When is Easter this year? I ask this question every year! This year, Easter occurs on April 16, 2017. Next year, Easter falls on April 1, 2018. I have a hard time remembering when it occurs in any given year. I think that March Easters are both early and unusual. Is that true?

Being a statistician, my first thought is to study the distribution of Easter dates. By analyzing the distribution, we can determine which dates are rare and which are common. How unusual are Easter dates in March? Are there patterns in the dates?

Let’s first look at the official determination for when Easter happens. The holiday falls on the Sunday after the Paschal Full Moon date of that year. What? To clarify, the Paschal Full Moon is the Ecclesiastical Full Moon that falls after March 20. Huh? This definition isn’t helping me! Let’s graph the data. That’ll clarify things!

In this post, I study the dates of when the Western Easter occurs to answer all of these questions. I’ve obtained all the Easter dates that occur within the Gregorian calendar, which runs from 1583 to 4099. You can download the CSV data file for Easter_dates.

## Graphing Counts of Easter Dates: 1583 to 4099

Graphing any dataset is a great way to get a quick sense of the data. Below, I graph the distribution of all Easter dates from 1583 to 4099. At a glance, this chart tells us which dates are common and rare. To fit on the graph, I coded the dates. For example, M27 is March 27 and A16 is April 16.

The X-axis shows us that Easter dates can range from March 22 to April 25. There are 35 possible dates. The distribution has an extended center where the count of Easters by date stays around the average of 72. The date with the most Easters is April 10, which has 102 (4.05%). The date with the fewest Easters is March 23, which has only 14 (0.56%).

It’s only in the extreme tails of the distribution where you find Easter dates that are very rare. The earliest three Easter dates (March 22 – 24) and the latest three Easter dates (April 23 – 25) are pretty unusual. The graph shows us that the earliest three dates are rarer than the latest three dates.

To demonstrate this, Easter happens on the first possible date of March 22 only 0.60% of the time. The holiday last occurred on March 22 in 1818, and it won’t fall on this date again until 2285. That’s a span of 467 years!

Conversely, Easter occurs on the last possible date of April 25 1.03% of the time. It last fell on March 22 in 1943 and won’t fall on this date again until 2038. That’s a period of 95 years. I might be alive to celebrate that one!

## How Rare are March Easters?

I suspect that when Easter falls in March people say it’s early. The previous graph showed us that most Easters fall within April. Let’s use a probability distribution plot to see exactly how often it falls in March.

The red area shows us that about 23% of all Easters happen in March. That’s about 1 out of 4 years. That’s not incredibly rare, but it is still a bit unusual. The last time it was in March was 2016, and we have to wait until March 31, 2024 for the next time. That eight-year gap between March Easters is unusually long!

Now we know which Easter dates are common and rare, let’s move on to patterns!

## Are There Patterns in the Easter Dates?

Do patterns exist in Easter dates? If Easter falls on a specific date this year, can we predict when it will fall on that date again? To answer this question, I’ll use another graph. The plot below displays the rate of first recurrences by the number of years.

The large spike at 11 years really pops out! This peak tells us that for 1,141 Easters (45%) the first time Easter repeats its date is in 11 years.

Let’s see how this 11-year pattern fits the next 10 Easters. The dates below indicate that 6 of the next ten Easters first reoccur on the same date in 11 years. That’s 60% of the Easters, which is a bit higher than the overall percentage (45%). In statistics, it’s crucial to understand the larger context before drawing conclusions.

Another thing that leaps out at me is the small number of possibilities for when Easter can first repeat a date. If a value does not appear on the first recurrence graph, Easter never repeats the date in that number of years. For example, an Easter date cannot first reappear in 1, 2, 3, 4, 7, 8, 9 years, and so on. In the 2517 Easters in the Gregorian calendar, there are only 24 possible values for when it can first repeat a date.

The official determination for when Easter happens only served to confuse me. However, standard data analysis procedures provided crystal clear answers about Easter dates.

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