Schwarzenegger’s Nastygram: One in 10 Billion?
EmailWhat are the odds California Gov. Arnold Schwarzenegger’s acrostic nastygram could have happened by random chance? My opening bid is about one in 10 billion.
That’s not the right answer, but it does provide a rough sense of what the governor’s up against. My aim's to point some well-deserved incredulity at his spokesman’s explanation that it happened by chance – and to invite readers with a stronger statistical bent than my own to figure the real odds.
This centers on today’s delightful story about Schwarzenegger’s recent veto of an uncontroversial piece of legislation sponsored by a California lawmaker who’d crossed him. As our Teddy Davis explains here, the first letter of each of seven lines in the governor’s message together spell two famously choice words.
The governor’s spokesman, possibly with a straight face, calls it “a weird coincidence.”
What are the odds? Here’s how not to figure it precisely, rather a quick and unsophisticated back-of-the-envelope calculation: If the odds of picking a particular letter at random are one in 26, doing it over seven selections (the number of letters in question) is (1/26)^7, or .0000000001245. Just about one in 10 billion.
Small odds.
This, though, admittedly is not my field. A real calculation would take into account other matters, such as the frequency with which the individual letters in question start words, the ordering odds and the chances of a line break appearing in just the right spot between the two words in question, as it does.
Go figure. Replies welcome, notation and all.
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Actually, you could possibly even include the first letter (so that it’s “I…” well, you know), which would make it 8 letters long which, by my calculation, would be 1 in about 108 trillion chance or so.
Of course, not every letter will have an equal chance of starting any given word, so you have to start there. Then you have to go to the chance that 7 (or 8) letters would just happen to start words on a new line in that order, and then you’d have to consider the chances that the paragraphs would just happen to break like that to form those words.
Methinks it’s a lot more than 1 in 10 billion (or maybe even more than 1 in 108 trillion)
Posted by: Josh | October 28, 2009, 1:04 pm 1:04 pm
By your method of calculation, (and leaving aside relative frequencies of letters) the odds would be the same for any sequence of seven letters. Thus, whatever the sequence of was formed by the first letter of each line, the odds would be 1 in 10 billion against it. So the actual sequence fares no worse than any other. What one should try to calculate is the odds that a random sequence of seven letters should be a sequence of English words, or perhaps a sequence of English words with an appropriate meaning. I guess you’d have to come up with some estimate of seven-letter sequences that express that meaning and divide it into the number of possible seven-letter sequences to get a meaningful estimate.
Posted by: Simon | October 28, 2009, 1:46 pm 1:46 pm
Thanks for o good rough calculation and an unusually accurate description of its limitations. Given the standard letter frequency guide “etaion shrdlu”, the odds probably get quite a bit longer, since these aren’t the most common consonants by any means. of course, that’s not quite the same as starting letter frequency.
On the other hand, in any odds calculation, you have to consider that this passage was selected ex post facto from many other possible passages by this and other governors. It’s possible that the odds of some governor doing this by accident sometime (as opposed to a particular time) could then go way, way up, maybe even to one in a a hundred thousand.
Posted by: mbw | October 28, 2009, 1:55 pm 1:55 pm
Using letter frequencies, the following script says the probability is 0.00000000000053937610200661%
Posted by: yc | October 28, 2009, 2:32 pm 2:32 pm
Link got deleted:
(remove the space, obv)
Posted by: yc | October 28, 2009, 2:45 pm 2:45 pm
Don’t forget to multiply the odds of this sequence in a 7 line letter by the odds of a veto letter being exactly 7 lines.
Posted by: AD13Resident | October 28, 2009, 2:51 pm 2:51 pm
I’m not a real statistician, but assigning a probability to each letter (never mind the space) based on its frequency in the English language, I get a probability of 1 in 5 trillion. That’s because, except for the “o,” all of the letters in the problem have less than average frequency and the “k” is only .0072 or seven chances in a thousand. But somebody better check me on this.
Posted by: Philip Meyer | October 28, 2009, 2:57 pm 2:57 pm
What are the chances it was done on purpose?
Posted by: JOe C. | October 28, 2009, 3:22 pm 3:22 pm
We should look for first-letter distributions, not all-letter distributions.
Based on this site’s info:
I got 1-in-900 billion odds of 7 randomly-selected words starting with those 7 letters. If we grant Arnie the benefit of the doubt, that he wanted to start the first paragraph with “f” and the second paragraph with “y”, then the odds go down to 1-in-270 million.
Posted by: Mike | October 28, 2009, 3:26 pm 3:26 pm
Actually — The odds of selecting any 7 letters (when repetition is not restricted) would be calculated as one in 26 to the power of 7, which is 8,031,810,176 or approximately one in 8 billion, NOT ONE IN 10 BILLION.
Posted by: SpinyNorman | October 28, 2009, 4:14 pm 4:14 pm
This is absurd. He obviously did it on purpose!
Posted by: Joe | October 28, 2009, 4:21 pm 4:21 pm
Not a math whiz, just a Python fan wanting to call out the giant hedgehog a couple posts back. What a silly bunt . . . what are the odds of that?
Posted by: John | October 28, 2009, 5:02 pm 5:02 pm
What are the odds for an Austrian bodybuilder to be embraced in Southern California by an industry that didn’t exist, become a movie star without knowing how to act, reach the Government of California through a recall and marry a Kennedy?
Posted by: Tomas Sancio | October 28, 2009, 6:55 pm 6:55 pm
Who has so worthless of a life that they bother to even look at what the first letter in a string of sentences might spell???
What if you took the 3rd letter after each occurrence of the capital letter “F”, and the 2nd letter after each occurrence of the letter “f”…. gee, lemme see….
Posted by: Fed_up_with_BOTH_Parties | October 29, 2009, 3:07 am 3:07 am
Digression: Decades ago, Paul Goodman wrote a book entitled “The Empire City”, in which he writes out in musical notation representing Morse code (half notes as dashes, quarter notes as dots) the same seven letter phrase being played on the drums by a Boy Scout band.
What are the chances? Obviously slim and none, with slim out of town.
I suppose the bill is numbered alphanumerically as 4Q.
Posted by: Nat Ehrlich | October 29, 2009, 1:57 pm 1:57 pm
The letter is great! It is completely subtle. I would never have looked down the side like that. Was there a copy of the letter floated with the side in yellow high-lights or something? A high-lighted letter could just show up somewhere, somehow or another without incriminating the governor’s office. I think it would have just gone over everyone’s head without some sort of a guide or hint. The governor’s probably mad that the whole letter doesn’t form a complete sentence. Way to go Arnold! (That legislator shouldn’t have just yelled at him at the fundraiser and then walked off.)
Posted by: Wendy Landers | October 30, 2009, 1:39 pm 1:39 pm
Well I thought about this.
How often could it happen?
Only rarely I suspect.
Chance isn’t an exact science.
And it’s difficult to guess.
Reasonable to assume though.
Even for a novice.
So there it is :)
Posted by: Suki | November 8, 2009, 9:16 am 9:16 am
You are setting the rules after the event. There are several many other words that could have been used. It could have been the last letter of everyline, or middle most, or diagonal. It did not have to be a a letter, it could have been an email, a printed speech, a bill. We would still be discussing this if it was some other random celebrity so it did not have to be Arnold. Think of all the kooks that find hidden messages in letter strings in the bible. Simple example: your mother produced 40,000 eggs, your father produce 100 of billion sperm, the chance that you could come into existence is nearly impossible but it happened.
Posted by: tjl | November 12, 2009, 10:15 am 10:15 am
Here are some other calculations. You can get more or less any number you want. The probabilities are essentially meaningless:
Posted by: Philip | February 5, 2010, 2:08 am 2:08 am