# Computing your Eddington number using the eddington package.

## Introduction

One statistic that cyclists might be interested to track is their Eddington number. The Eddington number for cycling, E, is the maximum number where a cyclist has ridden E miles on E distinct days. So to get a number of 30, you need to have ridden 30 miles or more on 30 separate days.

This package allows the user to compute Eddington numbers and more. For example, users can determine if a specific Eddington number is satisfied or how many rides of the appropriate distance are needed to increment their Eddington number. It also contains simulated data to demonstrate the package use.

## The Data

Loading the simulated data is simple. Let’s take a quick look at the first few lines.

library(eddington)
#>    ride_date ride_length
#> 1 2009-01-04        5.97
#> 2 2009-01-06       11.59
#> 3 2009-01-10       17.10
#> 4 2009-01-11       12.51
#> 5 2009-01-18       10.70
#> 6 2009-01-18        7.73

First, we need to establish the granularity of the data. As you can see above, there are at least two entries for 2009-01-18. Since this data simulates a rider who tracked each individual ride, there could be more than one ride per day in this dataset. Therefore, we need to transform the data to aggregate on day.

library(dplyr)

days <- rides %>%
group_by(ride_date) %>%
summarize(n = n(), total = sum(ride_length))

#> # A tibble: 6 × 3
#>   ride_date      n total
#>   <date>     <int> <dbl>
#> 1 2009-01-04     1  5.97
#> 2 2009-01-06     1 11.6
#> 3 2009-01-10     1 17.1
#> 4 2009-01-11     1 12.5
#> 5 2009-01-18     2 18.4
#> 6 2009-01-19     1 13.4

Let’s just take a quick peek at the summary stats:

summary(days)
#>    ride_date                n             total
#>  Min.   :2009-01-04   Min.   :1.000   Min.   : 2.17
#>  1st Qu.:2009-04-07   1st Qu.:1.000   1st Qu.:11.37
#>  Median :2009-07-15   Median :1.000   Median :15.02
#>  Mean   :2009-07-05   Mean   :1.404   Mean   :19.21
#>  3rd Qu.:2009-09-28   3rd Qu.:2.000   3rd Qu.:25.04
#>  Max.   :2009-12-31   Max.   :5.000   Max.   :77.71

### Histogram of Daily Mileages

This plot provides a histogram of daily mileages. Note the summary Eddington number is in dark red—we’ll see how that’s calculated in the next section.

## Computing Eddington Numbers

To compute the Eddington number, we use the E_num() function like so:

E_num(days$total) #> [1] 29 ### Cumulative E To see how the Eddington number progressed over the year, use E_cum(). It can be useful to add the vector as a new column onto the existing dataset: days$E <- E_cum(days$total) head(days) #> # A tibble: 6 × 4 #> ride_date n total E #> <date> <int> <dbl> <int> #> 1 2009-01-04 1 5.97 1 #> 2 2009-01-06 1 11.6 2 #> 3 2009-01-10 1 17.1 3 #> 4 2009-01-11 1 12.5 4 #> 5 2009-01-18 2 18.4 5 #> 6 2009-01-19 1 13.4 5 It might be more interesting to see that graphically: ## Addtional Functionality ### Incrementing to the Next Eddington Number So now that we know that the summary Eddington number was 29 for the year, let’s see how many more rides of length 30 or greater that we would have needed to increment the E to 30. E_next(days$total)
#> Your current Eddington Number is 29. You need 3 rides of 30 or greater
#> to get to an Eddington number of 30.

### Stretch Goals

An ambitious rider might be interested to see the number of rides required to reach a stretch goal. Say, how many more rides would have been needed to reach an E of 50? For that, we use E_req(), which stands for “required.”

E_req(days$total, 50) #> [1] 46 ### Check if a Dataset Satisfies an Arbitrary E We could also check to see if we’ve gotten to 30 by using E_sat(), which stands for “satisfies.” E_sat(days$total, 30)
#> [1] FALSE

## Conclusion

The text above should give you a good start in using the eddington package. Although this package was developed with bicycling in mind, it has applications for other users as well. The Eddington number is a specific application of computing the side length of a Durfee square. Another application is the Hirsch index, or h-index, which a popular number in bibliometrics.