In response to some questions at the APBRmetrics forum, I’ve put together a new NBA similarities network (Top 250 players version), wherein I use per-minute statistics, instead of my “patented” ratios method, just to see how it looks. In a lot of ways, this looks just as good or even better than the ratios version… I’m still somewhat torn, though: The ratios method, by ignoring time statistics completely, attempts to match players who, given a possession (or given an opponent with a possession), will do similar things with it, while the per-minute method does a better job of representing “substitutability.” I suppose I will let history be the judge, but I don’t think anyone loses when more pretty graphs are made:
NBA player similarities [pdf]
Another version with Extremely High Contrast Labels for Easy Reading: [pdf]
For more information, just refer back to my last post, which dealt with this same methodology applied to the NBA. I’ve done the same thing here with some of the top quarterbacks in NFL history. This time, I used propensity to rush vs. pass, and yds/att and yds/rush to color-code them. I’ll let you make your own analysis, football’s not my specialty:
Quarterback Network Diagram [pdf]
Having covered my operationalization of statistical similarity, and offered some evidence of its usefulness, I’d like to share what I perceive as the best part of the whole endeavor, the pictures. Using R and the sna package, along with the distances I’d previously computed [zip], I’ve put together a network diagram of player similarity. Basically, each player has two or three arrows coming out of him, pointing to the players that are most similar to him. Then, using some brilliant algorithm I don’t fully grasp, each player is plotted so that they all cluster together in groups, by similarity. I’ve then colored each player/node according to the usual formula, meaning that each is colored according, basically, to how their contributions are distributed. Past analysis has indicated that propensity to take shots, post-area stats, and perimeter-area stats (to apply somewhat arbitrary characterizations), are a good way of determining colors. See other posts for more on this. Anyway, I have two versions each of two different networks: Both .png and .pdf versions of the Top 250 players of the modern era, and then .png and .pdf versions of players 251-500, the second tier. (I recommend looking at the .pdfs first, because they’re higher-resolution, and easier to scroll around. Note that the .png and .pdf versions are different because of the way the plotting algorithm works… it’s the same data, shown in a somewhat different way.) I hope you find this interesting and/or useful, and please feel free to comment on the validity of this approach.
Tier One [pdf] [png]
Tier Two [pdf] [png]
Update: If you like those graphs, you will really really like these:
I’ve created a timeline of the ebb-and-flow of party politics in the US Senate since the beginning of the modern (Democrat & Republican-dominated) two-party era. Beginning with the antebellum 35th Congress, and progressing through to the 109th, this timeline tells the story of the evolution of politics in America as played out on the floor of the Senate.
Political Scientists, Historians, and even casual observers of political history have long noted the shift in ideological nature of the two major parties since the Civil War, and within the 20th Century alone–this timeline conveys a sense of that shift by depicting the scaled left-right ideological positions of each Senator along the vertical axis: a macro view of the entire time period illustrates the great distance between the parties up until the mid-20th Century, at which time Civil Rights-related issues began to create crosscutting cleavages within the parties, especially in the South. The bright green of Southern Democrats, voting with the Republicans in a Conservative Coalition, is readily apparent, as the distance between party medians converges.
Just as apparent is the realignment beginning in the late 1970s-early 1980s, where, as Political Scientists have documented, the polarization of the electorate and of elected officials became a dominant trend. This is illustrated both in the main timeline, and also by the series of density plots just below the main frame. At various times, the ideological distribution is obviously unimodal, or obviously bimodal: from the 79th to the 109th Congress we can witness the polarizing of the Senate, which according to the theory of Conditional Party Government, has lead to skewed policy outcomes.
This visualization rewards careful inspection–there are stories to be found everywhere: follow the positions of the Presidents, relative to their own party members; note how party leaders are typically close to their own party median, find patterns in individual states’ ideology over time–at any level of inspection, the data offer up a rational yet compelling history.
The ideological dimensions are determined based on Senate Roll-Call votes, and scaled to be historically consistent, such that comparisons may be made across historical eras. The measure is called DW-NOMINATE, and was developed by Kieth Poole and Howard Rosenthal. Please leave any comments or questions, as this work is constantly under progress.