Posted by: Ben | September 15, 2010

Hot-Hand Theory

My friend MonkeyPope gave me the book “The House Advantage:  Playing the Odds to Win Big in Business” by Jeffrey Ma, knowing full well I’d love reading it.  Ma is one of the members of the MIT team that Ben Mezrich wrote about in “Bringing Down the House:  The Inside Story of Six MIT Students Who Took Vegas”, about a team that made a fortune off signalling and counting cards at casino blackjack tables.

One of my favorite discussions in The House Advantage was on hot-hand theory, the idea that people can go on streaks, or simply, that you are more likely to succeed this time because you succeeded the last time, a violation of statistical randomness in most situations.

I think we’ve all sensed that when we are watching a sporting event, sometimes one team may be losing but it’s outplaying the other team and has merely gotten some bad breaks.  Then that team blows it open in the second half and wins.  We’ve seen Michael Jordan or Kobe Bryant line up for the shot at the buzzer, knowing they’ll make it.  We’ve seen Big Shot Bob or Derek Fisher take a 3 from the corner after a good ball rotation.  We’ve seen Favre and Elway lead their teams down the field at the end of the game, despite having a horrible rest of the game with no offensive movement.

What’s interesting is that people react to things wildly differently.  Some people see a disaster and run away from it or freeze up, while some charge forward into the fray to see if they can help.  Some athletes lose all their motivation after they’ve sealed a multi-million dollar contract.  Some seem to lose their hunger after they’ve won everything; just look at Roger Federer after he completed his career grand slam.  Some people would make a big shot or throw a nice pass and then feel like they didn’t deserve it, and they start missing the rest of their shots.  Some people always believe resolutely that they will make every shot, and so succeeding gives them even more confidence to feed off of.

These are microcosms of peoples’ larger personalities.  Some push harder when they win or lose, some relent.  Said Dr. John Eliot, by way of Jeffrey Ma, “One shot does not influence another shot.  One shot influences your psychology, and that psychology influences the next shot.”

There are some days when you go out to exercise and you just don’t feel up to it.  While you know how to do what you’re doing, your body doesn’t respond the way you need it to, no matter how much you’ve practiced.  Part of drilling is that your body starts to do certain tasks (like shooting a basketball) naturally or even mechanically, no matter how your mind, heart, or body feel.

There are other times when your legs feel like lead, but then you start making a couple shots and you snap into it.  Or you make a really nice shot and then your legs seem to give way the rest of the time, as your body ran out of juice.

Ma fortunately concludes nicely, saying, “It does a tremendous disservice to the statistics community as a whole if you walk into an audience with anyone who has played sports and champion the theory that there is no such thing as the hot hand. …  I believe that there are some shooters who at times become more confident due to early success, and this confidence leads to future success, that is, the hot hand.”

So how to build this into a real-world system?  You would need to take quantitative data about someone’s life within the context of his qualitative general mood, outlook on life, and typical response to pressure/success/failure.  Two people could have reached the same point but through vastly different ends of the extreme.  Like anything data-intensive, I guess, context is key.

Certainly we are not all just numbers, but shouldn’t we try to explore why and how we generate the numbers that we do?

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