Acknowledging incorrect facts but not incorrect logic

What is the chance of seeing an "Original Six" NHL Final, like we did this past season with Chicago facing Boston?

Well, the Finals are comprised of one team from each conference.  After realignment, five of the Original Six are in the East, and one (Chicago) is in the West.  Both conferences have fifteen teams.

So, if all teams have an equal chance, the probability is 5/15 (One of the five reaching in the east) multiplied by 1/15 (Chicago reaching in the west).  That's 1/45, or 2.2 percent.

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This came up in a recent article in Sports Illustrated:

"In the future, with only Chicago in the West, the random odds, calculated by David Madigan, chair of the statistics department at Columbia, shrink to 2.2%."

That made me a little sad, that an expert had to be quoted.  

I guess I can't really complain, because the writer had to do it ... even if he understood how to calculate the number -- which I suspect he did -- skeptical readers would believe he pulled the number out of his butt, if it suited their preconceptions.  

That got me wondering what the criterion is, for when you quote an expert as opposed to just stating a fact.   

"Over 82 games, an NHL team can accumulate as many as 164 standings points, according to Dr. Mary Doe, of the Mathematics department at Harvard."

That wouldn't happen, right?  Too simple: 82 games, times two points a game.  How about,

"The chance of a fair coin landing heads twice in a row is 25%, according to John Smith, mathematics professor at Yale and author of several texts on probability theory."

Probably not: the reporter would probably just explain how that 25% is calculated.  But what about more coins?

"The chance of a fair coin landing heads six times in a row is less than 2%, according to ..."

That one would probably happen.

This is just from my gut ... it almost seems like there's a rule, that if it's not something simple enough for most readers to understand, you're not allowed to just state it without having a source.  And that seems to be the case even if you know it for yourself.  It's almost like ... if it turns out to be wrong, it's important that it not be the reporter's fault.

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In that regard, it always seemed strange to me how journalism is so careful about correcting "facts," but so lax about acknowledging bad logic.  Here's an example I'm making up (but based on actual articles I've seen):

"Speeding on Anytown roads is at its highest level ever.  At any given time, 60 percent of city drivers are exceeding the limit, according to researchers at the Anystate Insurance Institute.  And the lack of enforcement exacts a hefty toll.  The Institute reports that 77 percent of all fatal multi-car collisions involved at least one speeding driver.  

"However, at a press conference yesterday, Mayor Doe downplayed this evidence that speeding kills, and resisted calls for additional enforcement."

Now, if the reporter accidentally misquoted the numbers, there would be a correction in the next day's paper:

"Yesterday, we reported an incorrect Insurance Institute statistic on the proportion of speeding drivers.  The correct figure is 70 percent, not 60 percent as reported.  The Anytown Daily News regrets the error."

But ... even if the facts were correct, the conclusion doesn't follow.

If 60 percent of drivers speed, then only 40 percent of drivers aren't speeding.  In that case, all things being equal, only 16 percent of two-car collisions -- 40 percent of 40 percent -- would involve only non-speeders.   That means 84 percent would involve at least one speeder.  But the actual number is only 77 percent.  At face value, those numbers actually suggest that speeding *prevents* accidents!  

So, you'd expect a correction:

"Yesterday, we incorrectly reported that Insurance Institute data proved that speeding is dangerous.  However, the quoted facts actually show no evidence that speeding kills, and could even be interpreted as evidence that speeding saves lives.  The Anytown Daily News regrets the error."

That would never happen, right?  You have to correct facts, but not logic.  

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From that same SI article:

"So there is at least a small chance that the 2013 finals ... is not last call for the Original Six.  But ... the bartender is checking his watch."

Well, it's not that small a chance.  Over the next 30 years, say, there's almost a 50-50 chance of at least one Original Six final.  (That's 100% minus (97.8 percent to the 30th power)).  But that's the author doing his own logic, not quoting the expert.  

It seems like that's another rule: you have to quote a source for the raw facts, but you can say anything you want about what those facts mean.  

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What's my point?  Um ... I'm not completely sure I have one.  Well, I guess, I find it frustrating how these things work.  Because, usually, if a conclusion is wrong, whether in journalism or academia or blogs or conversation, it's because of the logic, not the facts.  So the emphasis is backwards.  You get in deep trouble if you accidentally omit part of your dataset, even when it doesn't change your conclusion ... but, if you get the data right and badly misinterpret what it means, it's not a big deal.  

I'm all in favor of getting the facts right, but not at the expense of pretending that the reasoning doesn't matter.