Given any two points, a Sigmoid curve can be drawn between the two. As a result, all we need are two rows of data which define the two points in space. Below will lay out the steps to create a Sigmoid curve. And we will also re-create the chart that Jeffrey Shaffer has done with a table of over 2000 rows of data. This creation is inspired by Rody Zakovich's recent post. Rody also has been creating Sigmoid curves using two rows. Joe Mako, Chris Love and Alan Eldridge have done great work on creating curved line by data densification. I am just building on their prior work.

What is a Sigmoid function?

Its math function is written as

y(x)=1/(1+exp(-x)) or y(x)=1/(1+e^(-x))

The drawing of this function is as follows (Curve=y)
Using the Sigmoid curve for connecting two dots could be a better visual representation than just a straight line.

Implementation in Tableau

In our example to show the ranking change from 2012 to 2013, we need two rows data as follows
Then we need to define the number of points we need to draw the Sigmoid as smooth as it can be. Let's pick 49 as the number. Here the first point is at 2012, and the 49th is at 2013.
Another property of the Sigmoid curve is the range of horizontal coordinates. Let's define it to be from -6 to +6.

We will need to create the following calculated fields:
- Index = Index()
- X = 0.25*Index-6.25 (This maps the 49 points from index to horizontal coordinates.)
- Sigmoid = 1/(1+EXP(-X))
- Curve = [2012 Rank]+Sigmoid*([2013 Rank]-[2012 Rank])
Curve is the Y coordinate.
Next, let's create bins (Padded) based on Point. This will help us create the extra 47 points we need for drawing the Sigmoid curve, through data densification.

Drag X to Columns and Curve to Rows, and set them to compute along Padded. Now we will get our beautiful Sigmoid curve!