Dr Chernoff’s Guide to PEBA

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Updated: April 20, 2016

“Your face, my thane, is as a book where men May read strange matters.” ― William Shakespeare, Macbeth

Humans are visual beings primarily. We see patterns in all kinds of things from clouds to toasted bread. It is through patterns that our minds can best organize numeric data into meaningful information.

Chernoff faces are a method for doing that very thing. They allow us to organize multiple sets of data into the shape of human faces, allowing us to more easily see the patterns underlying the numbers. It is a useful tool for comparing things like baseball teams. Here we will use Chernoff faces to examine the state of the clubs of PEBA as of 19 June 2023.

We begin by identifying some data we’d like to include in our comparison. The data selected are the team totals for:

Standings:
GB – games behind division leader
W – wins

Batting :
OBP – on base percentage
SLG – slugging
AVG – batting average
b.K – batting strikeouts
b.BB – batting walks
SB – stolen bases

Pitching:
p.K – pitching strikouts
p.BB – pitching walks
p.HRA – pitching home runs against
p.OAVG – pitching opponent batting average
SHO – shutoouts
S – saves

These were mapped to various facial characteristics:

2023PEBAFaces1

OBP height of face
SLG width of face
GB structure of face
p.K height of mouth
b.K width of mouth
W smiling
p.BB height of eyes
b.BB width of eyes
b.HR height of hair
p.HRA width of hair
b.SB style of hair
b.AVG height of nose
p.OAVG width of nose
SHO width of ear
S height of ear

Faces were also generated to represent the league worst, best and average values. The worst in simply the set of minimum values. The best is the set of maximum values and the average is just that. Here’s what they look like:

2023PEBAFaces2

Teams with more wins smile more. Faces with ‘pointy hair’ denote a club that steals a lot of bases. A thick tall head of hair is the sign of a team that hits a lot of home runs. Squinty eyed teams takes more walks than they surrender. Teams with high OBP have longer faces versus broad faces for teams that have high SLG.

Some of this can be seen in the faces of PEBA arranged by division and division standing:

2023PEBAFaces3

Here are some interesting groups of top fives.

The runners are clubs that steal a lot of bags. They have pointy hairstyles. The numbers are SB.

2023PEBAFaces4

The gunners are the home run leaders with their ‘tall’ hair. Numbers denote HR.
2023PEBAFaces5

Teams that throw a lot of strikes have ‘tall’ mouths. Numbers are p.K
2023PEBAFaces6

Look at the big smiles on the teams with the most wins.
2023PEBAFaces7

Separated at birth? These clubs look like siblings due to their similar stats.
2023PEBAFaces8

What patterns do you see? Any surprises?