# The Eliot Deviation Index

### May 3, 2022

Did you ever want to know how straight a transit line's routing is? You probably didn't, but I did. I don't know any formula, calculation, or other data tell me how direct a route is compared to another. So I created one. Introducing the Eliot Deviation Index (EDI). I named it after me because I could.

So what exactly is the EDI? A transit line's EDI is a measure of how straight the routing is. The more deviations away from a straight line, the higher the line's EDI. A straight line has an EDI of 1.0.

How is the EDI calculated? Calculating the EDI requires the use of the Haversine formula, which is really complicated. Even with me being a wizard with math, I'm only in high school calculus as I write this and I can't explain the Haversine formula yet. For now, here's the Wikipedia article. What it does is calculate the distance between two points on a sphere. It can be used to find the distance between two points on the Earth using their latitudes and longitudes. There is a multiplier to include to convert the distance to miles.

In order to calculate a line's EDI, I needed to get the distance between every stop to the next. The Haversine formula is looped for each station pair. The EDI is the ratio of the line length to the distance between both termini.

There are also shortcomings of the EDI. The EDI doesn't do well with express routes along highways. Highways are fast, but might create a less straight routing. The EDI calculator doesn't know speed, just distance. Also water is a problem. It doesn't know where water exists. It's trigonometry, not geography. Routes like RIPTA's 60 would need to go straight through the water to see an EDI of 1.0.

As I write this, I'm still working on the EDI calculator, but I do have one EDI calculated. That is the MBTA Blue Line. The Blue Line, with 12 stations, has a track length of 6 miles (according to Wikipedia). The EDI calculator's line length is 5.76 miles (which is actually the sum of the straight lines between adjacent stations). The calculator calculated the distance between Bowdoin and Wonderland to be 5.10 miles, leaving the Blue Line with an EDI of 1.13.