# Radar charts and five-tool baseball players

**Online College Math Teacher**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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I was looking for an opportunity to practice with radar charts and I came across an article on five-tool baseball players, so this seemed like a perfect application for this kind of chart.

A radar chart is an alternative to a column chart to display three or more quantitative variables. The chart graphs the values in a circular manner around a center point.

The five tools in baseball are: (1) hitting for average; (2) hitting for power; (3) defense; (4) throwing; and (5) speed. A five-tool player excels in all five of these.

Among current players, Mike Trout is considered a five-tool player. The measurement of Trout’s five tools can be displayed in the following radar chart:

Trout is rated at 80 for hitting for average, 70 for hitting for power, and his lowest scores are 60 for defense, throwing and speed. This is based on a 20-to-80 rating system, where 80 is elite, 70 is plus-plus, and 60 is plus. Sorry – I could not get the points to line up with the concentric pentagons.

For comparison, here is a display of Aaron Judge’s ratings.

Judge is rated at 80 for hitting for power, 70 for hitting for average, 60 for defense, 70 for throwing, and 50 for speed, where the 50 is average at the major league level.

The results of several players can be displayed in a single radar chart, but this becomes hard to read. Three players are probably the maximum for readability.

The alternative to visualizing several players is either to create several individual radar charts or else to create a bar (horizontal) chart or a column (vertical) chart.

Each of the five tools is generally rated on a 20-to-80 scale, where 50 is average (for a major leaguer), 80 is elite, and every 10 points is supposed to represent one standard deviation. I suspect the standard deviation concept is more judgmental than mathematical. There is not a single rating system; some use traditional baseball statistics, and others use modern motion tracking data.

The numerical data above was obtained from an article by Jake Mintz in 2022 for Fox Sports https://www.foxsports.com/stories/mlb/trout-betts-rodriguez-the-definition-of-mlbs-five-tool-players . In Mintz’s data, all numbers are shown rounded to the nearest 10. Mintz only has five current players as five-tool players: Mike Trout, Mookie Betts, Trea Turner, Byron Buxton, and Julio Rodriguez. I tried graphing all five players in a single radar chart, but this was too hard to read. Mintz thinks a true five-tool player should have a grade of at least 60 in each of the five categories. By this measure, Aaron Judge is not quite a five-tool player due to a 50 in speed, and a number of elite major leaguers have at least one 50. Note that each category is considered separately. If there were some sort of weighting system, many people would weigh hitting with power as most important, followed by hitting for average, although perhaps the weights should vary by position with higher weights for defense and throwing for catcher, middle infielders, and center fielder. Pitchers have a different grading system.

What about Shohei Ohtani? At the time of his article, Mintz did not have sufficient data on Ohtani.

Mintz observes that Mike Trout worked one winter to improve his throwing, and Julio Rodriguez worked to increase his speed. This suggests that the ratings probably change over the life of a player and are dependent on when they are measured.

Other authors suggest that there is a sixth tool of exceptional players such as mental makeup and character. Another tool might be situational game awareness.

Modern motion tracking data by Statcast and others did not exist until fairly recently. Willie Mays is generally considered the greatest five-tool player. Using statistical measures, author Herm Krabbenhoft suggests Tris Speaker, Ty Cobb, and Honus Wagner should be considered as five tool players, although Krabbenhoft measures hitting for power with SLG (slugging percentage) and ISO (isolated power), not home runs https://sabr.org/journal/article/honus-wagner-baseballs-prototypical-five-tooler/ . A very different measure of hitting with power would be something like home run distance greater than 425 feet or launch angle and velocity.

What about Babe Ruth? We know Babe Ruth’s career numbers are .342 batting average and 714 home runs. I have not read anything about his defense, throwing, or speed. He did steal 123 bases, including home 10 times; maybe he was faster than we realize. He is remembered for getting thrown out stealing second to end the 1926 World Series, but perhaps the hit-and-run play was on, and Bob Meusel, the batter, swung and missed the pitch? See https://baseballegg.com/2019/10/30/babe-ruths-failed-stolen-base-attempt-ended-the-1926-world-series-or-is-that-what-really-happened/ . Ruth had 204 assists as an outfielder, which sounds like a lot. I wonder how he would have ranked in defense, throwing, and speed?

Here is my R code. I do like radar charts for comparing one to three observations over five variables, as a change of pace from column charts. I used the fmsb library for the radar charts. There is also a ggradar library, but I did not like its visualization. One of the quirks of fmsb is that the axis for each variable can have its own scale. Originally I used each variable’s max and min values, but the axes were out of sync, so I replaced this with the grand max and min. Also, I could not get the values, which are all multiples of ten, to line up on the concentric pentagons.

library(fmsb)

library(scales)

group = c(“Hit_avg”, “Hit_power”, “Defense”, “Throwing”, “Speed”)

player_names = c(“Trout”,”Betts”,”Judge”)

players <- data.frame(

row.names = player_names,

Hit_avg = c(80, 70, 70),

Hit_power = c(70,60,80),

Defense = c(60,70,60),

Throwing = c(60,80,70),

Speed = c(60,70,50))

players

# The row 1 should contain the maximum values for each variable

# The row 2 should contain the minimum values for each variable

# Data for cases or individuals should be given starting from row 3

# Define the variable ranges: maximum and minimum; however, want axes to have equal scales

max_min <- data.frame(

Hit_avg = c(max(players), min(players)),

Hit_power = c(max(players), min(players)),

Defense = c(max(players), min(players)),

Throwing = c(max(players), min(players)),

Speed = c(max(players), min(players)))

rownames(max_min) <- c("Max", "Min") # row 1 has max's, row 2 has min's.

df <- rbind(max_min, players)

df

player1_data <- df[c("Max", "Min", player_names[1]), ]

player2_data <- df[c("Max", "Min", player_names[2]), ]

player3_data <- df[c("Max", "Min", player_names[3]), ]

chart <- function(data, color, title){

radarchart(data, axistype = 0,

pcol = color, pfcol = scales::alpha(color, 0.5), plwd = 2, plty = 1,

vlabels = colnames(data), vlcex = 1.5,

cglcol = “black”, cglty = 1, cglwd = 0.8,

caxislabels = NULL,

title = title)

}

# Plot the data for players 1, 2, and 3 separately

chart(data=player1_data, color=”#00AFBB”, title=”MIKE TROUT 5 Tools”)

chart(data=player2_data, color=”#E7B800″, title=”MOOKIE BETTS 5 Tools”)

chart(data=player3_data, color=”#FC4E07″, title=”AARON JUDGE 5 Tools”)

# Plot the data for three players

chart(data=df, color=c(“#00AFBB”, “#E7B800”, “#FC4E07”), # blue-green, red-green, red-green

title=”TROUT, BETTS, JUDGE 5 Tools”)

legend(

x = “bottom”, legend = rownames(df[-c(1,2),]), horiz = FALSE,

bty = “n”, pch = 20 , col = c(“#00AFBB”, “#E7B800”, “#FC4E07”),

text.col = “black”, cex = 1.25, pt.cex = 1.5)

###########################################

# column graphs

library(tibble)

library(tidyr)

library(ggplot2)

# Reshape data to long format

players_long <- players %>%

rownames_to_column(“player”) %>%

pivot_longer(cols = -player, names_to = “group”, values_to = “value”)

# Common theme for graphs

common_theme <- theme(

legend.position=”right”,

plot.title = element_text(size=15, face=”bold”),

axis.title = element_text(size=15, face=”bold”),

axis.text = element_text(size=15, face=”bold”),

legend.title = element_text(size=15, face=”bold”),

legend.text = element_text(size=15, face=”bold”))

# Create column graph: Tool Ratings by Player

ggplot(players_long, aes(x = player, y = value, fill = group, title = “Tool Ratings by Player”)) +

geom_col(position = “dodge”) +

labs(x = “Player”, y = “Rating”, fill = “Group”) +

common_theme

# Create the column graph: Player Ratings for each Tool

ggplot(players_long, aes(x = group, y = value, fill = player)) +

geom_col(position = “dodge”) +

labs(x = “Group”, y = “Rating”, fill = “Player”, title = “Player Ratings for each Tool”) +

common_theme

### END

##################################################################################

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**Online College Math Teacher**.

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