Game Excitement Index: An In-Depth Exploration

Introduction

One of the NCAA Men’s Basketball metrics I’ve been fascinated with lately is that of Game Excitement Index. Game Excitement Index (GEI) attempts to quantify how exciting a particular game was after it has been played. Related metrics have been implemented for NFL games by Brian Burke, NBA games by InPredict (Mike Beuoy), and for March Madness by FiveThirtyEight. One can compute GEI for college basketball games using my ncaahoopR package, which I define as follows:

\[ \text{GEI} = \frac{2400}{t}\sum_{i = 2}^n |p_i - p_{i-1}| \] where \(t\) is the length of the game (in seconds), \(n\) is the number of plays in the game, and \(p_i\) is the home team’s win probability on play \(i\) of the game. One can think of GEI as a measure of the length of the win probability curve if it were to be unwound, normalized to the length of a standard regulation game. The reason I choose to normalize the length of games is that I don’t want sloppy “boring” games which simply happen to go to 2 or 3 overtimes to be pegged as more exciting. In general, this small normalization has little effect, as games that go deep into overtime are generally pretty exciting to begin with. Through this article, I hope to explore which games, teams, and conferences have produced the most exciting basketball this season, while showing off how one can use ncaahoopR to answer interesting college basketball questions.

Obtaining the Data

The below code uses ncaahoopR to

• Get each team’s schedule
• Compute GEI for each game this season

Note that a complete list of team’s can be found in the ids data frame built into the package.

library(ncaahoopR)
### Scrape All Schedules
i <- 1
for(team in ids$team) {
  print(paste("Getting Team:", i, " of ", 353))
  schedule <- get_schedule(team) %>%
    filter(date < Sys.Date()) %>%
    mutate("team" = team) 
  if(i == 1) {
    master <- schedule
  }else{
    master <- rbind(master, schedule)
  }
  i <- i + 1
}

### Get Unique Game IDs
game_ids <- 
  filter(master, !duplicated(game_id)) %>% 
  pull(game_id) %>% 
  unique()

### Compute GEI for Each Game
n <- length(game_ids)
df <- data.frame("game_id" = game_ids,
                 "gei" = NA)
for(i in 1:nrow(df)) {
  print(paste("GEI:", i, "of", n))
  df$gei[i] <- game_excitement_index(game_ids[i])
}
master <- left_join(master, df, by = "game_id")

Analysis

Below is a histogram of the Game Excitement Index for the 2018-19 season (for all games play-by-play data is avaiable). Through the first 6 weeks of the season, GEI has a mean of roughly 3.6 and standard deviation of about 2.6. GEI appears to follow some sort of Gamma distribution. The distribution is skewed right, with over 62 percent of games registing GEI less than 4.

We can see looking by the plot above that very few games have GEI greater than 10. In fact, 10 is the 99th percentile for GEI, and through 12/21/2018, only 23 games have achieved such a mark. Below are the most exciting games of the season.

Let’s take a closer look at the most exciting game of the season, VCU vs. St. John’s, an OT thriller in the Legend’s Classic championship game, during Thanksgiving “Feast Week”. We can make the win probability chart for the game using the function gg_wp_chart(), as follows.

gg_wp_chart(game_id = 401096927, home_col = "black", away_col = "red")

Next, we can look at which teams have the highest and lowest average GEI. Due to the skewed nature of the GEI distribution, it probably makes most sense to rank teams by median GEI. We can also classify games into a few different categories based on their GEI:

• Heart Pounders: GEI > 8
• Thrillers: 4 < GEI \(\leq\) 8
• Average Games: 1 < GEI \(\leq\) 4
• Duds: GEI < 1

## `summarise()` ungrouping output (override with `.groups` argument)