I'm trying to create a program that takes NBA lineup data, and creates a ven diagram to show the net rating for each combination of a certain number of players (either 2 or 3). For example, with two players, you would have an area for player A without player B, player B without player A, and players A and B playing together. The area of a circle represents the number of possessions played by that player (so circles can be different sizes) and the area of the intersection corresponds to the number of possessions played by that combination of players.
I have the data sorted, but my main problem is developing the math to determine the positions of the circles in the ven diagram. It's fairly easy with a two-circle ven diagram. However, I've found it's much more difficult with three circles. One strategy I considered was using the strategy from the two-circle ven diagram to find the intersection of A and B, and A and C, then rotate one of the circles around the center of A to create a third intersection with C. Screenshot of this strategy. Large circle is circle A, smaller circles are circles B and C The issue with this, however, is that I can't figure out how to adjust the area of the intersection of all three players, without changing the areas of intersection representing two players without one player. Does anyone have any ideas on how to solve this problem (it doesn't have to use the rotating circles idea)
You can't. If we normalize to the time A spent alone you have six values you want to represent, the ratio each other combination played to the time A played alone. We can also normalize the A circle to unit radius and you only have five adjustable parameters, the radii of the two other circles and the three distances between the centers. You need one more knob to turn.
One approach would be to allow one of the circles to become an ellipse. Even with circles I don't have a simple formula for the area of the three-way intersection based on the radii and distances between the centers. Another approach would be to do get the intersections right, then add or subtract area from the solo playing time pieces as required. That is nice because you have three values to represent and could hope to do it with three circles of the same radius, just using the three distances between the centers.