Visual-Baseball

This post will introduce you to an upcoming series of MLB radial axis graphs, where we examine the connections between all players at a franchise level. The plan is to feature two teams per week, with an overview of each graph’s structure and highlights within the graph. Each graph will have the same general appearance and functionality; only the underlying data and team color will change. Every post will provide a link to the interactive graph, allowing you to explore freely. One caveat – the graphs are best explored on tablets, laptops, or large monitors; phone screens will not work well.

Let’s begin with the general concept behind the radial axis approach. I selected this layout (using Gephi) to provide an intuitive graph that is both easy to understand and navigate. Using a radial axis graph, we can arrange the data points (nodes) based on the first season a player was with a franchise (e.g., 1964). Players starting in the same season will be arranged in a radian originating near the center of the display. In addition, the players’ nodes are then arranged based on the number of seasons spent with a franchise. Let’s have a quick look, using the Anaheim Angels graph:

There’s a lot going on here, but we’ll explain it in the next few sections. First, you can see the structure of the graph, with each season radiating out from the center. The first season for each franchise is located near the bottom center; this will be the longest radian, as every player is new to the team that season. For the Angels, that season is 1961. The seasons are arranged clockwise from there, eventually wrapping back around to the 2025 season:

Title, Legend, and Search

The title, legend, and search function are all contained within a static window to the left of the graph. This window provides simple information about the graph; selecting the More about this visualization option opens a new window that provides greater detail about the graph:

Specific players and their connections can be found using the Search function:

Player Nodes

Each node in the graph represents a specific player. We can hover over any node to see who the player is, and we can click on any node to find out more information about that player, in this case Jered Weaver:

We now have detailed information about Jered Weaver in the Information Pane to the right of the graph. Later in this post, we’ll walk through the graph statistics, but for now, we can see the first and last seasons played, the size (# of seasons), and at the bottom, all of the players Weaver played with for one or more seasons. Each of these Connections can be clicked on to update the display. The size attribute is reflected in the graph; players with more seasons will have larger nodes than those with just a season or two.

Player Connections

The thin gray lines between graph nodes represent the connections between players. The Connections section contains this information, as we just discussed. As you might expect, these connections (edges) aid us in viewing the overall structure of the graph.

Graph Statistics

Network graph analysis uses several calculations to help summarize a graph. These measures can seem rather technical and difficult to interpret. We will simplify things in our upcoming posts for each franchise. In this section, I’ll provide a simple overview of each metric displayed in the Information Pane.

The Degree statistic measures the number of connections a selected player has. Typically, players with lengthy careers have the most connections, but players with multiple shorter stints may also have high degree numbers.

The Eccentricity statistic measures the number of steps required to connect to the most distant node in the graph. This number will be higher (on average) for original franchises dating to 1901.

The Closeness Centrality statistic measures the relative importance (from 0 to 1) of any player within the network. Higher scores indicate an individual who is close to many other players in the network. In practical terms, players who were with a franchise near the middle of all seasons will tend to have higher scores; they may connect to players from both earlier and later eras.

The Betweenness Centrality statistic measures how important an individual node is (from 0 to 1) for traversing the network. Players with many connections are most likely to score high on this statistic.

The Harmonic Closeness Centrality statistic also measures the relative importance of a player (from 0 to 1) in the network. It is a variation on the original Closeness Centrality statistic. We will use this version in our series of franchise summaries.

Summary

That’s it for our overview of MLB radial axis graphs. We’ll start with individual franchises (alphabetized by name) in a couple of days, and will include summaries and a link to the interactive graph. As always, thanks for reading!