Ball Game Symmetry

Many of the fundamental laws of modern physics are based on laws of symmetry. (Which makes Emmy Noether a founder of modern physics.) Just as the Yin-Yang metaphor offers a way to view and deconstruct existence, symmetry is also a way to understand the world around us.

In the past (here and here, for instance) I’ve looked at various sports in abstract ways designed to bring out commonalities among groups of game types. (For instance, tennis, ping-pong, volley ball, badminton, squash, and racquetball, are all “volley” games with similar operation and constraints.)

Today I’m going to look at symmetry in various sports. As always, of course, focusing on baseball, because it’s so unique.

Also because I love it, but make no mistake: I love it because it’s so cool and unique and complex. Plus the whole thing with warm summers, hot dogs, cold beer, and good baseball.


One of the many things that turns out to be so interesting about baseball is how asymmetrical it is compared to other sports. There is an almost mirror symmetry to most games, but baseball displays that only in a few places.

I’ve had a note for about a year or so: “Baseball Symmetry: Play, Team, Field”

I’ve had to keep reminding myself what each of those three mean. Seems like the easiest thing is to finally write it all down in a post.


Wrigley Field

Field is an obvious one, a good place to start.

Nearly all sports have a rectangular field of play.

All the volley sports mentioned above do. So do the “soccer” sports: soccer, basketball, hockey, and lacrosse, for instance.

Importantly, both volley and soccer sports have mirror symmetry between opponents.

There is usually the concept of “sides” — one for each team. Further, there is typically a “goal,” which is attacked and must be defended, at each end.

These fields are also bilaterally symmetrical, they are the same from side to side. They have the same symmetry as all rectangles do.

The border of the rectangle is an important legal game boundary. Most such games have an “out-of-bounds” concept.

Fenway Park

The “bowling” sports (bowling, golf, horseshoes, bocce, curling) feature the concept of a “lane” with the (usually lone) player at one end and the “target” at the other (target shooting is a form of bowling sport).

The only symmetry of field in these is bilateral.

A line drawn down the lane splits it into mirror halves.

Golf lacks even that bilateral field symmetry. Each hole has its own distinct geometry, and the course can be any shape at all. About the only symmetry in golf is the round ball!


A baseball diamond, just the diamond itself, very nearly has bilateral symmetry. The exception is the runner’s lane leading to first base.

The diamond lacks front-to-back symmetry, because second base and home plate are different. (The pitcher’s mound isn’t centered front-to-back, either.)

A baseball field, however, is only bilaterally symmetrical in a rough sense.

The distance to the foul poles can vary in the same park, let alone in different ballparks. The rules only specify a minimum distance:

2.01: […] The distance from home base to the nearest fence, stand or other obstruction on fair territory shall be 250 feet or more. A distance of 320 feet or more along the foul lines, and 400 feet or more to center field is preferable. […]

The outfield fence, in both shape and height, is unique to each ballpark and not at all symmetrical from foul pole to foul pole (unless the designer was really in love with symmetry).

Of course all sports venues differ, but the playing fields usually don’t. In baseball, the playing field varies considerably from venue to venue.

That difference is part of the sport. Different ballparks are known as “hitter’s” or “pitcher’s” parks depending on who gets the advantage. Large outfields with distant fences tend to be pitcher’s parks.


Working backwards (on my note), batting next: Team.

In most sports that even have teams, the teams are symmetrical.

There are the same number of players filling the same number of roles. The symmetry tends to be pretty exact with teams.

Baseball is not an exception in the overall sense, but it does differ in what happens during play.

Usually there is balance in the opposing teams. It may be that, as in football, there are separate offensive and defensive teams, but the number of players facing each other is roughly symmetrical.

In the soccer sports, possession switches fluidly, so the players on the field shift between acting defensively and offensively. The team symmetry is even stronger then.

Volley sports trade possession back and forth between symmetrical teams.

The golf sports tend to focus on individual performance, but to the extent teams exist, they are symmetrical. My bowling league, for instance, had teams of four members each.


In professional baseball, there is a 25-man roster (which plays games) and the 40-man roster (which includes the 25-man roster plus players who can be “called up” if necessary).

In this sense, the teams are absolutely symmetrical, but the content of those rosters does vary a bit between teams. Some may carry 12 pitchers in the 25-man roster, others may carry 13.

Other than needing to fill the nine field positions, which includes pitching, there aren’t many constraints (those realities provide plenty).

So teams may be symmetrical in the large, if not in the details.

The situation during play, however, is entirely different!

In baseball, the defense consists of the entire team on the field, all nine players. The offense consists of a single player at the plate. While there can be up to three other offensive players on base, the situation is still decidedly unsymmetrical.

“Bases full” — odds of four against nine — still makes the defending team sweat. The asymmetry of play is balanced by the damage that single batter can do.

In some regards, baseball is a symmetrical battle between the pitcher and the batter. The pitcher does get a lot more support, again because well-hit balls win games.


Lastly, there is Play.

There is a natural asymmetry in the very idea of offense and defense, yet there is also a Yin-Yang balance, which is a symmetry. Further, the roles of offense and defense switch back and forth, which enhances the symmetry.

Most sports view this symmetry as fundamental to fair play. Each team or player gets a fair — equal (symmetrical!) — chance.

In volley and soccer sports, offense and defense shift rapidly. The regular back-and-forth nature of volley sports earns them their name.

In the soccer sports, possession (offense) is taken by defensive action or received (due to offensive error).

Baseball, along with most bowling sports, involves taking turns. Players take turns (“at bats” in baseball), and sides take turns.

Football (and rugby, I assume) have “downs” which is turn-taking combined with the possibility of losing possession.

All of this is very symmetrical and not what I meant by “Play.”


What I meant is how the game plays out as you watch it. How symmetrical the activity on the field is.

The late George Carlin, as part of his classic routine comparing baseball and football, said that, “Baseball is the only major sport that appears backward in a mirror.”

Thinking about that prompted the note that prompted this post; he’s right.

It’s even just possible we could remove the word “major” from his quote.


Assume we watch a game of any sport with the following caveats:

  1. There is no text or numbers visible.
  2. We do not know any of the players (or the team).
  3. We do not know the stadium, field, or course.

The question is, can we tell the difference if that game is reflected in a mirror? (Given we get no clues from signs or a player’s handedness or how the stadium looks.)

‘Round they go. Counter-clockwise!

I think Carlin is right; every other game has mirror symmetry. The baseball rules require the players run the bases in the correct order.

All other games would look the same reflected in a mirror.

Golf? We don’t know the course or if the players are right- or left-handed. (This applies to all sports involving throwing or using hands.)

Bowling? The pins aren’t labeled (no numbers allowed).

The only exception I can think of is NASCAR. They always drive counter-clockwise. I don’t know how traditional that is in other racing.


So there it is. Baseball (and NASCAR) has a special element that identifies it from all other sports: You’d know if you were in Mirror World if you watched a baseball game!

Stay reflective, my friends.

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

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