Problems with user-defined function output in shiny

Hello everyone, this is my first post to the R studio community. I created an NBA win-probability model a few weeks ago and have been trying to create a shiny app that will generate the output from my model for which I have created a user-defined function.

In my user interface I want a place to enter numeric input value for "Home Points", "Away Points", and "Time Remaining". Once, values have been entered for these values I want the user to click an action button. After the action button is clicked I simply want the app to display the output from my function in the main panel. However, I am unable to figure out how to get this to work.

Here is my code:


# Define UI for application that calculates win probability
ui <- fluidPage(
   # Application title
   titlePanel("Win Probability"),
   # Sidebar layout with inputs and output definitions
     #sidebar panel for inputs
        #Add numeric input for home team points
        numericInput(inputId = "home.pts", label = h3("Home Points"), value = 0),
        #Add numeric input for away team points
        numericInput(inputId = "away.pts", label = h3("Away Points"), value = 0),
        #Add numeric input for time remaining in fourth quarter
        numericInput(inputId = "time", label = h3("Time Remaining"), value = 0),
        #Add action buttion
      # Show output

win_prob <- function(time, home.pts, away.pts) {
  #calculate point difference
  diff <- home.pts - away.pts
  #Store intercept and betas
  intercept <- 0.09564935
  b_time <- 0.01087832
  b_diff <- 0.5243092
  b_interact <- -0.03066952
  #calculate and store logit
  logit <- intercept + (time*b_time) + (diff*b_diff) + ((time*diff)*b_interact)
  #function to change logit to probability
  logit2prob <- function(logit) {
    odds <- exp(logit)
    prob <- odds/(1+odds)
  #Store probability
  prob <- logit2prob(logit)

# Define server to return win probability
server <- function(input, output) {
  #Store reactive values
  home.pts <- reactive({input$home.pts})
  away.pts <- reactive({input$away.pts})
  time <- reactive({input$time})
  output$win_prob <- renderPrint({win_prob(reactive({input$home.pts}), reactive({input$away.pts}), reactive({input$time}))})

# Run the application 
shinyApp(ui = ui, server = server)

If someone can please help me I would greatly appreciate it!

Thank you!