Topological Analysis of Baseball Batting Data

For this analysis I examined baseball hitting data from the 2015 season from the Lahman Database at http://www.seanlahman.com/. My objective was to categorize different types of offensive players. 

This following plots were created by using CEDAR with eccentricity and density as the lens functions.

The coloring on this first plot is based on number of games played in a season by each player. The blue nodes contain players with a lower number of games played, while red indicates a higher number of games played. As we will see in other plots, the number of games played is correlated with many other statistics. This intuitively makes sense, because players who play in more games have more opportunities to increase their other statistics. 

The first identifiable group was "low impact hitters and pitchers". These players are identified by the low number of games they played in, and thus low numbers of other statistics. Pitchers fall into this category because they typically have a very small number of at-bats per season, especially for those pitchers in the American League because of the designated hitter rule. Having a higher number of games played than at-bats is also typical of pitchers, particularly for the American League. This group is the circled flare on the right side of the graph below. These players had an average of 22.8 games played and 6.2 at bats. This group is circled below.

Coloring by Games Played

Now when we color by number of hits, we see a similar coloring scheme. The players who played in a higher number of games also had more successful hits. The next group I identified were what I call "role players." These players had a higher number of games played and at-bats than the low impact players, but a lower number of hits than every day players. This players would be used in pinch hitting situations or as substitutes for every day guys when they need a day off. They averaged 115.2 at-bats over 48.2 games played. This group is circled below.

Coloring by Hits

The next group I identified were "high impact hitters." These players have a high number of home runs, RBIs, and doubles. These hitters averaged 32.8 doubles and 25.8 home runs, and 83.5 RBIs. This group is circled in the two graphs below.

Coloring by Home Runs

Coloring by RBI

High-impact hitters also are more likely to be intentionally walked than other types of players, so that they don't have the opportunity do drive in more runs. This is apparent from the following coloring, based on intentional walks.

Coloring by Intentional Walks

The next group I identified was what I call every day players. These players appeared in most games throughout the season and had a high number of at bats, but didn't have as many RBIs, home runs, or hits as the high-impact hitters. They averaged 14.1 home runs, 56.4 RBIs, and 120.46 hits while appearing in an average of 120.5 games.

Finally, I considered another group of players as "transitional/ on the fence players" if they were between the every day players and the role players, including some of the role players with a higher number of at bats and hits. These players played in an average of 68.1 games, with 195.8 at-bats. These players are getting more playing time than most other role players, but are on the verge of being every day players.

Coloring by Hits