sports

The above is a 3D multidimensional scaling representation of the similarity of 14 popular sports. At least 3 dimensions are necessary to represent the similarity matrix; here I've rotated the plot so as to make the different points (sports) clear.

Euclidean distance between the sports is closely related to their similarity, but since this is a 2D projection of three coordinates, I also included edges (lines) between the sports as an extra cue to distance. The thickness and coloring of the edges is mapped to the similarity values (red/thin is "dissimilar", while blue/thick is "similar"). For each sport edges were drawn to the three nearest neighbors - sometimes those were very similar (e.g. the hockey triangle), sometimes very distant (baseball is very close to cricket, but it's next nearest neighbors are very far away: golf and ping pong).

Okay, so what constitutes "similarity" here? I made a list of 28 "sports properties" based entirely on my own subjective knowledge of the included sports. Undoubtedly a better list could be composed, but this is an okay first approximation. The set of properties works as a "present or not" binary value for each sport.