 L 26 L 2 W 23 W 22 L 5
18 DAVID SUNDEEN MI 11342094 1600 1600 4.0 W 47 W 9 L 1 W 32 L 19 W 38 L 10
19 DIPANKAR ROY MI 14862333 1564 1564 4.0 D 15 W 10 W 52 D 28 W 18 L 4 L 8
20 JASON ZHENG MI 14529060 1595 1595 4.0 L 40 W 49 W 23 W 41 W 28 L 2 L 9
21 DINH DANG BUI ON 15495066 1563 1563 4.0 W 43 L 1 W 47 L 3 W 40 W 39 L 6
22 EUGENE L MCCLURE MI 12405534 1555 1555 4.0 W 64 D 52 L 28 W 15 H L 17 W 40
23 ALAN BUI ON 15030142 1363 1363 4.0 L 4 W 43 L 20 W 58 L 17 W 37 W 46
24 MICHAEL R ALDRICH MI 13469010 1229 1229 4.0 L 28 L 47 W 43 L 25 W 60 W 44 W 39
25 LOREN SCHWIEBERT MI 12486656 1745 1745 3.5 L 9 W 53 L 3 W 24 D 34 L 10 W 47
26 MAX ZHU ON 15131520 1579 1579 3.5 W 49 W 40 W 17 L 4 L 9 D 32 L 11
27 GAURAV GIDWANI MI 14476567 1552 1552 3.5 W 51 L 13 W 46 W 37 D 14 L 6 U
28 SOFIA ADINA STANESCU-BELLU MI 14882954 1507 1507 3.5 W 24 D 4 W 22 D 19 L 20 L 8 D 36
29 CHIEDOZIE OKORIE MI 15323285 1602 1602 3.5 W 50 D 6 L 38 L 34 W 52 W 48 U
30 GEORGE AVERY JONES ON 12577178 1522 1522 3.5 L 52 D 64 L 15 W 55 L 31 W 61 W 50
31 RISHI SHETTY MI 15131618 1494 1494 3.5 L 58 D 55 W 64 L 10 W 30 W 50 L 14
32 JOSHUA PHILIP MATHEWS ON 14073750 1441 1441 3.5 W 61 L 8 W 44 L 18 W 51 D 26 L 13
33 JADE GE MI 14691842 1449 1449 3.5 W 60 L 12 W 50 D 36 L 13 L 15 W 51
34 MICHAEL JEFFERY THOMAS MI 15051807 1399 1399 3.5 L 6 W 60 L 37 W 29 D 25 L 11 W 52
35 JOSHUA DAVID LEE MI 14601397 1438 1438 3.5 L 46 L 38 W 56 L 6 W 57 D 52 W 48
36 SIDDHARTH JHA MI 14773163 1355 1355 3.5 L 13 W 57 W 51 D 33 H L 16 D 28
37 AMIYATOSH PWNANANDAM MI 15489571 980 980 3.5 B L 5 W 34 L 27 H L 23 W 61
38 BRIAN LIU MI 15108523 1423 1423 3.0 D 11 W 35 W 29 L 12 H L 18 L 15
39 JOEL R HENDON MI 12923035 1436 1436 3.0 L 1 W 54 W 40 L 16 W 44 L 21 L 24
40 FOREST ZHANG MI 14892710 1348 1348 3.0 W 20 L 26 L 39 W 59 L 21 W 56 L 22
41 KYLE WILLIAM MURPHY MI 15761443 1403 1403 3.0 W 59 L 17 W 58 L 20 X U U
42 JARED GE MI 14462326 1332 1332 3.0 L 12 L 50 L 57 D 60 D 61 W 64 W 56
43 ROBERT GLEN VASEY MI 14101068 1283 1283 3.0 L 21 L 23 L 24 W 63 W 59 L 46 W 55
44 JUSTIN D SCHILLING MI 15323504 1199 1199 3.0 B L 14 L 32 W 53 L 39 L 24 W 59
45 DEREK YAN MI 15372807 1242 1242 3.0 L 5 L 51 D 60 L 56 W 63 D 55 W 58
46 JACOB ALEXANDER LAVALLEY MI 15490981 377 377 3.0 W 35 L 7 L 27 L 50 W 64 W 43 L 23
47 ERIC WRIGHT MI 12533115 1362 1362 2.5 L 18 W 24 L 21 W 61 L 8 D 51 L 25
48 DANIEL KHAIN MI 14369165 1382 1382 2.5 L 17 W 63 H D 52 H L 29 L 35
49 MICHAEL J MARTIN MI 12531685 1291 1291 2.5 L 26 L 20 D 63 D 64 W 58 H U
50 SHIVAM JHA MI 14773178 1056 1056 2.5 L 29 W 42 L 33 W 46 H L 31 L 30
51 TEJAS AYYAGARI MI 15205474 1011 1011 2.5 L 27 W 45 L 36 W 57 L 32 D 47 L 33
52 ETHAN GUO MI 14918803 935 935 2.5 W 30 D 22 L 19 D 48 L 29 D 35 L 34
53 JOSE C YBARRA MI 12578849 1393 1393 2.0 H L 25 H L 44 U W 57 U
54 LARRY HODGE MI 12836773 1270 1270 2.0 L 14 L 39 L 61 B L 15 L 59 W 64
55 ALEX KONG MI 15412571 1186 1186 2.0 L 62 D 31 L 10 L 30 B D 45 L 43
56 MARISA RICCI MI 14679887 1153 1153 2.0 H L 11 L 35 W 45 H L 40 L 42
57 MICHAEL LU MI 15113330 1092 1092 2.0 L 7 L 36 W 42 L 51 L 35 L 53 B
58 VIRAJ MOHILE MI 14700365 917 917 2.0 W 31 L 2 L 41 L 23 L 49 B L 45
59 SEAN M MC CORMICK MI 12841036 853 853 2.0 L 41 B L 9 L 40 L 43 W 54 L 44
60 JULIA SHEN MI 14579262 967 967 1.5 L 33 L 34 D 45 D 42 L 24 H U
61 JEZZEL FARKAS ON 15771592 955 955 1.5 L 32 L 3 W 54 L 47 D 42 L 30 L 37
62 ASHWIN BALAJI MI 15219542 1530 1530 1.0 W 55 U U U U U U
63 THOMAS JOSEPH HOSMER MI 15057092 1175 1175 1.0 L 2 L 48 D 49 L 43 L 45 H U
64 BEN LI MI 15006561 1163 1163 1.0 L 22 D 30 L 31 D 49 L 46 L 42 L 54

Calculate the Average Pre-Rating of Opponents for Each Player

In order to find the average pre-rating of opponents for each player, Ineed to remove the status (W, L, or D) in each round. Then, match and replace each opponent player number with their pre-rating number for each round. The average pre-rating of opponents for each player is the sum of all the opponents’ pre-rating divided by the total number of games played.

df6 <- df5[c('Pair_Num','Prerating')]
df5$Round_1 <- df6$Prerating[match(df5$Round_1,df6$Pair_Num)]
df5$Round_2 <- df6$Prerating[match(df5$Round_2,df6$Pair_Num)]
df5$Round_3 <- df6$Prerating[match(df5$Round_3,df6$Pair_Num)]
df5$Round_4 <- df6$Prerating[match(df5$Round_4,df6$Pair_Num)]
df5$Round_5 <- df6$Prerating[match(df5$Round_5,df6$Pair_Num)]
df5$Round_6 <- df6$Prerating[match(df5$Round_6,df6$Pair_Num)]
df5$Round_7 <- df6$Prerating[match(df5$Round_7,df6$Pair_Num)]
df5$AverageRtg <- round(rowMeans(df5[,6:12], na.rm=TRUE))

Average <- df5
colnames(Average) <- c("Player Number", "Player Name", "State", "Pre-Rating","Total Points", "Opponent 1", "Opponent 2", "Opponent 3", "Opponent 4", "Opponent 5", "Opponent 6", "Opponent 7", "Average Pre-Rating of Opponents")

rownames(Average) <- NULL

kbl(Average) %>%
  kable_classic() %>%
  add_header_above(c("Player Information" = 5 , "Opponent Pre-Rating for Each Round" = 8))
Player Information
Opponent Pre-Rating for Each Round
Player Number Player Name State Pre-Rating Total Points Opponent 1 Opponent 2 Opponent 3 Opponent 4 Opponent 5 Opponent 6 Opponent 7 Average Pre-Rating of Opponents
1 GARY HUA ON 1794 6.0 1436 1563 1600 1610 1649 1663 1716 1605
2 DAKSHESH DARURI MI 1553 6.0 1175 917 1716 1629 1604 1595 1649 1469
3 ADITYA BAJAJ MI 1384 6.0 1641 955 1745 1563 1712 1666 1663 1564
4 PATRICK H SCHILLING MI 1716 5.5 1363 1507 1553 1579 1655 1564 1794 1574
5 HANSHI ZUO MI 1655 5.5 1242 980 1663 1666 1716 1610 1629 1501
6 HANSEN SONG OH 1686 5.0 1399 1602 1712 1438 1365 1552 1563 1519
7 GARY DEE SWATHELL MI 1649 5.0 1092 377 1666 1712 1794 1411 1553 1372
8 EZEKIEL HOUGHTON MI 1641 5.0 1384 1441 1610 1411 1362 1507 1564 1468
9 STEFANO LEE ON 1411 5.0 1745 1600 853 1641 1579 1649 1595 1523
10 ANVIT RAO MI 1365 5.0 1604 1564 1186 1494 1686 1745 1600 1554
11 CAMERON WILLIAM MC LEMAN MI 1712 4.5 1423 1153 1686 1649 1384 1399 1579 1468
12 KENNETH J TACK MI 1663 4.5 1332 1449 1655 1423 NA 1794 1384 1506
13 TORRANCE HENRY JR MI 1666 4.5 1355 1552 1649 1655 1449 1384 1441 1498
14 BRADLEY SHAW MI 1610 4.5 1270 1199 1641 1794 1552 1655 1494 1515
15 ZACHARY JAMES HOUGHTON MI 1220 4.5 1564 1604 1522 1555 1270 1449 1423 1484
16 MIKE NIKITIN MI 1604 4.0 1365 1220 NA 1436 1553 1355 NA 1386
17 RONALD GRZEGORCZYK MI 1629 4.0 1382 1403 1579 1553 1363 1555 1655 1499
18 DAVID SUNDEEN MI 1600 4.0 1362 1411 1794 1441 1564 1423 1365 1480
19 DIPANKAR ROY MI 1564 4.0 1220 1365 935 1507 1600 1716 1641 1426
20 JASON ZHENG MI 1595 4.0 1348 1291 1363 1403 1507 1553 1411 1411
21 DINH DANG BUI ON 1563 4.0 1283 1794 1362 1384 1348 1436 1686 1470
22 EUGENE L MCCLURE MI 1555 4.0 1163 935 1507 1220 NA 1629 1348 1300
23 ALAN BUI ON 1363 4.0 1716 1283 1595 917 1629 980 377 1214
24 MICHAEL R ALDRICH MI 1229 4.0 1507 1362 1283 1745 967 1199 1436 1357
25 LOREN SCHWIEBERT MI 1745 3.5 1411 1393 1384 1229 1399 1365 1362 1363
26 MAX ZHU ON 1579 3.5 1291 1348 1629 1716 1411 1441 1712 1507
27 GAURAV GIDWANI MI 1552 3.5 1011 1666 377 980 1610 1686 NA 1222
28 SOFIA ADINA STANESCU-BELLU MI 1507 3.5 1229 1716 1555 1564 1595 1641 1355 1522
29 CHIEDOZIE OKORIE MI 1602 3.5 1056 1686 1423 1399 935 1382 NA 1314
30 GEORGE AVERY JONES ON 1522 3.5 935 1163 1220 1186 1494 955 1056 1144
31 RISHI SHETTY MI 1494 3.5 917 1186 1163 1365 1522 1056 1610 1260
32 JOSHUA PHILIP MATHEWS ON 1441 3.5 955 1641 1199 1600 1011 1579 1666 1379
33 JADE GE MI 1449 3.5 967 1663 1056 1355 1666 1220 1011 1277
34 MICHAEL JEFFERY THOMAS MI 1399 3.5 1686 967 980 1602 1745 1712 935 1375
35 JOSHUA DAVID LEE MI 1438 3.5 377 1423 1153 1686 1092 935 1382 1150
36 SIDDHARTH JHA MI 1355 3.5 1666 1092 1011 1449 NA 1604 1507 1388
37 AMIYATOSH PWNANANDAM MI 980 3.5 NA 1655 1399 1552 NA 1363 955 1385
38 BRIAN LIU MI 1423 3.0 1712 1438 1602 1663 NA 1600 1220 1539
39 JOEL R HENDON MI 1436 3.0 1794 1270 1348 1604 1199 1563 1229 1430
40 FOREST ZHANG MI 1348 3.0 1595 1579 1436 853 1563 1153 1555 1391
41 KYLE WILLIAM MURPHY MI 1403 3.0 853 1629 917 1595 NA NA NA 1248
42 JARED GE MI 1332 3.0 1663 1056 1092 967 955 1163 1153 1150
43 ROBERT GLEN VASEY MI 1283 3.0 1563 1363 1229 1175 853 377 1186 1107
44 JUSTIN D SCHILLING MI 1199 3.0 NA 1610 1441 1393 1436 1229 853 1327
45 DEREK YAN MI 1242 3.0 1655 1011 967 1153 1175 1186 917 1152
46 JACOB ALEXANDER LAVALLEY MI 377 3.0 1438 1649 1552 1056 1163 1283 1363 1358
47 ERIC WRIGHT MI 1362 2.5 1600 1229 1563 955 1641 1011 1745 1392
48 DANIEL KHAIN MI 1382 2.5 1629 1175 NA 935 NA 1602 1438 1356
49 MICHAEL J MARTIN MI 1291 2.5 1579 1595 1175 1163 917 NA NA 1286
50 SHIVAM JHA MI 1056 2.5 1602 1332 1449 377 NA 1494 1522 1296
51 TEJAS AYYAGARI MI 1011 2.5 1552 1242 1355 1092 1441 1362 1449 1356
52 ETHAN GUO MI 935 2.5 1522 1555 1564 1382 1602 1438 1399 1495
53 JOSE C YBARRA MI 1393 2.0 NA 1745 NA 1199 NA 1092 NA 1345
54 LARRY HODGE MI 1270 2.0 1610 1436 955 NA 1220 853 1163 1206
55 ALEX KONG MI 1186 2.0 1530 1494 1365 1522 NA 1242 1283 1406
56 MARISA RICCI MI 1153 2.0 NA 1712 1438 1242 NA 1348 1332 1414
57 MICHAEL LU MI 1092 2.0 1649 1355 1332 1011 1438 1393 NA 1363
58 VIRAJ MOHILE MI 917 2.0 1494 1553 1403 1363 1291 NA 1242 1391
59 SEAN M MC CORMICK MI 853 2.0 1403 NA 1411 1348 1283 1270 1199 1319
60 JULIA SHEN MI 967 1.5 1449 1399 1242 1332 1229 NA NA 1330
61 JEZZEL FARKAS ON 955 1.5 1441 1384 1270 1362 1332 1522 980 1327
62 ASHWIN BALAJI MI 1530 1.0 1186 NA NA NA NA NA NA 1186
63 THOMAS JOSEPH HOSMER MI 1175 1.0 1553 1382 1291 1283 1242 NA NA 1350
64 BEN LI MI 1163 1.0 1555 1522 1494 1291 377 1332 1270 1263

Calculate the Expected Score of Each Player

The formula to calculate the expected score of each player was found in href=“https://en.wikipedia.org/wiki/Elo_rating_system#Theory”> Wikipedia.

The expected score of a player is \[E_A=\frac{1}{1+10^{\frac{R_B-R_A}{400}}}\] where \[R_A\] stands for the player’s pre-rating and \[R_B\] stands for the opponent’s pre-rating.

The difference of the actual score and expected score is ‘Total Points’-‘Expected Score’.

Below is a plot graph of the actual score and the expected score of each player.

# Expected <- Rating

# Expected$Round_1 <- 1/(1+10^(((as.numeric(Expected$Round_1))-(as.numeric(Expected$Total_Points)))/400))
# Expected$Round_2 <- 1/(1+10^(((as.numeric(Expected$Round_2))-(as.numeric(Expected$Total_Points)))/400))
# Expected$Round_3 <- 1/(1+10^(((as.numeric(Expected$Round_3))-(as.numeric(Expected$Total_Points)))/400))
# Expected$Round_4 <- 1/(1+10^(((as.numeric(Expected$Round_4))-(as.numeric(Expected$Total_Points)))/400))
# Expected$Round_5 <- 1/(1+10^(((as.numeric(Expected$Round_5))-(as.numeric(Expected$Total_Points)))/400))
# Expected$Round_6 <- 1/(1+10^(((as.numeric(Expected$Round_6))-(as.numeric(Expected$Total_Points)))/400))
# Expected$Round_7 <- 1/(1+10^(((as.numeric(Expected$Round_7))-(as.numeric(Expected$Total_Points)))/400))
# 
# Expected$Round_1 <- 1/(1+10^(((as.numeric(Expected$Total_Points))-(as.numeric(Expected$Round_1)))/400))
# Expected$Round_2 <- 1/(1+10^(((as.numeric(Expected$Total_Points))-(as.numeric(Expected$Round_2)))/400))
# Expected$Round_3 <- 1/(1+10^(((as.numeric(Expected$Total_Points))-(as.numeric(Expected$Round_3)))/400))
# Expected$Round_4 <- 1/(1+10^(((as.numeric(Expected$Total_Points))-(as.numeric(Expected$Round_3)))/400))
# Expected$Round_5 <- 1/(1+10^(((as.numeric(Expected$Total_Points))-(as.numeric(Expected$Round_4)))/400))
# Expected$Round_6 <- 1/(1+10^(((as.numeric(Expected$Total_Points))-(as.numeric(Expected$Round_5)))/400))
# Expected$Round_7 <- 1/(1+10^(((as.numeric(Expected$Total_Points))-(as.numeric(Expected$Round_6)))/400))

Expected <- df5[c('Pair_Num', 'Player_Name','State','Prerating','Total_Points','Round_1','Round_2','Round_3','Round_4','Round_5','Round_6','Round_7')]
Expected$Round_1 <- 1/(1+10^(((as.numeric(Expected$Round_1))-(as.numeric(Expected$Prerating)))/400))
Expected$Round_2 <- 1/(1+10^(((as.numeric(Expected$Round_2))-(as.numeric(Expected$Prerating)))/400))
Expected$Round_3 <- 1/(1+10^(((as.numeric(Expected$Round_3))-(as.numeric(Expected$Prerating)))/400))
Expected$Round_4 <- 1/(1+10^(((as.numeric(Expected$Round_4))-(as.numeric(Expected$Prerating)))/400))
Expected$Round_5 <- 1/(1+10^(((as.numeric(Expected$Round_5))-(as.numeric(Expected$Prerating)))/400))
Expected$Round_6 <- 1/(1+10^(((as.numeric(Expected$Round_6))-(as.numeric(Expected$Prerating)))/400))
Expected$Round_7 <- 1/(1+10^(((as.numeric(Expected$Round_7))-(as.numeric(Expected$Prerating)))/400))

Expected$Expected_Score <- round(rowSums(Expected[,6:12], na.rm=TRUE), digits = 2)
Expected$Difference <- round((as.numeric(Expected$Total_Points))-(as.numeric(Expected$Expected_Score)), digits = 2)


ggplot(data = Expected, aes(x=Expected_Score, y=Total_Points, color=State)) + geom_point()

Below is a table of the expected score for each player.

Expected$Round_1 <- round(as.numeric(Expected$Round_1), digits=2)
Expected$Round_2 <- round(as.numeric(Expected$Round_2), digits=2)
Expected$Round_3 <- round(as.numeric(Expected$Round_3), digits=2)
Expected$Round_4 <- round(as.numeric(Expected$Round_4), digits=2)
Expected$Round_5 <- round(as.numeric(Expected$Round_5), digits=2)
Expected$Round_6 <- round(as.numeric(Expected$Round_6), digits=2)
Expected$Round_7 <- round(as.numeric(Expected$Round_7), digits=2)

Expected$Positive_Difference <-abs(Expected$Difference)

Expected$Relative_Percentage_Difference <- (as.numeric(Expected$Difference))/(as.numeric(Expected$Expected_Score))

Expected$Relative_Percentage_Difference <- round(as.numeric(Expected$Relative_Percentage_Difference), digits=2)




colnames(Expected) <- c("Player Number", "Player Name", "State", "Pre-Rating","Total Points", "Opponent 1", "Opponent 2", "Opponent 3", "Opponent 4", "Opponent 5", "Opponent 6", "Opponent 7", "Expected Score","Difference", "Positive Difference", "Relative Percentage Difference")

rownames(Expected) <- NULL
datatable(Expected)

Over Performers

Over performers are players who have a total score greater than their expected score. I can determine which player is a over performer by viewing their difference from their actual score. If the player’s difference is positive, then they are an over performer. Below is a table of the over performers. 56% of the players were over performers.

Overperformer <- Expected%>%
  filter(Difference >0)

Overperformer <- Overperformer[c('Player Name','State','Pre-Rating','Total Points','Expected Score','Difference','Positive Difference','Relative Percentage Difference')]
datatable(Overperformer)
library(scales)
Percentage_of_Overperformers <- percent(nrow(Overperformer)/nrow(Expected))
Percentage_of_Overperformers
## [1] "56%"

Top 5 Over Performers

Below are the top 5 over performers.

Top_Five <- Overperformer%>%
  filter(rank(desc(Difference)) <=5)
Top_Five <- Top_Five[c('Player Name','State','Pre-Rating','Total Points','Expected Score','Difference','Positive Difference','Relative Percentage Difference')]
datatable(Top_Five)

Under Performers

Under performers are players who have a total score less than their expected score. If the player’s difference is negative, then they are an over performer.

Below is a table of the over performers. 44% of the players were under performers.

Underperformer <- Expected%>%
  filter(Difference <0)%>%
  arrange(Difference)

Underperformer <- Underperformer[c('Player Name','State','Pre-Rating','Total Points','Expected Score','Difference','Relative Percentage Difference')]

datatable(Underperformer)
Percentage_of_Underperformers <- percent(nrow(Underperformer)/nrow(Expected))
Percentage_of_Underperformers
## [1] "44%"

Top 5 Underperformers

Below are the top 5 under performers.

Bottom_Five <- Underperformer[1:5,]
Bottom_Five <- Bottom_Five[c('Player Name','State','Pre-Rating','Total Points','Expected Score','Difference','Relative Percentage Difference')]
datatable(Bottom_Five)

Conclusion

56% of the players were over performers and 44% of the players were under performers.

The top 5 over performers were: 1. ADITYA BAJAJ 2. ANVIT RAO 3. ZACHARY JAMES HOUGHTON 4. AMIYATOSH PWNANANDAM 5. JACOB ALEXANDER LAVALLEY

The top 5 performers were: 1. LOREN SCHWIEBERT 2. GEORGE AVERY JONES 3. JARED GE 4. RISHI SHETTY 5. JOSHUA DAVID LEE