Eliot Deviation Index

What if there was a measure of how straight a transit line's routing is? How direct is this routing? I had those questions on the afternoon of May 3, 2022. Those were the fundamental questions behind the Eliot Deviation Index - the measure that answers those questions. Put simply, the Eliot Deviation Index of a transit route is the ratio between the line distance and the displacement.

What exactly is the Eliot Deviation Index and how is it calculated? The measurement is calculated by adding together the straight line distances between each stop, and then dividing it by the displacement of the route. The calculator uses the Haversine formula and spherical trigonometry to determine distances. By definition, the Eliot Deviation Index is a linear approximation, and any other calculations claiming to be the "true Eliot Deviation Index" that do not match with the measurements on this website are false and should not be trusted.

In most cases, the Eliot Deviation Index of a route is greater than or equal to 1.0 (that's how the math should ideally work), but there are a few cases where the Eliot Deviation Index is between 0.9 and 1.0. This is due to the curvature of the Earth and the use of spherical (not linear) trigonometry.

Not every transit line is eligibile for an Eliot Deviation Index. There are three criteria that all routes must meet.
1. The line must begin and end at different stops. No loops allowed.
2. The line must have at least three stops.
3. The line must not end along the return journey to the beginning.

Try it Yourself
Want to see the magic of mathematics in action? There is a button at the top of this page that says "Calculator", which will bring you to the online calculator, where you can check out detailed stop listings for any route that has an officially calculated Eliot Deviation Index. You can also use the stop listing on this website to create a custom route and see what the Eliot Deviation Index would be.

Would you like to contribute to the database? There's a whole contribution guide here to help you. Please follow it.

Special Thanks
The Eliot Deviation Index could not have made it this far without some help.
Thanks to those first interested in the measurement in May 2022, when there were only 300 stops in our database.
Thanks to those who questioned the definition of this measurement, in order for me to further clarify what is eligibile and what is not. Not every bus route is the same.
Thanks to the team at my high school who allowed me to tell the story of the Eliot Deviation Index to the rising seniors in the class of 2023.
Thanks to Stormy Kara for providing the stop listings for various CTA and Pace bus routes.