code.Rmd

---
title: "k-means"
author: "restu dn"
date: "4/5/2021"
output: word_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
# Introduction

From Wikipedia: 


# Feature engineering

```{r, warning=FALSE, message=FALSE}
# Load libraries
library(tidyverse)
library(scales)
library(ggthemes)
library(kableExtra)
library(plotly)

options(scipen = 999)

fifa_data <- read_csv("../input/data.csv") %>% select(-X1)

fifa_data <- fifa_data %>%
  mutate(ValueMultiplier = ifelse(str_detect(Value, "K"), 1000, ifelse(str_detect(Value, "M"), 1000000, 1))) %>%
  mutate(ValueNumeric_pounds = as.numeric(str_extract(Value, "[[:digit:]]+\\.*[[:digit:]]*")) * ValueMultiplier) %>%
  mutate(Position = ifelse(is.na(Position), "Unknown", Position))


fifa_data <- fifa_data %>%
  mutate(WageMultiplier = ifelse(str_detect(Wage, "K"), 1000, ifelse(str_detect(Wage, "M"), 1000000, 1))) %>%
  mutate(WageNumeric_pounds = as.numeric(str_extract(Wage, "[[:digit:]]+\\.*[[:digit:]]*")) * WageMultiplier)


positions <- unique(fifa_data$Position)

gk <- "GK"
defs <- positions[str_detect(positions, "B$")]
mids <- positions[str_detect(positions, "M$")]
f1 <- positions[str_detect(positions, "F$")]
f2 <- positions[str_detect(positions, "S$")]
f3 <- positions[str_detect(positions, "T$")]
f4 <- positions[str_detect(positions, "W$")]
fwds <- c(f1, f2, f3, f4)

fifa_data <- fifa_data %>% 
  mutate(PositionGroup = ifelse(Position %in% gk, "GK", ifelse(Position %in% defs, "DEF", ifelse(Position %in% mids, "MID", ifelse(Position %in% fwds, "FWD", "Unknown")))))

fifa_data <- fifa_data %>%
  mutate(AgeGroup = ifelse(Age <= 20, "20 and under", ifelse(Age > 20 & Age <=25, "21 to 25", ifelse(Age > 25 & Age <= 30, "25 to 30", ifelse(Age > 30 & Age <= 35, "31 to 35", "Over 35")))))
```


# Overall Ratings
```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
fifa_data %>%
  ggplot(aes(x= Overall)) +
  geom_histogram(color = "white", fill = "darkgrey") +
  ggtitle("Player Ratings Are Normally Distributed", subtitle = "The mean can be used as a measure of central tendancy") +
  theme_fivethirtyeight() +
  theme(axis.text.y = element_blank())
```


## Age vs Overall Rating
```{r, fig.width=12, fig.height=8}
fifa_data %>%
  filter(!PositionGroup %in% c("GK", "Unknown")) %>%
  group_by(Age) %>%
  summarise(Rating = mean(Overall)) %>%
  ggplot(aes(x= Age, y= Rating, group = 1)) +
  geom_line(color = "grey50", size = 1) +
  ggtitle("The Age Curve Flattens Off", subtitle = "Player ratings tend not to get better after the age of 30") +
  xlab("Age") +
  theme_fivethirtyeight() +
  theme(axis.title = element_text(), axis.title.y = element_blank(), axis.title.x = element_text(face = "bold"))
```



```{r, fig.width=12, fig.height=8}
fifa_data %>%
  filter(!PositionGroup %in% c("GK", "Unknown")) %>%
  group_by(PositionGroup, Age) %>%
  summarise(Rating = mean(Overall)) %>%
  ggplot(aes(x= Age, y= Rating, group = PositionGroup)) +
  geom_line(size = 1, color = "grey50") +
  theme_fivethirtyeight() +
  facet_wrap(~ PositionGroup, ncol = 1) +
  theme(strip.background = element_rect(fill = "darkgrey"), strip.text = element_text(colour = "white", face = "bold"))
```


# Player Valuations

```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
p <- fifa_data %>%
  ggplot(aes(x= ValueNumeric_pounds)) +
  geom_histogram(color = "white", fill = "darkgrey") +
  scale_x_continuous(labels = dollar_format(prefix = "€")) +
  ggtitle("Player Valuations Are Heavily Skewed", subtitle = "Long tail indicates there are some extreme outliers") +
  theme_fivethirtyeight()

p +
  geom_text(data = subset(fifa_data, Name == "Neymar Jr"), aes(x= ValueNumeric_pounds, y= 500, label=Name), color = "purple") +
  geom_text(data = subset(fifa_data, Name == "L. Messi"), aes(x= ValueNumeric_pounds, y= 1000, label=Name), color = "purple") +
  geom_text(data = subset(fifa_data, Name == "K. De Bruyne"), aes(x= ValueNumeric_pounds, y= 200, label=Name), color = "purple") +
  geom_text(data = subset(fifa_data, Name == "E. Hazard"), aes(x= ValueNumeric_pounds, y= 500, label=Name), color = "purple") +
  geom_text(data = subset(fifa_data, Name == "P. Dybala"), aes(x= ValueNumeric_pounds, y= 1000, label=Name), color = "purple")
  

```


## Age vs Valuations
```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
fifa_data %>%
  ggplot(aes(x= AgeGroup, y= ValueNumeric_pounds)) +
  geom_boxplot(fill = "darkgrey") +
  scale_y_log10(labels = dollar_format(prefix = "€")) +
  ggtitle("Players Are In High Demand In Their Mid-20s", subtitle = "Valuation on a log scale, so differences \nbetween the age groups are significant") +
  theme_fivethirtyeight()
```


## Position vs Valuations

```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=12}
a <- fifa_data %>%
  filter(PositionGroup != "Unknown") %>%
  ggplot(aes(x= PositionGroup, y= ValueNumeric_pounds)) +
  geom_boxplot(fill = "darkgrey") +
  scale_y_log10(labels = dollar_format(prefix = "€")) +
  ggtitle("Positions to Break The Piggybank", subtitle = "Attackers and midfielders bring the fans to games... \nPay them the money!") +
  theme_fivethirtyeight()


b <- fifa_data %>%
  filter(PositionGroup != "Unknown") %>%
  ggplot(aes(x= Position, y= ValueNumeric_pounds)) +
  geom_boxplot(fill = "darkgrey") +
  scale_y_log10(labels = dollar_format(prefix = "€")) +
  coord_flip() +
  theme_fivethirtyeight() +
  facet_wrap(~ PositionGroup, scales = "free") +
  theme(strip.background = element_rect(fill = "darkgrey"), strip.text = element_text(colour = "white", face = "bold"))

gridExtra::grid.arrange(a, b)

```


## Player Rating and Valuations


```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
fifa_data %>%
  filter(PositionGroup != "Unknown") %>%
  ggplot(aes(x= Overall, y= ValueNumeric_pounds)) +
  geom_point(position = "jitter", color = "darkgrey") +
  ggtitle("Higher Ratings Cost More Money", subtitle = "There are still some high rating players that \ndon't cost an arm and a leg") +
  scale_y_continuous(labels = dollar_format(prefix = "€")) +
  theme_fivethirtyeight() +
  annotate("text", x= 70, y= 97000000, label = paste0("Spearman Correlation: ", round(cor(fifa_data$Overall, fifa_data$ValueNumeric_pounds, method = "spearman"),4)), color = "darkgreen", size = 8)

```


## Correlations with a players Overall rating

```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=12}
gk_vars <- fifa_data %>% select(contains("GK")) %>% names()


spearman_cor_with_overall <- fifa_data %>%
  filter(Position != "GK") %>%
  select_if(is.numeric) %>%
  select(-gk_vars, -ID, - `Jersey Number`, -ValueMultiplier, -WageMultiplier) %>% 
  as.matrix() %>%
  na.omit() %>%
  cor(method = "spearman") 

pearson_cor_with_overall <- fifa_data %>%
  filter(Position != "GK") %>%
  select_if(is.numeric) %>%
  select(-gk_vars, -ID, - `Jersey Number`, -ValueMultiplier, -WageMultiplier) %>% 
  as.matrix() %>%
  na.omit() %>%
  cor()

cor_colnames <- colnames(spearman_cor_with_overall)

spearman_cor_with_overall <- spearman_cor_with_overall[,2] %>% data.frame()
spearman_cor_with_overall <- cbind(cor_colnames, spearman_cor_with_overall) %>% arrange(desc(`.`))

pearson_cor_with_overall <- pearson_cor_with_overall[,2] %>% data.frame()
pearson_cor_with_overall <- cbind(cor_colnames, pearson_cor_with_overall) %>% arrange(desc(`.`))

spearman_cor_with_overall %>% left_join(pearson_cor_with_overall, by = "cor_colnames") %>% 
  rename(Feature = cor_colnames, Spearman = `..x`, Pearson = `..y`) %>% filter(Feature != "Overall") %>% head(10)


# spearman_cor_with_overall %>% left_join(pearson_cor_with_overall, by = "cor_colnames") %>% 
#   rename(Feature = cor_colnames, Spearman = `..x`, Pearson = `..y`) %>% filter(Feature != "Overall") %>% tail(10)

```

## Which positions are skilled in which attributes

```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=12}
tile_data <- fifa_data %>%
  select_if(is.numeric) %>%
  select(-gk_vars) %>%
  left_join(fifa_data %>% select(ID, Position, PositionGroup), by = "ID") %>%
  filter(Overall >= 70) %>%
  select(-ID, -`International Reputation`, -`Jersey Number`, -`Skill Moves`, -Special, -ValueMultiplier, -ValueNumeric_pounds, -`Weak Foot`, -Age, -Overall, -Potential, -starts_with("Wage"))


tile_data <- tile_data %>%
  filter(Position != "GK") %>%
  gather(key = Attribute, value = Value, -Position, -PositionGroup) %>%
  group_by(PositionGroup, Position, Attribute) %>%
  summarise(MedianValue = median(Value, na.rm = T))

tile_data %>%
  filter(Position != "Unknown") %>%
  ggplot(aes(x= Attribute, y= Position)) +
  geom_tile(aes(fill = MedianValue), colour = "black") +
  geom_text(aes(label = MedianValue)) +
  scale_fill_gradient(low = "purple", high = "green") +
  ggtitle("Centre Backs Are Strong, Left Forwards Are Agile", subtitle = "Analysing the median ratings for each of the attributes for \neach position for players with and overall rating over 75") +
  theme_fivethirtyeight() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), strip.text = element_text(face = "bold", size = 12), legend.position = "none") +
  facet_wrap(~ PositionGroup, scales = "free", ncol = 1)

```

***

# Helping me manage a team

## Young Player Analysis

```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
holder <- fifa_data %>%
  mutate(RoomToGrow = Potential - Overall) %>%
  arrange(desc(RoomToGrow)) %>%
  head(n=20) %>%
  select(Name, Value, Overall, Age, RoomToGrow, Position) %>%
  gather(key = Mult, value = ExpectedValue, -Name, -Value, -Age, -Position) %>%
  mutate(Mult = factor(x=Mult, levels = c("RoomToGrow", "Overall")))


holder %>%
  ggplot(aes(x= Name, y= ExpectedValue, fill = Mult)) +
  geom_bar(stat = "identity", position = "stack", color = "black") +
  coord_flip() +
  scale_fill_manual(values = c("Overall" = "green", "RoomToGrow" = "violet")) +
  ggtitle("Players To Grow With Your Team", subtitle = "Plotted are the 20 players with the highest remaining room to grow") +
  theme_fivethirtyeight() +
  theme(legend.position = "none") +
  geom_text(data = subset(holder, Mult == "Overall"), aes(x= Name, y= 10, label=paste(Position, Value, Age, sep = ", "))) +
  annotate("text", x= 14.5, y= 80, label = "The 'potential' left \nin the player")
####### Need to put in a left pointing arrow


```


## When does potential end?

```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
fifa_data %>%
  group_by(Age) %>%
  summarise(Potential = mean(Potential),
            Overall = mean(Overall)) %>%
  ggplot(aes(x= Age)) +
  geom_line(aes(y= Potential), color = "purple", size = 1) +
  geom_line(aes(y= Overall), color = "grey50", size = 1) +
  annotate("text", x= 30, y=71, label = "Potential meets overall\ntalent at 29 years old", color = "purple") +
  ggtitle("Potential And Overall Talent Converges", subtitle = "The average ratings were taken for each age") +
  theme_fivethirtyeight()
```



# Free Valuation Players

```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
fifa_data %>%
  filter(ValueNumeric_pounds == 0, PositionGroup != "Unknown") %>%
  mutate(PotentialOver80 = ifelse(Potential >= 80, "Yes", "No")) %>%
  ggplot(aes(x= Age, y= Overall)) +
  geom_vline(xintercept = 30, color = "black", linetype = 2) +
  geom_hline(yintercept = 65, color = "black", linetype = 2) +
  geom_text(aes(label = Name, colour = PotentialOver80), check_overlap = T) +
  scale_colour_manual(values = c("lightgrey", "purple")) +
  theme_fivethirtyeight() +
  theme(axis.text = element_text(face = "bold"), legend.position = "none") +
  ggtitle("There's No Such Thing As A Free Lunch... Or Is There?", subtitle = "Plotting player age versus their overall rating for all players with a \nvaluation of €0. Purple names have potential over 80.") +
  annotate("text", x= 20, y= 79, label = "Rebuilding \ntarget area", size = 8, color = "darkgreen") +
  annotate("text", x= 43, y= 79, label = "Win-Now \ntarget area", size = 8, color = "darkgreen")
  
  
  
```

***

# Which Team do I want to manage

## Team Age
```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
age_avg <- mean(fifa_data$Age)
age_sd <- sd(fifa_data$Age)

team_age <- fifa_data %>%
  group_by(Club) %>%
  summarise(AvgAge = mean(Age)) %>%
  mutate(AgeZ_score = (AvgAge - age_avg) / age_sd)

team_age <- team_age %>%
  mutate(AgeType = ifelse(AgeZ_score <0, "Below", "Above"))


team_age <- team_age %>%
  arrange(desc(AgeZ_score)) %>%
  head(20) %>%
  rbind(team_age %>% arrange(desc(AgeZ_score)) %>% tail(20))


team_age %>%
  ggplot(aes(x= reorder(Club,AgeZ_score), y= AgeZ_score)) +
  geom_bar(stat = 'identity', aes(fill = AgeType), colour = "white") +
  geom_text(aes(label = round(AvgAge,1))) +
  scale_fill_manual(values = c("purple", "green")) +
  coord_flip() +
  ggtitle("Nordic Clubs Are Younger Than South American Clubs", subtitle = "Ranking the 20 oldest playing lists vs the 20 youngest playing lists") +
  theme_fivethirtyeight() +
  theme(legend.position = "none", axis.text.x = element_blank())


```


## Team Overall Talent

```{r,message=FALSE, warning=FALSE, fig.width=12, fig.height=8}

top_20_overall_clubs <- fifa_data %>%
  group_by(Club) %>%
  summarise(AverageRating = mean(Overall, na.rm = T)) %>%
  arrange(desc(AverageRating)) %>%
  head(n = 20) %>% pull(Club) 

fifa_data %>%
  filter(Club %in% top_20_overall_clubs) %>%
  mutate(Top3 = ifelse(Club %in% c("Juventus", "Napoli", "Inter"), "Yes", "No")) %>%
  ggplot(aes(x= reorder(Club,Overall), y= Overall, fill = Top3)) +
  geom_boxplot(color = "black") +
  scale_fill_manual(values = c("lightgrey", "purple")) +
  ggtitle("Italian Teams Have The Highest Overall Ratings", subtitle = "The average overall rating of the 20 highest rated teams in the game, sorted in descending order") +
  coord_flip() +
  theme_fivethirtyeight() +
  theme(legend.position = "none")
```


```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
fifa_data %>%
  mutate(ElitePlayers = ifelse(Overall >= 85, "Elite", "Not Elite")) %>%
  group_by(Club, ElitePlayers) %>%
  filter(ElitePlayers == "Elite") %>%
  summarise(NumberElitePlayers = n()) %>%
  filter(NumberElitePlayers >1) %>%
  mutate(Top3 = ifelse(Club %in% c("Juventus", "Napoli", "Inter"), "Yes", "No")) %>%
  arrange(desc(NumberElitePlayers)) %>%
  ggplot(aes(x= reorder(Club,NumberElitePlayers), y= NumberElitePlayers, fill = Top3)) +
  geom_col(color = "black") +
  scale_fill_manual(values = c("lightgrey", "purple")) +
  ggtitle("However If You Define Talent As Number Of Superstars", subtitle = "Plotted are clubs with more than one 'elite' player. Elite players being those with a rating greater than 85") +
  scale_y_continuous(breaks = seq(0,12,1))+
  coord_flip() +
  theme_fivethirtyeight() +
  theme(legend.position = "none")

```


## Deadly Teams Up Front

```{r}
fifa_data <- fifa_data  %>%
  mutate(AttackingRating = (Finishing + LongShots + Penalties + ShotPower + Positioning) /5)

fifa_data %>%
  filter(PositionGroup %in% c("MID", "FWD")) %>%
  group_by(Club) %>%
  summarise(NumberOfAttackers = n(), TeamAttackingRating = mean(AttackingRating)) %>%
  arrange(desc(TeamAttackingRating)) %>% head(50) %>%
  DT::datatable()

```


## Team Wage Bills and Value for Money

```{r, fig.width=12, fig.height=8}
fifa_data %>% 
  group_by(Club) %>% 
  summarise(TotalWages = sum(WageNumeric_pounds, na.rm = T),
            AverageRating = mean(Overall, na.rm = T)) %>%
  mutate(ValueForMoney = TotalWages / AverageRating) %>%
  arrange(desc(TotalWages)) %>% head(n= 20) %>%
  mutate(Top2 = ifelse(Club %in% c("Real Madrid", "FC Barcelona"), "Top", ifelse(Club %in% c("Inter", "Milan", "Napoli"), "Val", "No"))) %>%
  ggplot(aes(x= reorder(Club, TotalWages), y= TotalWages, fill = Top2)) +
  geom_col(colour = "black") +
  geom_text(aes(label = dollar(round(ValueForMoney), prefix = "€"), hjust = 0)) +
  scale_fill_manual(values = c("lightgrey", "purple", "green")) +
  scale_y_continuous(labels = dollar_format(prefix = "€")) +
  coord_flip() +
  ggtitle("The Spaniards Really Know How To Spend, \nBut Italians Are Shrewd", subtitle = "The 20 highest weekly wage bills in FIFA19 and how much one rating point costs in wages") +
  theme_fivethirtyeight() +
  theme(legend.position = "none")

```


```{r, fig.width=12, fig.height=8}
fifa_data %>% 
  group_by(Club) %>% 
  filter(!is.na(Club)) %>%
  summarise(TotalWages = sum(WageNumeric_pounds, na.rm = T),
            AverageRating = mean(Overall, na.rm = T)) %>%
  mutate(ValueForMoney = TotalWages / AverageRating) %>%
  arrange(desc(ValueForMoney)) %>% tail(n= 20) %>%
  mutate(Over70 = ifelse(AverageRating >= 70, "Yes", "No")) %>%
  ggplot(aes(x= reorder(Club, -TotalWages), y= TotalWages, fill = Over70)) +
  geom_col(colour = "black") +
  geom_text(aes(label = dollar(round(ValueForMoney), prefix = "€"), hjust = 1)) +
  scale_fill_manual(values = c("lightgrey", "green")) +
  scale_y_continuous(labels = dollar_format(prefix = "€")) +
  coord_flip() +
  ggtitle("Extracting Value For Money", subtitle = "The 20 clubs who spend the least amount of wage pounds per overall rating point.\nHighlighted clubs have an average rating over 70") +
  theme_fivethirtyeight() +
  theme(legend.position = "none")

```


***


# K-Means Clustering

```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
# Get data ready
data_cluster <- fifa_data %>%
  filter(PositionGroup != "Unknown") %>%
  filter(PositionGroup != "GK") %>%
  mutate(RoomToGrow = Potential - Overall) %>%
  select_if(is.numeric) %>%
  select(-ID, -`Jersey Number`, -AttackingRating, -starts_with("Value"), - starts_with("Wage"), -starts_with("GK"), -Overall)


scaled_data <- scale(data_cluster)

set.seed(109)
# Initialize total within sum of squares error: wss
wss <- 0
# For 1 to 30 cluster centers
for (j in 1:30) {
  km.out <- kmeans(scaled_data, centers = j, nstart = 20)
  # Save total within sum of squares to wss variable
  wss[j] <- km.out$tot.withinss
}


# create a DF to use in a ggplot visualisation
wss_df <- data.frame(num_cluster = 1:30, wgss = wss)

# plot to determine optimal k
ggplot(data = wss_df, aes(x=num_cluster, y= wgss)) + 
  geom_line(color = "lightgrey", size = 2) + 
  geom_point(color = "green", size = 4) +
  theme_fivethirtyeight() +
  geom_curve(x=14, xend=8, y=300000, yend= 290500, arrow = arrow(length = unit(0.2,"cm")), size =1, colour = "purple") +
  geom_text(label = "k = 8\noptimal level", x=14, y= 290000, colour = "purple") +
  labs(title = "Using Eight Clusters To Group Players", subtitle = "Selecting the point where the elbow 'bends', or where the slope of \nthe Within groups sum of squares levels out")


# Set k equal to the number of clusters corresponding to the elbow location
k <- 8

# Create a k-means model on wisc.data: wisc.km
wisc.km <- kmeans(scale(data_cluster), centers = k, nstart = 20)

# add the cluster group back to the original DF for all players other than GK and Unknown
cluster_data <- fifa_data %>%
  filter(PositionGroup != "Unknown") %>%
  filter(PositionGroup != "GK") %>%
  mutate(Cluster = wisc.km$cluster)

```


```{r, message=FALSE, warning=FALSE, fig.width=12, fig.height=8}
# create a new DF with just some select variables for analysis
cluster_analysis <- cluster_data %>%
  select(ID, Name, Club, Age, PositionGroup, Overall, Cluster, ValueNumeric_pounds)

# how have the clusters been split between position groups
table(cluster_analysis$Cluster, cluster_analysis$PositionGroup)


# create an arranged DF for analysis
cluster_arranged <- cluster_analysis %>%
  mutate(Cluster = as.character(Cluster)) %>%
  arrange(desc(Overall)) %>% 
  group_by(Cluster)
```


```{r, message=FALSE, warning=FALSE, fig.width=15, fig.height=8}
# build the plot for each of the 20 highest rated players in each cluster
p  <- cluster_analysis %>%
  mutate(Cluster = paste("Cluster: ", Cluster, sep = "")) %>%
  arrange(desc(Overall)) %>% 
  group_by(Cluster) %>%
  slice(1:20) %>%
  mutate(Under27 = ifelse(Age < 27, "Yes", "No")) %>%
  ggplot(aes(x= Overall, y= ValueNumeric_pounds)) +
  geom_point(position = "jitter", shape = 21, color = "black", size = 2, aes(text = paste(Name, PositionGroup), fill = Under27)) +
  scale_fill_manual(values = c("purple", "green")) +
  scale_y_continuous(labels = dollar_format(prefix = "€")) +
  ggtitle("Player's overall rating plotted against their value for the \n20 highest rated players in each cluster") +
  facet_wrap(~ factor(Cluster), scales = "free", ncol = 2) +
  theme_fivethirtyeight() +
  theme(legend.position = "none", strip.text = element_text(face = "bold", size = 12))

# plot output
ggplotly(p, height = 700, width = 900)

```


```{r}
return_similar_players <- function(player, num_results, return_within_fraction) {
  
  cluster_filter <- cluster_analysis$Cluster[cluster_analysis$Name == player]
  player_value <- cluster_analysis$ValueNumeric_pounds[cluster_analysis$Name == player]
  
  cluster_analysis %>%
    filter(Cluster == cluster_filter,
           ValueNumeric_pounds >= (player_value * (1- return_within_fraction)) & ValueNumeric_pounds <= (player_value * (1 + return_within_fraction))) %>%
    head(num_results)

}


return_similar_players("I. Perišić", 100, .05) %>% DT::datatable()

```