Applied Probability

 February 6, 2012
Posted by Jay Livingston

Long-odds prop bets are sucker bets.  The odds that bookmakers offer are nowhere near the true probability.  But expected values matter only if you’re playing a large number of times, which is what the house is doing.  The bettor is betting just once, and 50-to-one odds sounds like a lot.

Take yesterday’s game. The odds that the first points of the game would be the Giants scoring a safety were 50-1.  That’s what the bookies offered.

But what is the true probability?  In the previous NFL season, there were 2077 scores, not counting point-after-touchdown.  Here is the breakdown (I found the data here).

• Touchdowns      1270
• Field Goals           794
• Safeties                    13

The probability of the first score being a safety by either team is 2064 to 13 or about 160 to 1.  The probability of the first score being a safety by a specified side is double that.  Even if that specified side is the Giants and their defense is twice as good as the Patriots defense, that still makes the probability at least 200 to 1.  The Las Vegas books were offering only 50 - 1, one-fourth of the correct odds.  So the expected return on a $1000 bet is $250 – a $750 loss.   What a ripoff.

Of course, not everyone feels duped.

Somewhere, someone is walking around with an I ♥ Brady t-shirt. 

HT: My colleague Faye Glass, though she tells me this picture is all over the Internet.

Guess Again

February 3, 2012

Posted by Jay Livingston

Prediction is hard, especially about the future, even the very near future. The New York Times that arrived early this morning reported the wisdom of the economic crowd.

A few hours later, the Times Website had this.

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February 3, 2012

U.S. Jobless Rate Falls to 8.3 Percent, a 3-Year Low

By MOTOKO RICH

The United States economy gained momentum in January, adding 243,000 jobs, the second straight month of better-than-expected gains.

The unemployment rate fell to 8.3 [emphasis added]
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The reported number was 80% higher.  The experts were off by 108,000 jobs.

Speaking of predictions,  I asked my students yesterday to predict the score of the Superbowl.  The class mean had the Giants winning 28 to 24 or 25, though no individual guess had those two numbers.  The bookmakers have it the other way – Patriots by 3.  We were closer to agreement on the under-over, which is 54 in Las Vegas, 52-53 in University Hall 3008.

If the final score is close to the class prediction, I may revise Monday’s lesson plan to include Galton and the Wisdom of Crowds (an earlier post on that is here).

This Goon for Hire

 February 2, 2012
Posted by Jay Livingston

In basketball, assaulting another player on the court used to be called, in ancient times, “playing dirty.”  In more up-to-date language, it is a gift bestowed. Jabbing an elbow into the another player’s face or clotheslining a player who is in midair is called “giving the hard foul.” 

Of course, you don’t want your starters fouling out.  So some observers believe that teams have specialists – designated hitters – who the coach sends in to do this giving.

To verify that the basketball goon is not a myth, Nick Jaroszewicz at the Harvard College Sports Analysis Collective looked at patterns of fouls in the major conferences of the NCAA (the “Big 6”).   He was looking for players who didn’t play many minutes but who did pick up a high number of fouls in their brief moments on the court.  He found nine.



Jaroszewicz notes that six of the nine are in the Big East.  He might have added, but didn’t, that five of the nine are white, a proportion well in excess of that race’s overall representation in these conferences.

Name It and Frame It

February 1, 2012
Posted by Jay Livingston
(Cross-posted at Sociological Images.)

It can take a while to find the right word.  But a mot juste may be crucial for framing a political issue. If you like the idea of men being able to marry men, and women women, what should you call the new laws that would allow that?

The trouble with “gay marriage” and even “same-sex marriage” is that these terms suggest – especially to conservatives – some kind of special treatment for the minority.  It’s as though gays are getting a marriage law just for them. 

At last, the gay marriage forces seem to have come up with a term that invokes not special treatment but a widely-held American value that’s for everyone – equality.  A bill in  New Jersey has been in the news this week, mostly because Gov. Christie says he will veto it.  The bill is a “marriage equality” law.

The governor is in a bit of a squeeze.  As a Republican with ambitions beyond New Jersey’s borders, he can’t very well be for gay marriage.  But if his opponents can frame the matter their way, he now has to come out against equality.  Which is why the governor continues to refer to the issue as “same-sex marriage.”* 

It’s like “abortion rights” or even “women’s rights.” A phrase like that might rally women to your cause, but if you want broader support, you need a flag that every American can salute.  I’m not familiar with the history of abortion rights so I don’t know how it happened, but those who want to keep abortion legal have managed to frame the issue as one of freedom to choose.   They have been so successful that the media routinely refer to their side as “pro-choice.”   To oppose them is to oppose both freedom and individual choice, principles which occupy a high place in the pantheon of American values.

It’s not clear that the “marriage equality” movement has been similarly successful, at least not yet.  I did a quick Lexis-Nexis search sampling the last week of the months January and July going back to 2007.  I looked for three terms

• Same-sex marriage
• Gay marriage
• Marriage equality

The general trend for all three is upwards as more legislatures consider bills, with big jumps when a vote becomes big news – that blip in July 2011 is the New York State vote.  But the graph can’t quite show how “marriage equality” has risen from obscurity.  That first data point, July 2007, is a 4.  Four mentions of “marriage equality” while the other terms had 25 and 50 times that many.  As of last week, “gay” and “same sex” still outnumber “equality,” but the score is not nearly so lopsided. 

Here is a graph of the ratio of “equality” to each of the other two terms.  From nearly 1 : 20 (one “marriage equality” for every 20 “gay marriages”) the ratio has increased to 1 : 3 and even higher when the discussion gets active. 

If the movement is successful, that upward trend should continue.  When you hear Fox News referring to “marriage equality laws,” you’ll know it’s game over.
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* Christie is usually politically adept, but he’s stumbling on this one.  He referred to a gay legislator as “numb nuts” (literally, that might not necessarily be a liability for a politician caught in a squeeze).   Christie also said that he’s vetoing the bill so that the matter can be put on the ballot as a referendum – you know, like what should have happened with civil rights in the South. 

I think people would have been happy to have a referendum on civil rights rather than fighting and dying in the streets in the South.

Several critics, including Numb Nuts, responded that, yes, Southern whites would have been happy to have civil rights left up to the majority.  African Americans not so much.  (If you’re looking for an illustration of Tocqueville’s “tyranny of the majority,” the post-Reconstruction South might be a good place to start.)  The analogy is obvious – race : 1962 :: sexual orientation : 2012 – even if it was not the message the governor intended.