TGV on Hot Hands
Tversky, Gilovich and Vallone wrote a famous paper "debunking" the idea of a "hot hand." When they did so, they conflated two very different questions:
1) Is it sensible to feed the ball to a player with a "hot hand," since he has a greater chance of making his next shot? I.e., is there predictive value in this phenomena?
2) Is the impression that players have that sometimes they are "on" and sometimes not an illusion? I.e., does the phenomena exist at all?
The findings of their paper, if accurate (and recent research suggests they are not), would show that there is no predictive value in hot streaks, whether or not they really exist. But by defining "hot streaks" as simply being this predictive value, the authors, without any basis for doing so, also claimed that players' perception of being "on" at certain times is just an illusion.
So any reader complaining that my recently posted model "does not follow the TGV definition" of a "hot hand" is simply demanding that I make the same mistake that TGV made!
That is ridiculous: My disputing the TGV definition of a hot hand cannot be refuted by insisting I use the TGV definition of a hot hand!
UPDATE: And by the way, in this post, I quite deliberately created a model in which:
1) Hot streaks are statistically undetectable; and
2) Hot streaks offer no predictive leverage for a player's next shot.
So it was somewhat stunning to see criticisms of my model based on the fact that in it, hot streaks are statistically undetectable, and offer no predictive leverage for a player's next shot.
Since 1) and 2) were the whole point of my model!
1) Is it sensible to feed the ball to a player with a "hot hand," since he has a greater chance of making his next shot? I.e., is there predictive value in this phenomena?
2) Is the impression that players have that sometimes they are "on" and sometimes not an illusion? I.e., does the phenomena exist at all?
The findings of their paper, if accurate (and recent research suggests they are not), would show that there is no predictive value in hot streaks, whether or not they really exist. But by defining "hot streaks" as simply being this predictive value, the authors, without any basis for doing so, also claimed that players' perception of being "on" at certain times is just an illusion.
So any reader complaining that my recently posted model "does not follow the TGV definition" of a "hot hand" is simply demanding that I make the same mistake that TGV made!
That is ridiculous: My disputing the TGV definition of a hot hand cannot be refuted by insisting I use the TGV definition of a hot hand!
UPDATE: And by the way, in this post, I quite deliberately created a model in which:
1) Hot streaks are statistically undetectable; and
2) Hot streaks offer no predictive leverage for a player's next shot.
So it was somewhat stunning to see criticisms of my model based on the fact that in it, hot streaks are statistically undetectable, and offer no predictive leverage for a player's next shot.
Since 1) and 2) were the whole point of my model!
PhenomenON.
ReplyDeleteOh admit it Thomas. What you really want to say ends not in ON, but OFF!
DeleteGene, suppose that God told you that hot hands exist. If you were given that fact, and given no access to sports statistics, a priori what would you think the probability would be that hot hands would be undetectable?
ReplyDeleteTo put my question another way, do you at least acknowledge that the undetectability of hot hands, if true, would substantially decrease the probability that hot hands exist?
Lets assume that basketball players occasionally enter states where they have a greater chance of sinking a shot than when they are not in the state.
ReplyDeleteLets also assume there 4 are parameters st work.
- the likelihood for entering the state
- the likelihood for staying in the state
- the shot success rate in the state
- the shot success rate out of the state
Based on these 4 parameters sometimes "hot-hands" can be statically identified , sometimes not. The vast majority of times the configuration of the 4 parameters will make hot-hands detectable.
So Gene is correct that sometimes "hot-hands" exists but cannot be statically identified. Its not clear to me if he sees this this is as just a theoretical possibility or if there is something about hot-hands that makes this undectability the normal state of affairs.
statically = statistically
DeleteOK, so I see that all that is required is for the outcome of each shot to be independent of the outcome of the previous shot (50% for my first 2 parameters) and (for each shot) there to be "states" that are entered (with consistent probability?) and that cause the success rate to vary.
DeleteI think if these criteria are met then the outcome will appear random, but someone who has access to the "states" could game the system.
I would also like to make the point that even in your model, if it is the case that players know when they have a hot hand, that would have predictive value for them. It would only not have predictive value for someone who has no idea when a player has a hot hand.
ReplyDeleteRight! And in my last post, I just showed how if a bettor could detect it -- "He's got that look in his eye again" -- he could make money off of it.
DeleteThis is one of the ways pros make money off of marks in poker games: they can detect the marks' "tells" with much more skill than the marks can detect theirs. So the pros have many times the information the marks do: they might know, for instance, that the mark just drew the card needed for a flush, while the mark has no idea what the pro holds.