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.