When Is Leap Day Most Likely To Happen?


Anyone hoping for an answer besides the 29th of February either suspects I’m doing some clickbait thing, maybe talking about that time Sweden didn’t quite make the transition from the Julian to the Gregorian calendar, or realizes I’m talking about days of the week. Are 29ths of February more likely to be a Sunday, a Monday, what?

The reason this is a question at all is that the Gregorian calendar has this very slight, but real, bias. Some days of the week are more likely for a year to start on than other days are. This gives us the phenomenon where the 13th of months are slightly more likely to be Fridays than any other day of the week. Here “likely” reflects that, if we do not know a specific month and year, then we can’t say which of the seven days the calendar’s rules give us for the date of the 13th.

Or, for that matter, if we don’t know which leap year we’re thinking of. There are 97 of them every 400 years. Since 97 things can’t be uniformly spread across the seven days of the week, how are they spread?

This is what computers are for. You’ve seen me do this for the date of Easter and for the date of (US) Thanksgiving. Using the ‘weekday’ function in Octave (a Matlab clone) I checked. In any 400-year span of the Gregorian calendar — and the calendar recycles every 400 years, so that’s as much as we need — we will see this distribution:

Leap Day will be a this many times
Sunday 13
Monday 15
Tuesday 13
Wednesday 15
Thursday 13
Friday 14
Saturday 14
in 400 years

Through to 2100, though, the calendar is going to follow a 28-year period. So this will be the last Saturday leap day until 2048. The next several ones will be Thursday, Tuesday, Sunday, Friday, Wednesday, and Monday.

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

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