Update app.R

app.R

@@ -1,4 +1,3 @@
-# Load required libraries
 library(shiny)
 library(plotly)
 library(gridlayout)
@@ -21,6 +20,7 @@ library(png)
 library(xgboost)
 library(httr)
 library(jpeg)
+library(zoo)  # For rolling mean calculation
 
 pdf(file = NULL)
 Sys.setenv(TZ='EST')
@@ -98,48 +98,53 @@ pitcher_summary <- function(game_pk,date){
 }
 
 break_plot <- function(game){
-  ggplot()+
-    geom_point(game,mapping = 
-                 aes(x=HB, y = IVB,color = pitch_name),size = 4) +
-    geom_vline(xintercept = 0,  color = "lightblue",linewidth = 1,linetype = 4)+
-    geom_hline(yintercept = 0,  color = "lightblue",linewidth = 1,linetype = 4)+
-    xlab("Horizontal Break from Pitcher's Perspective (in) ")+
-    ylab("Induced Verical Break (in)") +
-    xlim(-25,25) +
-    ylim(-25,25) +
-    ggthemes::theme_igray()+
-    theme(panel.grid.minor = element_line(color = "gray",
-                                          size = 0.25,
-                                          linetype = 1))+
-    guides(color = guide_legend(title = "Pitch Type"))
+  ggplot(game, aes(x = HB, y = IVB, color = pitch_name)) +
+    geom_point(size = 2) +
+    geom_vline(xintercept = 0, color = "lightblue", linewidth = 1, linetype = 4) +
+    geom_hline(yintercept = 0, color = "lightblue", linewidth = 1, linetype = 4) +
+    labs(x = "Horizontal Break (in)", y = "Induced Vertical Break (in)", 
+         title = "Pitch Movement") +
+    xlim(-25, 25) +
+    ylim(-25, 25) +
+    # scale_x_continuous(breaks = seq(-20, 20, by = 20)) +
+    # scale_y_continuous(breaks = seq(-20, 20, by = 20)) +
+    theme_minimal() +
+    theme(
+      legend.position = "bottom",
+      plot.title = element_text(hjust = 0.5, face = "bold"),
+      panel.grid.minor = element_line(color = "gray", size = 0.25, linetype = 1),
+      aspect.ratio = 1  # This ensures the plot is square
+    ) +
+    guides(color = guide_legend(title = "Pitch Type", nrow = 1))
 }
 
 pitch_plot <- function(game){
-  ggplot()+
-    geom_point(game,mapping = 
-                 aes(x=px, y = pz,color = pitch_name),size = 3.5) +
-    geom_segment(aes(x=-0.71,xend = 0.71, y = 1.5,yend = 1.5))+
-    geom_segment(aes(x=-0.71,xend = 0.71, y = 3.6,yend = 3.6))+
-    geom_segment(aes(x= 0.71,xend = 0.71, y = 1.5,yend = 3.6))+
-    geom_segment(aes(x=-0.71,xend = -0.71, y = 1.5,yend =3.6))+
-    xlab(" ")+
-    ylab(" ") +
-    xlim(-3,3)+
-    ylim(0.2,4)+
+  ggplot(game, aes(x = px, y = pz, color = pitch_name)) +
+    geom_point(size = 3.5) +
+    geom_segment(aes(x = -0.71, xend = 0.71, y = 1.5, yend = 1.5)) +
+    geom_segment(aes(x = -0.71, xend = 0.71, y = 3.6, yend = 3.6)) +
+    geom_segment(aes(x = 0.71, xend = 0.71, y = 1.5, yend = 3.6)) +
+    geom_segment(aes(x = -0.71, xend = -0.71, y = 1.5, yend = 3.6)) +
+    labs(x = NULL, y = NULL, title = "Pitch Location") +
+    xlim(-3, 3) +
+    ylim(0.2, 4) +
     coord_fixed(ratio = 1) +
-    ggthemes::theme_few()+
-    guides(color = guide_legend(title = "Pitch Type"))+
-    theme(axis.text.x=element_blank(), 
-          axis.ticks.x=element_blank(), 
-          axis.text.y=element_blank(), 
-          axis.ticks.y=element_blank())
+    theme_minimal() +
+    theme(
+      legend.position = "bottom",
+      plot.title = element_text(hjust = 0.5, face = "bold"),
+      axis.text = element_blank(),
+      axis.ticks = element_blank()
+    ) +
+    guides(color = guide_legend(title = "Pitch Type", nrow = 1))
 }
 
 # Load models
-FB <- xgb.load('FB.model')
-Off <- xgb.load('Off.model')
-Break <- xgb.load('Break.model')
+# FB <- xgb.load('FB.model')
+# Off <- xgb.load('Off.model')
+# Break <- xgb.load('Break.model')
 model <- xgb.load('TimStuff2.model')
+
 calculate_VAA <- function(vz0, ay, az, vy0, y0) {
   -atan((vz0+(az*(-sqrt((vy0*vy0)-(2*ay*(y0-(17/12))))-vy0)/
                 ay))/(-sqrt((vy0*vy0)-(2*ay*(y0-(17/12))))))*(180/pi)
@@ -163,32 +168,24 @@ scale_TimStuff <- function(raw_score, model_mean, model_sd) {
   result <- 100 - (scaled_score * 10)
   return(result)
 }
+
 calculate_primary <- function(data){
   data <- data %>%
-    # Group by pitch_name, Pitcher Name, Pitcher Id, and date
     group_by(pitch_name, `Pitcher Name`, `Pitcher ID`, date) %>%
-    
-    # Count occurrences and calculate average start_speed, IVB, and HB for each group
     mutate(
       pitch_count = n(),
       avg_start_speed = mean(start_speed, na.rm = TRUE),
       avg_IVB = mean(IVB, na.rm = TRUE),
       avg_HB = mean(HB, na.rm = TRUE)
     ) %>%
-    
     ungroup() %>%
-    # Group by Pitcher Name, Pitcher Id, and date
     group_by(`Pitcher Name`, `Pitcher ID`, date) %>%
-    
-    # Add a column to identify the highest occurrence
     mutate(
       is_highest_occurrence = case_when(
         pitch_count == max(pitch_count) ~ 1,
         TRUE ~ 0
       )
     ) %>%
-    
-    # If there's a tie, use avg_start_speed as a tiebreaker
     mutate(
       is_highest_occurrence = case_when(
         is_highest_occurrence == 1 & pitch_count == max(pitch_count[is_highest_occurrence == 1]) & 
@@ -196,15 +193,11 @@ calculate_primary <- function(data){
         TRUE ~ 0
       )
     ) %>%
-    
-    # Calculate primary pitch metrics
     mutate(
       primary_speed = avg_start_speed[is_highest_occurrence == 1][1],
       primary_IVB = avg_IVB[is_highest_occurrence == 1][1],
       primary_HB = avg_HB[is_highest_occurrence == 1][1]
     ) %>%
-    
-    # Ungroup to remove grouping structure
     ungroup()
 }
 
@@ -219,7 +212,6 @@ calculate_timstuff <- function(game) {
            is_strike_swinging = ifelse(is_strike_swinging, 1, 0),
            Pitch = pitch_name,
            ishandL = ifelse(phand == "L",1,0))
-  # game <- calculate_primary(game)
   
   feature_vars <- c("ishandL","start_speed", "IVB", "HB", "EAA", "x0", "z0", "spin_rate","SADiff","primary_speed","primary_IVB","primary_HB")
   complete_rows <- complete.cases(game[, feature_vars])
@@ -229,15 +221,12 @@ calculate_timstuff <- function(game) {
   
   rhp <- game_complete
   
-  # rhp <- game_complete[game_complete$ishandL == 0]
-  # 
-  # lhp$TimStuff <- scale_TimStuff(predict(model, as.matrix(cbind(lhp$ishandL,lhp$start_speed, lhp$IVB, lhp$HB, lhp$EAA, lhp$x0, lhp$z0, lhp$spin_rate, lhp$SADiff,lhp$primary_speed,lhp$primary_IVB,lhp$primary_HB))), -0.00249975,  0.007566558)
-  
   rhp$TimStuff <- scale_TimStuff(predict(model, as.matrix(cbind(rhp$ishandL,rhp$start_speed, rhp$IVB, rhp$HB, rhp$EAA, rhp$x0, rhp$z0, rhp$spin_rate, rhp$SADiff,rhp$primary_speed,rhp$primary_IVB,rhp$primary_HB))), -0.00249975,  0.007566558)
   
   game_complete <- rbind(rhp,game_na)
   return(game_complete)
 }
+
 summary_table <- function(game) {
   rows <- nrow(game)
   game <- calculate_primary(game)
@@ -273,7 +262,30 @@ summary_table <- function(game) {
     ) %>%
     arrange(-Pitches)
   
-  return(sumtable)
+  result <- sumtable %>%
+    select(Pitch, Pitches, `Pitch%`, `Avg. Velo`, `Spin Rate`, Extension,IVB, HB, VAA, `CSW%`, `Whiff%`, `TimStuff+`) %>%
+    rename(
+      "Type" = Pitch,
+      "#" = Pitches,
+      "Velo" = `Avg. Velo`,
+      "Spin" = `Spin Rate`,
+      "Ext" = Extension,
+      "Use%" = `Pitch%`
+    ) %>%
+    mutate(
+      "Use%" = paste0(`Use%`, "%"),
+      "Spin" = format(round(Spin), big.mark = ","),
+      Velo = round(Velo, 1),
+      Ext = round(Ext, 1),
+      IVB = round(IVB, 1),
+      HB = round(HB, 1),
+      VAA = round(VAA, 1),
+      `CSW%` = paste0(`CSW%`, "%"),
+      `Whiff%` = paste0(`Whiff%`, "%")
+    ) %>%
+    arrange(desc(`#`))
+  
+  return(result)
 }
 
 # Initialize schedule data
@@ -322,59 +334,57 @@ sbteamA <- distinct(sbteamA)
 
 # UI Definition
 ui <- fluidPage(
-  tags$head(
-    tags$style(HTML("
-      @media (max-width: 768px) {
-        .sidebar { width: 100%; float: none; }
-        .main-content { margin-left: 0; }
-        .selectize-input { font-size: 14px; }
-        .form-group { margin-bottom: 10px; }
-        .action-button { width: 100%; }
-      }
-    "))
-  ),
+  theme = bs_theme(version = 5, bootswatch = "flatly"),
   titlePanel("2024 MLB/AAA/FSL Summary Cards"),
   sidebarLayout(
     sidebarPanel(
-      width = 2,
-      dateInput("date", "Date:"),
-      selectizeInput("level", "Level:", c("MLB", "AAA", "FSL", "College (Statcast Parks Only)")),
-      selectizeInput("homeT", "Home Team:", mlbteamH[,1]),
-      selectizeInput("awayT", "Away Team:", mlbteamA[,1]),
-      selectizeInput("gamenum", "Game Number (For Doubleheaders):", c("1", "2")),
+      width = 3,
+      dateInput("date", "Date:", value = Sys.Date()),
+      selectizeInput("level", "Level:", 
+                     c("MLB", "AAA", "FSL", "College (Statcast Parks Only)"),
+                     options = list(
+                       placeholder = 'Select a level',
+                       onInitialize = I('function() { this.setValue(""); }')
+                     )),
+      selectizeInput("homeT", "Home Team:", NULL),
+      selectizeInput("awayT", "Away Team:", NULL),
+      selectizeInput("gamenum", "Game Number:", c("1", "2")),
       actionButton("update", "Find Pitcher", icon("magnifying-glass"),
-                   style = "color: #FFFFFF; background-color: #0077B6; width: 100%;"),
-      selectizeInput("pitcher", "Pitcher Name:", c(" ")),
+                   class = "btn-primary btn-block"),
+      selectizeInput("pitcher", "Pitcher Name:", NULL),
       textInput("title", "Card Title"),
       actionButton("update1", "Make Card", icon("plus"),
-                   style = "color: #FFFFFF; background-color: #0077B6; width: 100%;"),
-      downloadButton("downloadPlot", "Download Card")
+                   class = "btn-success btn-block"),
+      downloadButton("downloadPlot", "Download Card", class = "btn-info btn-block")
     ),
     mainPanel(
-      plotOutput("combinedPlot", height = "900px",width = "1350px")
+      plotOutput("combinedPlot", height = "900px", width = "100%")
     )
   )
 )
+
 server <- function(input, output, session) {
   observeEvent(input$level, {
     if(input$level == "AAA"){
-      updateSelectizeInput(session = getDefaultReactiveDomain(),"homeT","Home Team:",choices =  aaateamH[,1])
-      updateSelectizeInput(session = getDefaultReactiveDomain(),"awayT","Away Team:",choices =  aaateamA[,1])
+      updateSelectizeInput(session, "homeT", "Home Team:", choices = aaateamH[,1])
+      updateSelectizeInput(session, "awayT", "Away Team:", choices = aaateamA[,1])
     }
     if(input$level == "FSL"){
-      updateSelectizeInput(session = getDefaultReactiveDomain(),"homeT","Home Team:",choices =  fslteamH[,1])
-      updateSelectizeInput(session = getDefaultReactiveDomain(),"awayT","Away Team:",choices =  fslteamA[,1])
+      updateSelectizeInput(session, "homeT", "Home Team:", choices = fslteamH[,1])
+      updateSelectizeInput(session, "awayT", "Away Team:", choices = fslteamA[,1])
     }
     if(input$level == "MLB"){
-      updateSelectizeInput(session = getDefaultReactiveDomain(),"homeT","Home Team:",choices =  mlbteamH[,1])
-      updateSelectizeInput(session = getDefaultReactiveDomain(),"awayT","Away Team:",choices =  mlbteamA[,1])
+      updateSelectizeInput(session, "homeT", "Home Team:", choices = mlbteamH[,1])
+      updateSelectizeInput(session, "awayT", "Away Team:", choices = mlbteamA[,1])
     }
     if(input$level == "College (Statcast Parks Only)"){
-      updateSelectizeInput(session = getDefaultReactiveDomain(),"homeT","Home Team:",choices =  sbteamH[,1])
-      updateSelectizeInput(session = getDefaultReactiveDomain(),"awayT","Away Team:",choices =  sbteamA[,1])
+      updateSelectizeInput(session, "homeT", "Home Team:", choices = sbteamH[,1])
+      updateSelectizeInput(session, "awayT", "Away Team:", choices = sbteamA[,1])
     }
   })
   
+  game_data <- reactiveVal()
+  
   observeEvent(input$update, {
     tryCatch({
       if(input$level == "AAA"){
@@ -383,7 +393,7 @@ server <- function(input, output, session) {
           filter(teams_home_team_name == input$homeT) %>%
           filter(teams_away_team_name == input$awayT) %>%
           filter(game_number == input$gamenum)
-        pname <- pitcher_summary(pname[,6],input$date)
+        pname <- pitcher_summary(pname[,6], input$date)
       }
       if(input$level == "FSL"){
         pname <- fslid %>%
@@ -391,7 +401,7 @@ server <- function(input, output, session) {
           filter(teams_home_team_name == input$homeT) %>%
           filter(teams_away_team_name == input$awayT) %>%
           filter(game_number == input$gamenum)
-        pname <- pitcher_summary(pname[,6],input$date)
+        pname <- pitcher_summary(pname[,6], input$date)
       }
       if(input$level == "MLB"){
         pname <- mlbid %>%
@@ -399,7 +409,7 @@ server <- function(input, output, session) {
           filter(teams_home_team_name == input$homeT) %>%
           filter(teams_away_team_name == input$awayT) %>%
           filter(game_number == input$gamenum)
-        pname <- pitcher_summary(pname[,6],input$date)
+        pname <- pitcher_summary(pname[,6], input$date)
       }
       if(input$level == "College (Statcast Parks Only)"){
         pname <- sbid %>%
@@ -407,92 +417,73 @@ server <- function(input, output, session) {
           filter(teams_home_team_name == input$homeT) %>%
           filter(teams_away_team_name == input$awayT) %>%
           filter(game_number == input$gamenum)
-        pname <- pitcher_summary(pname[,6],input$date)
+        pname <- pitcher_summary(pname[,6], input$date)
       }
       
       if(nrow(pname) == 0) {
         showNotification("No pitchers found for the selected game.", type = "warning")
       } else {
-        updateSelectizeInput(session = getDefaultReactiveDomain(),"pitcher","Pitcher:",choices =  pname[,3])
+        updateSelectizeInput(session, "pitcher", "Pitcher:", choices = unique(pname$`Pitcher Name`))
+        game_data(pname)
       }
     }, error = function(e) {
       showNotification(paste("Error finding pitchers:", e$message), type = "error")
     })
   })
   
+  rolling_timstuff <- reactive({
+    req(input$update1, game_data())
+    game <- game_data() %>% filter(`Pitcher Name` == input$pitcher)
+    game <- calculate_timstuff(game)
+    game %>%
+      arrange(date) %>%
+      group_by(pitch_name) %>%
+      mutate(rolling_timstuff = rollmean(TimStuff, k = 5, fill = NA, align = "right"),
+             pitch_number = row_number()) %>%
+      ungroup()  # Make sure to ungroup after the grouping operations
+  })
+  
   combinedPlot <- reactiveVal()
   observeEvent(input$update1, {
+    req(game_data())
     tryCatch({
-      if(input$level == "MLB"){
-        id <- mlbid %>%
-          filter(date == as.character.Date(input$date)) %>%
-          filter(teams_home_team_name == input$homeT) %>%
-          filter(teams_away_team_name == input$awayT) %>%
-          filter(game_number == input$gamenum)
-        game <- pitcher_summary(id[,6],input$date)
-        game <- game %>%
-          filter(`Pitcher Name`  == input$pitcher)
-        id <- as.character(game[1,4])
-      }
-      if(input$level == "FSL"){
-        id <- fslid %>%
-          filter(date == as.character.Date(input$date)) %>%
-          filter(teams_home_team_name == input$homeT) %>%
-          filter(teams_away_team_name == input$awayT) %>%
-          filter(game_number == input$gamenum)
-        game <- pitcher_summary(id[,6],input$date)
-        game <- game %>%
-          filter(`Pitcher Name`  == input$pitcher)
-        id <- as.character(game[1,4])
-      }
-      if(input$level == "AAA"){
-        id <- aaaid %>%
-          filter(date == as.character.Date(input$date)) %>%
-          filter(teams_home_team_name == input$homeT) %>%
-          filter(teams_away_team_name == input$awayT) %>%
-          filter(game_number == input$gamenum)
-        game <- pitcher_summary(id[,6],input$date)
-        game <- game %>%
-          filter(`Pitcher Name`  == input$pitcher)
-        id <- as.character(game[1,4])
-      }
-      if(input$level == "College (Statcast Parks Only)"){
-        id <- sbid %>%
-          filter(date == as.character.Date(input$date)) %>%
-          filter(teams_home_team_name == input$homeT) %>%
-          filter(teams_away_team_name == input$awayT) %>%
-          filter(game_number == input$gamenum)
-        game <- pitcher_summary(id[,6],input$date)
-        game <- game %>%
-          filter(`Pitcher Name`  == input$pitcher)
-        id <- as.character(game[1,4])
-      }
+      game <- game_data() %>% filter(`Pitcher Name` == input$pitcher)
       
       if(nrow(game) == 0) {
         showNotification("No data available for the selected pitcher.", type = "warning")
         return()
       }
       
-      break_plot <- break_plot(game)
-      pitch_plot <- pitch_plot(game)
+      break_plot <- break_plot(game) +
+        theme(legend.position = "none")
+      
+      pitch_plot <- pitch_plot(game) +
+        theme(legend.position = "none")
       
-      table_plot <- tableGrob(summary_table(game), theme = ttheme_default(
-        core = list(fg_params = list(cex = 1.7)),
-        colhead = list(fg_params = list(cex = 1.2)),
-        rowhead = list(fg_params = list(cex = 2.5))))
-      table_plot$widths[[1]] <- unit(0, "cm")
+      # Create a formatted table
+      table_data <- summary_table(game)
+      num_rows <- nrow(table_data)
       
-      text_grobs <- which(sapply(table_plot$grobs, function(g) {
-        g$name == "core-fg-1" && inherits(g$children[[1]], "text")
-      }))
+      table_plot <- tableGrob(table_data, rows = NULL, theme = ttheme_minimal(
+        core = list(fg_params = list(hjust = 0.5, x = 0.5), bg_params = list(fill = "white")),
+        colhead = list(fg_params = list(hjust = 0.5, x = 0.5, fontface = "bold"), bg_params = list(fill = "#f0f0f0")),
+        rowhead = list(fg_params = list(hjust = 0.5, x = 0.5), bg_params = list(fill = "white"))
+      ))
       
-      for (i in text_grobs) {
-        text <- table_plot$grobs[[i]]$children[[1]]$label
-        table_plot$grobs[[i]]$children[[1]]$label <- sub("^\\d+\\s*", "", text)
+      # Set a fixed total height for the table, adjusting row heights based on number of pitches
+      total_height <- unit(1, "npc")
+      row_height <- total_height / (num_rows + 1)  # +1 for header row
+      table_plot$heights <- unit(rep(row_height, num_rows + 1), "npc")
+      
+      # Adjust column widths
+      table_plot$widths <- unit(c(0.1, 0.06, 0.06, 0.08, 0.1, 0.06, 0.08, 0.08, 0.08, 0.1, 0.1, 0.1), "npc")
+      
+      # Add alternating row colors
+      for(i in seq(2, nrow(table_plot), 2)) {
+        table_plot$grobs[[i]]$gp$fill <- "#f9f9f9"
       }
       
-      grid.newpage()
-      grid.draw(table_plot)
+      id <- as.character(game$`Pitcher ID`[1])
       
       mlb_url <- paste0("https://midfield.mlbstatic.com/v1/people/", id, "/mlb/300?circle=false")
       milb_url <- paste0("https://midfield.mlbstatic.com/v1/people/", id, "/milb/300?circle=false")
@@ -508,13 +499,76 @@ server <- function(input, output, session) {
         img_grob <- textGrob("Image not available", gp = gpar(col = "red", fontsize = 20))
       }
       
-      combined <- grid.arrange(
-        arrangeGrob(table_plot, img_grob, ncol = 2, widths = c(2/3, 1/3)),
-        arrangeGrob(break_plot, pitch_plot, ncol = 2),
-        nrow = 2,
-        top = textGrob(paste(input$title, "Made by @TimStats (Data: MLB)", sep = " "), gp = gpar(fontsize = 20, font = 2))
+      # Create the rolling TimStuff+ graph
+      rolling_data <- rolling_timstuff()
+      timstuff_plot <- ggplot(rolling_data, aes(x = pitch_number, y = rolling_timstuff, color = pitch_name)) +
+        geom_line(size = 1) +
+        geom_point(size = 1) +
+        theme_minimal() +
+        labs(title = "5-Pitch Rolling TimStuff+",
+             x = "Pitch Number", y = "TimStuff+") +
+        ylim(70, 130) +
+        scale_x_continuous(breaks = seq(5, 55, by = 5), limits = c(5,NA)) +
+        theme(
+          plot.title = element_text(hjust = 0.5, face = "bold"),
+          legend.position = "none",
+          panel.grid.major.x = element_line(color = "gray", size = 0.5)
+        )
+      
+      # Create title and data source text
+      title_text <- textGrob(
+        paste(input$pitcher, format(input$date, "%m/%d/%y"), "Summary Card by @TimStats"),
+        gp = gpar(fontsize = 16, fontface = "bold")
+      )
+      data_source_text <- textGrob(
+        "Data: MLB",
+        gp = gpar(fontsize = 8),
+        x = unit(1, "npc") - unit(2, "mm"),
+        y = unit(2, "mm"),
+        just = c("right", "bottom")
+      )
+      
+      # Create a horizontal legend
+      legend <- get_legend(
+        ggplot(rolling_data, aes(x = pitch_number, y = rolling_timstuff, color = pitch_name)) +
+          geom_point(size = 5) +
+          theme(legend.position = "bottom",
+                legend.title = element_blank(),
+                text = element_text(size = 12.5),
+                #legend.key.size = unit(.5,"cm"),
+                legend.box = "horizontal" ) +
+          guides(color = guide_legend(nrow = 1))
       )
       
+      # Combine all plots
+      combined <- grid.arrange(
+        arrangeGrob(
+          arrangeGrob(
+            img_grob,
+            title_text,
+            ncol = 1,
+            heights = c(4, 1)
+          ),
+          pitch_plot,
+          ncol = 2,
+          widths = c(1, 1)
+        ),
+        arrangeGrob(
+          break_plot,
+          timstuff_plot,
+          ncol = 2,
+          widths = c(1, 1)
+        ),
+        #arrangeGrob(
+        legend,
+        #),
+        #arrangeGrob(
+        table_plot,
+        #),
+        data_source_text,
+        nrow = 5,
+        heights = c(1.2, 1.2, 0.05, 1.1, 0.05)  # Adjusted these values
+      )
       combinedPlot(combined)
       
       output$combinedPlot <- renderPlot({