Friday the 13th

[den]

Comes after Thursday the 12th

Comes before Saturday the 14th.

that's all there is to it.

Comments

[klishnor.livejournal.com]

You do know that statistically, the 13th falls on a Friday more than it does any other day of the week.

[starcat-jewel.livejournal.com]

That doesn't make sense. Do you have the proof easily available, or a link to same?

[klishnor.livejournal.com]

I used to have a mathematical proof back when I was in the 6th form at school (back in nineteen hundred and frozen stiff), given to the class by a math's teacher in a General Studies course. He was demonstrating various mathematical and statistical oddities, like the impossibility of giants (at least in the traditional shape) and why that relates to elephants walking on their toes, why building a small version of an airship is not a good way to test for stability in a larger version, why we have so much trouble estimating probabilities and many other things.

What's happened to that set of notes in the years since then I have no idea.

I'll check with a few statisticians I know to see if they've got it.

[klishnor.livejournal.com]

Just found a page which gives some detail. It seems that you have to live for a LONG time for the effect to appear.
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Claim:
The 13th of the month is more likely to fall on a Friday than on any other day of the week.

Truth:
That's true or false, depending on what you mean.

One of the first things to do with claims of "likely" is to determine the scope. The choice of timescale determines whether this claim is as valid as stated.

It is false

The Gregorian (and Julian, for that matter) calendar has 14 possible single year calendars. Pick a weekday for January 1st and whether it is a leap year, and that gives the calendar (that's how those perpetual calendars in almanacs work).

In a normal, stable, situation those calendars repeat in a cycle of 28 years. Within that normal cycle of years, the distribution of 13ths to Fridays is exactly 1/7 of the total. The seven leap year calendars have a total of 12 Fridays which fall on the 13th of the month. The total for the 7 non-leap year calendars is the same.

In the 28 years, you get each leap year once and each non-leap year three times, for a total of 48 Fridays on the 13th of the month. Since 28 years have 336 months, and 48 * 7 is 336, this is exactly even.

But it is also true.

The discussion above focused on the case of normal year cycles within the Gregorian calendar. That means that it holds for timescales which do not cross exceptional years (that includes my lifespan and the lifespans of everyone likely to be reading this).

But there are times when the normal cycling of years is disrupted. In a sense, that was the whole point of establishing the Gregorian calendar.

Within the Gregorian calendar, centennial years (those evenly divisible by 100) are only leap years if they are also divisible by 400. For example: 1800, 1900 and 2100 are not leap years. (1700 wouldn't have been, had the calendar change been adopted by then.)

When a timeframe crosses one of these, the frequency of the calendar repetitions gets skewed, and the distribution is no longer even. This is because replacing that single leap year with a non leap year not only replaces that year. It also disrupts the cycle of years such that an entire section of the sequence is omitted.

Any particular year may have one, two or three 13ths falling on Friday. If the section dropped has an average number of Friday the 13ths greater than 12/7 (1.7142) then the overall average will drop. If the omitted section has an average less than 12/7, the overall average will rise.

Crunching the numbers for a 400 year segment yields this distribution:-

Sunday 687
Monday 685
Tuesday 685
Wednesday 687
Thursday 684 Min
Friday 688 Max
Saturday 684 Min

The expected number for each day with an even distribution would be:-
400 years * 12 months / 7 calendar days = 685.714

Conclusion

So, it seems that if you are Duncan MacLeod, then you experience Friday the 13th more often then Monday the 13th. But for the rest of us, it is all evenly spread out.
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So statistically, and over a long period, it's true, but most people won't see any difference in their lifetime, and a maximum difference of 4 over 400 years would probably go unnoticed anyway.