Statistical Analyses on Roger Federer s Performances in 2013 and 2014 James Kong,

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1 Statistical Analyses on Roger Federer s Performances in 2013 and 2014 James Kong, kong.james@berkeley.edu Introduction Tennis has become a global sport and I am a big fan of tennis. Since I played college tennis for Cal, and I would like to do statistical analyses to my favorite player of all time - Roger Federer, about his performances in 2013 and 2014.Here were why I specifically choose these two years: In 2013: A. He had a back injury throughout his career, but in 2013, it was his lowest point of his career. B. He hadn t reached a grand slam final for the first time in 10 years ( ), and he had the lowest win/loss record in his entire career. In 2014: A. He changed his coach from Paul Annacone to one of the tennis legends - Stefan Edberg. B. He changed his racket for the first time in his career. One year may not be long or short, but it could turn things upside down for Federer. I m going to examine all of his match records from 2013 and 2014, excluding Davis Cup which is an individual represent his country to participate a team event that battle against other countries. It occurs every year, but not every professional play Davis Cup each year, so I would leave Davis Cup out for the analysis. I was going to use various methods to analyze his performances so it would be fitting to show his worst and one of his good years after a short period of time. The data I got was from Datahub, which compiled men s and women s tennis results from 2000 to Website: Methods: I wanted to achieve a couple things for 2013 and 2014 results. Objectives were: 1. How many sets he had won and lost 2. How many tournaments he had won and how many tournaments he had lost in the finals 3. His winning percentage Per Year 4. His performances in the 4 Grand Slams (Australian Open, French Open, Wimbledon, US Open) Per Year 5. Which surface he performed better (Hard, Clay, Grass) 6. Show his Total Wins Per Surface Per Year Imported datasets for 2013 and Also, I filtered which I would take some columns that are useful to do analysis - tournament, date, surface, round, best of, winner, loser, Wsets, Lsets. results_13 <- read.csv("/users/kingkong1/desktop/gis Work/R/Roger Federer's Analysis/Final Project/full_r esults_2013.csv", header = TRUE) results_14 <- read.csv("/users/kingkong1/desktop/gis Work/R/Roger Federer's Analysis/Final Project/full_r esults_2014.csv", header = TRUE) subset_13 <- results_13[, c(3, 4, 6, 7, 8, 9,10, 11, 26, 27) ] subset_14 <- results_14[, c(3, 4, 6, 7, 8, 9,10, 11, 26, 27) ] Filtered results by combining wins and losses. The column headings were as following from two datasets. rf_13 <- subset_13[which(subset_13$winner == 'Federer R.' subset_13$loser == 'Federer R.'), ] rf_14 <- subset_14[which(subset_14$winner == 'Federer R.' subset_14$loser == 'Federer R.'), ] head(rf_13)

2 Tournament Date Court Surface Round Best.of 183 Australian Open 1/15/13 Outdoor Hard 1st Round Australian Open 1/17/13 Outdoor Hard 2nd Round Australian Open 1/19/13 Outdoor Hard 3rd Round Australian Open 1/21/13 Outdoor Hard 4th Round Australian Open 1/23/13 Outdoor Hard Quarterfinals Australian Open 1/25/13 Outdoor Hard Semifinals 5 Winner Loser Wsets Lsets 183 Federer R. Paire B Federer R. Davydenko N Federer R. Tomic B Federer R. Raonic M Federer R. Tsonga J.W Murray A. Federer R. 3 2 head(rf_14) Tournament Date Court Surface Round Best.of 4 Brisbane International 1/1/14 Outdoor Hard 2nd Round 3 12 Brisbane International 1/3/14 Outdoor Hard Quarterfinals 3 14 Brisbane International 1/4/14 Outdoor Hard Semifinals 3 15 Brisbane International 1/5/14 Outdoor Hard The Final Australian Open 1/14/14 Outdoor Hard 1st Round Australian Open 1/16/14 Outdoor Hard 2nd Round 5 Winner Loser Wsets Lsets 4 Federer R. Nieminen J Federer R. Matosevic M Federer R. Chardy J Hewitt L. Federer R Federer R. Duckworth J Federer R. Kavcic B. 3 0 Noticed that both datasets columns headings were identical; I was going to do a merge between tables. However, I couldn t merge tables because I didn t have unique IDs to join two tables. In addition, if I had had joined two tables, my data would be messed up because it would use a column from one table to join to the others, which would comprise results and changed the data structure. Therefore, I would use append because number of columns and column headings were identical. Also, I will show the strings of the append; replace NA values to 0 on the sets he won and lost. rf_13_14 <- rbind(rf_13,rf_14) str(rf_13_14) 'data.frame': 142 obs. of 10 variables: $ Tournament: Factor w/ 72 levels "Abierto Mexicano",..: $ Date : Factor w/ 560 levels "1/1/13","1/10/13",..: $ Court : Factor w/ 2 levels "Indoor","Outdoor": $ Surface : Factor w/ 3 levels "Clay","Grass",..: $ Round : Factor w/ 8 levels "1st Round","2nd Round",..: $ Best.of : int $ Winner : Factor w/ 244 levels "Almagro N.","Alund M.",..: $ Loser : Factor w/ 388 levels "Aguilar J.","Ali Mutawa J.M.",..: $ Wsets : int $ Lsets : int rf_13_14$wsets[is.na(rf_13_14$wsets)] <- 0 rf_13_14$lsets[is.na(rf_13_14$lsets)] <- 0 Changed the columns type - Date and added a new column Year to categorize all matches that Federer played in 2013 or rf_13_14$date <- as.date(rf_13_14$date, format = "%m/%d/%y") rf_13_14$year <- format(rf_13_14$date, format = "%Y") Comments: Later, when I did sum, subract or other statistical functions, I wouldn t get errors saying in my columns that had NA values or can t sort by dates/year.

3 1. How many sets he won and lost library(plyr) rf_win_loss <- ddply(rf_13_14, ~Year, summarise, Sets_won = sum(wsets), Sets_Loss = sum(lsets)) print(rf_win_loss) Year Sets_won Sets_Loss How many tournaments he had won and had lost in the final by year. I had to subset wins and losses in the final, so I used round = the final & winner = federer to specify my subset. It was because that was the only way to know if he had won a tournament or not, and vice versa. After that, I bind two datasets to see his overall performances in finals whether wins or losses, and then added a column with condition statement, if winner = Federer R, print Win, else Loss. rf_tournaments_won <- rf_13_14[which(rf_13_14$round == "The Final" & rf_13_14$winner == "Federer R."), ] rf_tournaments_lost <- rf_13_14[which(rf_13_14$round == "The Final" & rf_13_14$loser == "Federer R."), ] rf_tournament_record <- rbind(rf_tournaments_won, rf_tournaments_lost) rf_tournament_record$w_l <- ifelse(rf_tournament_record$winner == "Federer R.", "Win", "Loss") print(head(rf_tournament_record)) Tournament Date Court Surface 1355 Gerry Weber Open Outdoor Grass 575 Dubai Tennis Championships Outdoor Hard 1347 Gerry Weber Open Outdoor Grass 2011 Western & Southern Financial Group Masters Outdoor Hard 2383 Shanghai Masters Outdoor Hard 2495 Swiss Indoors Indoor Hard Round Best.of Winner Loser Wsets Lsets Year W_L 1355 The Final 3 Federer R. Youzhny M Win 575 The Final 3 Federer R. Berdych T Win 1347 The Final 3 Federer R. Falla A Win 2011 The Final 3 Federer R. Ferrer D Win 2383 The Final 3 Federer R. Simon G Win 2495 The Final 3 Federer R. Goffin D Win Separated 2013 and 2014 records and found out W-L record by calculating the frequency. library(knitr) Warning: package 'knitr' was built under R version rf_tournament_record$date <- as.date(rf_tournament_record$date, format = "%m/%d/%y") rf_tournament_record$year <- format(rf_tournament_record$date, format = "%Y") final_records_2013 <- rf_tournament_record[rf_tournament_record$year == 2013, ] final_records_2014 <- rf_tournament_record[rf_tournament_record$year == 2014, ] freq_2014 <- count(final_records_2014, c("w_l", "Year")) freq_2013 <- count(final_records_2013, c("w_l", "Year")) c <- cbind(freq_2013,freq_2014) W_L <- c[order(c$freq ),] colnames(w_l)[c(1,4)] <- "Number of Finals" colnames(w_l)[c(3,6)] <- "Total" kable(w_l) Number of Finals Year Total Number of Finals Year Total 2 Win Win Loss Loss Comments: From the table above, there were significant changes between 2013 and 2014 s win-loss record. Even though 2014 had more losses in the final, he still won more finals compared to 2013.

4 3. His winning percentage from 2013 to Added Year and W_L columns, and organize them by categories to both years. rf_13$date <- as.date(rf_13$date, format = "%m/%d/%y") rf_13$year <- format(rf_13$date, format = "%Y") rf_13$w_l <- ifelse(rf_13$winner == "Federer R.", "Win", "Loss") rf_14$date <- as.date(rf_14$date, format = "%m/%d/%y") rf_14$year <- format(rf_14$date, format = "%Y") rf_14$w_l <- ifelse(rf_14$winner == "Federer R.", "Win", "Loss") 2013 and 2014 winning percentage total_percentages_2013 <- count(rf_13, c("w_l", "Year")) print(total_percentages_2013) W_L Year freq 1 Loss Win winning_percentages_2013 <- total_percentages_2013$freq/ sum(total_percentages_2013$freq) print( winning_percentages_2013[2]) [1] total_percentages_2014 <- count(rf_14, c("w_l", "Year")) print(total_percentages_2014) W_L Year freq 1 Loss Win winning_percentages_2014 <- total_percentages_2014$freq/ sum(total_percentages_2014$freq) print( winning_percentages_2014[2]) [1] 0.85 Now, I transformed the digits to actual percentage using % sign. To do that, I wrote a empty function and then added the winning percentage of both years. Then, Put 2013 and 2014 percentages together in matrix and used new labels. percent <- function(x, digits = 2, format = "f",...) { paste0(formatc(100 * x, format = format, digits = digits,...), "%") } percentage_2013 <- percent(winning_percentages_2013[2]) percentage_2014 <- percent(winning_percentages_2014[2]) matrix_2013_2014 <- matrix(c(percentage_2013, percentage_2014), nrow = 2, ncol = 1, byrow = TRUE) dimnames(matrix_2013_2014) = list( c("2013", "2014"), c("win - Loss Percent/ Year")) kable(matrix_2013_2014) % % Win - Loss Percent/ Year 4. His performances in 4 Grand Slams (Australian Open, French Open,

5 Wimbledon, US Open) 1st, I made each round from text to sequence of numbers. It was because I could better represent which round he made per grand slam in descending method, only if I had numeric columns. E.g. 1st,2nd,3nd,4th, quarter final,semi final, the final -> 1,2,3,4,5,6,7 grandslams_2013 <- rf_13[which(rf_13$tournament == "Australian Open" rf_13$tournament == "French Open" rf_13$tournament == "Wimbledon" rf_13$tournament == "US Open"), ] grandslams_2013$round_number <- c(1,2,3,4,5,6,1,2,3,4,5,1,2,1,2,3,4) grandslams_2014 <- rf_14[which(rf_14$tournament == "Australian Open" rf_14$tournament == "French Open" rf_14$tournament == "Wimbledon" rf_14$tournament == "US Open"), ] grandslams_2014$round_number <- c(1,2,3,4,5,6,1,2,3,4,1,2,3,4,5,6,7,1,2,3,4,5,6) grandslams_2013_loss <- grandslams_2013[which(grandslams_2013$loser == "Federer R."), ] grandslams_2014_loss <- grandslams_2014[which(grandslams_2014$loser == "Federer R."), ] Reordered the factor as the calendar year grand slam played in the sequence - Aussie Open -> French Open -> Wimbledon -> US Open, so that when projecting graphs, it would be according to this level I set up. library(ggplot2) Warning: package 'ggplot2' was built under R version grandslams_2013_loss$tournament <- factor(grandslams_2013_loss$tournament, levels = c("australian Open", "French Open", "Wimbledon", "US Open")) graph_2013 <- ggplot(grandslams_2013_loss, aes(x = Tournament, y = Round_Number, group = 1)) + geom_line(colour = "red", linetype = "longdash") + ggtitle("2013 Grand Slam Results") + labs( x = "Grand Slam", y = "Round Number") + geom_point(shape = 13,colour = "grey60", size = 2) + geom_text(aes(label = Round), vjust = 2, hjust = 0, nudge_y = 0.3, colour = "blue", check_overlap = FALSE) + theme(panel.background = element_rect(fill = "grey")) graph_2013 Create 2014 Grand Slam results.

grandslams_2014_loss$tournament <- factor(grandslams_2014_loss$tournament, levels = c("australian Open", "French Open", "Wimbledon", "US Open")) graph_2014 <- ggplot(grandslams_2014_loss, aes(x =

6 grandslams_2014_loss$tournament <- factor(grandslams_2014_loss$tournament, levels = c("australian Open", "French Open", "Wimbledon", "US Open")) graph_2014 <- ggplot(grandslams_2014_loss, aes(x = Tournament, y = Round_Number, group = 1)) + geom_line(colour = "gray", linetype = "dotdash") + ggtitle("2014 Grand Slam Results") + labs( x = "Grand Slam", y = "Round Number") + geom_point(shape= 8, fill = "white", size = 2) + geom_text(aes(label = Round), vjust = 2, hjust = 0, nudge_y = 0.3, colour = "red", check_overlap = FALSE) + theme(panel.grid.minor = element_line(colour = "red", linetype = "dotted")) graph_2014 Lined them up together in the same plot because it might show different perspective. grandslams_combine_res <- rbind(grandslams_2013_loss, grandslams_2014_loss) graph_combine <- ggplot(data=grandslams_combine_res, aes(x=factor(tournament), y=round_number, group=year, colour=year)) + ggtitle("2013 vs 2014 Grand Slam Results") + xlab(" Grand Slam ") + ylab( "Round Number ") + geom_line(aes(linetype = Year)) + scale_linetype_manual(values=c("twodash", "dotted")) + scale_color_brewer(palette="paired") + theme_minimal() + geom_point(aes(shape=year)) + theme(legend.text = element_text(size = 10, colour = "red", angle = 10), legend.background = element_rect(colour = "black"), panel.background = element_rect(fill = "white")) graph_combine

7 Comments: Federer did extremely well in 3 out of 4 Grand Slams from 2013 to Which surface he performed better (Hard, Clay, Grass) and combine both years to do regression analysis First, I would add columns that represent each match played in each surface as 1, else 0. E.g. I created 3 columns to represent number of matches played in each surface. These 3 columns - hard, clay and grass would be independent variables. Second, depedent variable would be total number of sets he lost (column = Lsets) Third, my hypothesis: Total number of sets he lost had no relationship on 3 surfaces. rf_13_14$hard <- ifelse(rf_13_14$surface == "Hard", 1, 0) rf_13_14$clay <- ifelse(rf_13_14$surface == "Clay", 1, 0) rf_13_14$grass <- ifelse(rf_13_14$surface == "Grass", 1, 0) regression_l <- lm( Lsets ~ Hard + Clay + Grass, data = rf_13_14) summary(regression_l) Call: lm(formula = Lsets ~ Hard + Clay + Grass, data = rf_13_14) Residuals: Min 1Q Median 3Q Max Coefficients: (1 not defined because of singularities) Estimate Std. Error t value Pr(> t ) (Intercept) * Hard Clay Grass NA NA NA NA --- Signif. codes: 0 '***' '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: on 139 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 2 and 139 DF, p-value: plot(regression_l)

9 From the regression mode, the variables were all 1s and 0s. Therefore, there were no variation in the plots as the graphs showed. In addition, they were one sided and clustered in space. Moreover, from the summary, it showed that p-value was too high; normally, in a good model, p-value would be below 0.5%. Also, R- squared was negative which hypothesis could be rejected since there were relationships in the model and variables were not randomly distributed. 6. Show his Total Wins Per Surface Per Year 2013 and 2014 Surfaces performance summary. To calculate total wins per surface, it would be better to add a numeric column for every win = 1, else 0, and calculate sum of each win/ surface

10 rf_13$number <- ifelse(rf_13$w_l == "Win", 1,0) surface_2013 <- data.frame(tapply(rf_13$number, rf_13$surface,sum)) surface_2013$year < colnames(surface_2013) <- c("total Wins", "Year") rf_14$number <- ifelse(rf_14$w_l == "Win", 1,0) surface_2014 <- data.frame(tapply(rf_14$number, rf_14$surface,sum)) surface_2014$year < colnames(surface_2014) <- c("total Wins", "Year") surface_performance <- rbind(surface_2013, surface_2014) surface_performance$surface <- c("clay", "Grass", "Hard") Surface results in barplot by year. surface_performance$year<- as.character(surface_performance$year) surface_combine <- ggplot(data = surface_performance, aes(x = Surface, y = `Total Wins`, group = Year, fi ll = Year)) + ggtitle("total Wins Per Surface") + theme(plot.title = element_text(lineheight=.8, face="bold")) + geom_bar( stat = 'identity', color = 'black', position="dodge") + geom_text(aes(label=`total Wins`), vjust=1.5, colour="white", position=position_dodge(.9), size=5) + scale_fill_manual(values= c("#d8b365", "#5ab4ac")) surface_combine Facets the barplot result to look at different angle surface_combine_facet <- ggplot(data = surface_performance, aes(x = Surface, y = `Total Wins`, group = Ye ar, fill = Year)) + geom_bar( stat = 'identity', color = 'red', position="dodge") + geom_text(aes(label=`total Wins`), vjust=1.5, colour="black", position=position_dodge(.9), size=5) + scale_fill_brewer(palette = "Spectral") surface_combine_facet + facet_grid(year ~.) + theme(legend.position="none", strip.text.x = element_text(size=8, angle=75), strip.text.y = element_text(size=12, face="bold"), strip.background = element_rect(colour="red", fill="#ccccff"))

11 Conclusion Roger Federer performed significantly better in terms of statistics including number of win-loss sets and finals he won and lost, win-loss percentage, Grand Slam results, and wins per year. Perhaps, change of racket and coach helped him to bring back his old self.

Model Selection Erwan Le Pennec Fall 2015

Model Selection Erwan Le Pennec Fall 2015 library("dplyr") library("ggplot2") library("ggfortify") library("reshape2") Model Selection We will now use another classical dataset birthwt which corresponds