Odds are Good

This is annoying, because it (again) shows that people have an impoverished sense of what probability means.

Because they can't wrap their head around an "event."

The incident:  Michigan lottery "picks" same 4-digit number two days in a row?  What are the odds of THAT happening?  It must be (pick one:  God.  Fraud.  Sign that probability isn't real.  Etc.)

Well, it depends on what you mean by "THAT" in the paragraph above.  Consider:

• 44 US states have lotteries. Let's say they all have a 4-digit game, to keep things simple.
• There is a lottery result every day, all 365 days per year.
• The chances of hitting any given number is 1/10,000  (because 0000 is a possibility, up to 9999, by ones)

 So, if "THAT" is the chance of the Michigan lottery having exactly the same number two days in a row, then THAT is pretty unlikely.  It's 1/10,000 every day, because it's the chance of hitting yesterday's number again today.

But if we are talking about one state lottery somewhere (there was nothing special about it being Michigan, ex ante) on some day in given year (there was nothing special about those two days), then THAT is just the chance one lottery out of 44 picks the same number on consecutive days, out of 365 (since it could happen on the first day, but that would be across years).

If there are 44 4-digit lotteries every day, and the probability of getting a different number in each particular lottery is 9,999/10,000, that means that the probability of duplicate numbers in SOME state (out of 44), on a given day, is .00439.

But we do that 365 times per year.  Since the chance of no duplicates in all 44 states, on a given day, is .9956, the chances of no duplicates for a year is .9956^365 or .2007.

If that's right (and I'm just doing this back-of-the-envelope, so I've probably made a mistake in logic or calculation!), that means that in any given year the chances of a duplicate lottery, two consecutive days the same number, in some state, is about 80%.

Does that sound right?  If you carry out to multiple years, say 5 years, the chances of getting at least one duplicate in at least one state are better than .999.  It will be a little more complicated in real lotteries, because they are not all simple "pick four digits between 0 and 9," but the same sort of logic applies.

With the caveat, again, that I have likely made a mistake.  The question, then, is whether consecutive duplicates are really as common as this calculation implies.  Thoughts?

Example.....  Example.....  Example..... Explanation.

Excellent example...

Lagniappe:  Scott de M suggests an exercise, left to the reader:  Prove that some athlete, somewhere, in some sport, has a jersey number that matches both  his age and number of wins he has played in.

Is Kim Williams in bed with Big Vegan?

Well he's the president-elect of the American College of Cardiology.

And he's a vegan.

So naturally, "some critics suggested that Dr. Williams and the college were “unduly influenced by industry,”"

Ah yes, he must be in the pocket of the notorious Big Vegan cartel!

Is this a great country or what?

V is for Victory!

Last Friday, writing about our no good, terrible jobs report I said:

The interesting question is whether this is just a soon to be revised blip on the road to full employment or if this is a harbinger of another spring-summer slowdown after a promising fall and winter. Last year showed a definite V shape in job growth as did 2011 to a lesser extent.

In the comments on a subsequent post about bad thesis advisors, I was excoriated for the above statement as follows:

its bogus (because with one reference - one's own eyes - it clearly is bogus). I'm not sure macro is much better than literary theory

OK. So I took the jobs numbers for 2011 and 2012, averaged them by month and plotted the monthly averages. Here's what I got:

Sweet fancy Moses. As I live and breathe, it's a V-SHAPED CYCLE.

Take THAT literary theorists.

Let me see you average Derrida and Foucault by month and get such a nice looking V out of it.

Macro rules.

Job wars

Nothing takes worse of a beating in presidential elections than do facts and figures.  We know that (a) our employment levels have not recovered to their pre-recession levels and (b) job losses in this recession are far worse than in any post-war recession.

But yet someone manages to produce this (clic the pic for an even more misleading image):

So this "recovery" is "normal", even though we know it isn't.

The trick is accomplished in three steps. The first is by using the total number of jobs and not taking into account that the labor force is much larger now than it was in 1990 or 2001. The second is to date the chart from the bottom of the recession. The third is to ignore all the other post-war recessions.


The invaluable Calculated Risk blog provides a more accurate view about the strength of our current recovery (clic the pic for an even more enlightening image):

Yes people, that is actually where we are and what we are still up against. The first graph is roughly comparing the upward sloping part of the red line against the upward sloping part of the brown line (the 2001 recession and recovery) on a total number of job basis instead on of a percentage of jobs basis, and trying to get you to think that we are better off in this recovery than we were in the 2001 recovery, which of course is utter nonsense.

On a more positive note, I am fairly certain that Bin Laden is actually dead.