Which date would you guess has the fewest birthdays?

February 29 seems like an easy answer because it happens less often.

But what happens if I compare average births each time a date occurs?

My question: How do birth counts vary across dates and days of the week?

• Social Security Administration birth data, published by FiveThirtyEight.
• United States, January 1, 2000 to December 31, 2014.
• 5,479 rows and 62,187,024 recorded births.
• Each row gives the birth count for one calendar day.
• Columns: year, month, date of month, day of week, and births.

Source: FiveThirtyEight (n.d.), U.S. Births, using Social Security Administration data.

These records cover births in this period. They do not describe everyone alive today or the whole world.

Frequency: the number of recorded births on a particular date.

Relative frequency: that date’s share of all recorded births.

Mean: the average birth count each time a calendar date occurs.

I compare the observed results with an equal-likelihood model. This helps check whether birthdays are spread evenly through the calendar.

The calculations describe this dataset. They are not estimates of every future year’s pattern.

Let \(B_{dy}\) be births on calendar date \(d\) in year \(y\). Let \(n_d\) be the number of times that date occurs in the dataset.

\[ \bar B_d = \frac{\sum_y B_{dy}}{n_d} \]

For September 12:

\[ \bar B_{\text{Sep 12}} = \frac{191{,}024}{15} \approx 12{,}735 \]

Most dates occur 15 times, but February 29 occurs 4 times. Using an average avoids ranking it last simply because it occurs less often.

Choose one birth at random from the recorded births. Its probability of having birthday \(d\) is:

\[ \widehat p_d = \frac{\text{total births on date }d} {\text{total recorded births}} \]

For September 12:

\[ \widehat p_{\text{Sep 12}} = \frac{191{,}024}{62{,}187{,}024} \approx 0.003072 = 0.3072\% \]

If all calendar days had equal birth counts, September 12’s share would be \(15/5479 \approx 0.2738\%\). February 29’s share would be \(4/5479\).

# this part is for ranking dates by average births -MP
birthday_ranking <- birthday_summary %>%
  arrange(desc(average_births)) %>%
  select(birthday, average_births, occurrences)

# this part is for checking the five highest averages -MP
head(birthday_ranking, 5)

arrange(desc(...)) puts the highest average first.

select() keeps the columns needed to understand the ranking.

head(..., 5) returns the first five dates. I use this ranking on the next slide.

September 12 has the highest average in these records.

Four of the five highest dates fall in September. December 19 also appears, so the highest dates do not all belong to one month.

Darker squares show higher averages. September has many dark squares. White gaps mark dates that do not exist.

September 12 averaged about 1.98 times as many births as December 25.

Christmas Day had the lowest daily count in 14 of the 15 years. The exception was May 5, 2013.

February 29 had the lowest total. December 25 had the lowest average per occurrence. These answer different questions.

Why did December 25 have the fewest births in almost every year?

Published research offers an explanation:

Some planned C-sections and induced births are scheduled before or after Christmas to fit families’ and medical staff’s holiday schedules, helping explain fewer births on December 25.

The researchers found that some births shifted away from major holidays to nearby dates.

Source: Jacobson, Kogelnik, and Royer (2020), Holiday, Just One Day Out of Life, NBER Working Paper 27326.

Weekends averaged 8,040 births per day, compared with 12,675 on weekdays: 36.6% fewer.

Births still happened every day. The weekend averages were simply lower.

Hover over a point to inspect its birthday. I use the leap year 2000 only to position dates on the axis, so February 29 fits.

Birthdays were not equally frequent in these U.S. records.

September 12 had the highest average birth count. Christmas Day had the lowest.

The weekday graph also showed fewer daily births on weekends.

Outside research supports delivery scheduling as a contributor to holiday birth patterns. The dataset alone cannot establish that explanation.

The findings apply to U.S. births during 2000–2014. Different countries or years may have different patterns. Changes in annual birth totals also affect these averages.

FiveThirtyEight. (n.d.). U.S. Births [Data set]. GitHub.

https://github.com/fivethirtyeight/data/tree/master/births

File analyzed: US_births_2000-2014_SSA.csv

The repository identifies the Social Security Administration as the original source of the 2000–2014 birth counts.

FiveThirtyEight’s accompanying article explores calendar patterns. The summaries and graphs in this presentation come from calculations using the CSV.

Jacobson, M., Kogelnik, M., & Royer, H. (2020).

Holiday, just one day out of life: Birth timing and post-natal outcomes (Working Paper No. 27326).

National Bureau of Economic Research.

https://doi.org/10.3386/w27326

This research supports the holiday-scheduling explanation. The birth-count dataset itself does not contain delivery-method information.

Presentation: R Markdown with ioslides.

Data summaries: dplyr.

Static graphs: ggplot2.

Interactive graph: Plotly.

Labels and tables: scales and knitr.