the metaphysics of the hot hand, or streak, vs the statistics

[mosta]

I've never actually seen the research, but I'm given to understand that statisticians have disproven the idea that sometimes you're hot and sometimes you're not (with maybe rare exceptions).

I believe in math and all that, but I also know that as a (decent but far from great) pool player, some days I can't hit the ball straight and sometimes I know I can't miss. and sometimes I elevate my game. is the statistical argument that none of my sessions are measurably distinguishable from each other in terms of objective performance distribution?

supposing that there is a consistency in the distribution of my performances over the long term, I can think of two explanations and I'm wondering if they are meaningfully distinguishable.

1. my expectation and standard devation are always the same and my hot feeling is an illusion that I make up after the fact when I run well.

2. sometimes I have it and sometimes I don't, but what is random is when the hot hand will start and when it will end.

is it possible to distinguish in this way: 1. you always shoot the same with the same randomly distributed error; and 2. sometimes you shoot better but when it will come and when it will go is random?

[chrisnice]

Im not realy sure what it is you are saying but here is my take. Running hot in Poker, BJ, etc is an illusion. You will never be able to predict with any accuracy beforehand whether you will run hot or cold.

In regards to other games which can not be reduced to pure math. Basketball, golf, pool, etc., better or below average play can be attributed to more than just regular variance allthough I think there are other factors which come into consideration rather than running hot or cold.

[MathEconomist]

1 and 2 are indistinguishable if in the case of 2 your "hot streaks" really are random in starting and ending. That is, if you're just as well off plugging in your average game as a predictor of your next game given the streak you're on as you are using some predictor that conditions on your most recent games, then 1 and 2 are only meaningful from a psychological standpoint.

However, I would imagine that for games like pool there actually is some consistency in your performance from game to game so that hot and cold streaks are real though overblown in that people are too quick to attribute luck to "being in the zone".

Even in poker, there is probably some persistence to hot and cold streaks (though I haven't analyzed any data on this) since the quality of your play varies in a not entirely random fashion, but it might be difficult to find because it's a needle in the haystack of the random variance of the cards.

[mosta]

sorry I should have been more clear. I'm only talking about streaks in the context of physical activities--sports generally. common wisdom among educated people is supposed to be that getting hot and playing at a higher level over a period doesn't happen in demonstrable fact (if I understand correctly).

there might be a simpler point that I overlooked, which is that by definition being hot must be over a stretch. generally one wouldn't say one is hot or not turn by turn (though you could...). I guess this is why they use independence test of successive events to try to detect streaks. something I haven't quite understood.

maybe my questions or distinctions are confused, or confusing, but I'm hoping at least that someone will try to convince me that on the days I play pool and I think I'm on and I'm ready to raise the stakes, that I'm only imagining it--or deluding myself.

[mosta]

like in basketball. sometimes people think a player is "on." like they see better or their coordination is better for a spell--some kind of special moment of relaxtion and concentration. so you'd want to let them have the ball. but isn't research supposed to show that in fact that player's likelihood of scoring at that moment is no different than it was last quarter or last game?

the way I was thinking you might be able to reconcile the two positions (allow the notion of being hot and the statistical proof of not being hot) is that we say the player may be in a state of elevated performance, but the likelihood of it ending by the next shot causes the overall distribution to be uniform.

but then there is the point I considered above that although it might end, if the player _was_ hot, then there must have been some span of elevated performance. and is the point of the statisticians that this has been shown to be untrue?

[chrisnice]

Just to be clear im talking out of my ass here but all things being equal I would think that whether or not you ate your Wheaties that morning would better explain your hot streak.

[MathEconomist]

Ok, I think I understand what you are asking now.

First, as far as I know, no one has disproven the existence of hot streaks in sports. I'm certainly no expert in this (though I have a solid background in statistics I am not a statistician and haven't studied these issues), but I think all that's been shown is we can't find a way to make streaks predictive. But all this shows is that any persistence of streaks is small relative the ambiant variation (of course non-existant is a type of small). I think most statistical tests that we'd use in such situations probably have very low power to pick out the hypothesis of no streaks versus some small amount of persistance in streaks, and I don't think it's ever been shown that it's definitely the case that the BEST predictor of short term future performance is simply plugging in your average, only that we haven't found a better predictor from the data.

But assuming that we have shown for sure that hot streaks don't exist (I should say here since I haven't been careful with my wording that when I say this I mean simply that such streaks are only something we can say in retrospect like running good or running bad in poker. Clearly streaks do exist, in fact they are guaranteed to happen if the process is at all random) then it doesn't matter what we say about them. Statistics can't distinguish between elevated ability that comes and goes at random or the streaks happening for some other reason ("pure luck"). And, in fact, I'm not even sure that such a distinction is meaningful even in a non-statistical sense. If you can't control or predict the "hotness", then it doesn't matter whether you attibute it to pure luck or being lucky enough to have your "A game".

[GreekHouse]

I think it's pretty obvious that these streaks are not entirely based on pure statistics the way a card game is. For instance, try running a marathon, not sleeping for 48 hours, or taking massive quantities of illicit drugs before doing some sort of physical activity, I think you would find that your performance is much worse on average.

However, if someone is a professional athelete, you should still see a strong correlation between streaks and overall performance, though there might not be a 100% correlation with a normal distribution. A good player will tend to have hot streaks and cold streaks just like a bad player. The difference is that his bad streaks will generally not be as bad, and his good streaks will be better.

In basketball for instance, I think saying someone is a streaky shooter is really just a euphemism for an overrated shooter. People see them get hot and assume that they're really good, but then they go through extended slumps. Of course, if they were really as good as everyone thought, they would not have streaks as bad as their bad streaks (or at least not as frequently).

In general, I think that how much variance a player has is related to the psychological fortitude of that player. To use another example, a baseball player (no matter how good) will inevitably go through a minor slump. A good player will shrug it off and continue to do things in the same way that made them a good hitter in the first place. A lesser player might get easily frustrated and start trying to fix things by changing his batting stance or becoming impatient at the plate. The result of this is that the player starts doing things that make him a worse player than if he didn't do them, and can often go into a more prolonged slump.

[Uethym]

Check out "How We Know What Isn't So" by Thomas Gilovich. In the first chapter the author looks at the shooting statistics for one season of the Philadelphia 76ers. He looks at the probability of a player making his next shot in seven different circumstances:
- missed last three
- missed last two
- missed last shot
- regardless of prior shot
- made last shot
- made last two
- made last three

For nearly every player, there is a small *negative* correlation as you work your way down the list given above, possibly because the defense is collapsing onto the scorer, possibly due to randomness. But it's pretty clear from the data that there's no evidence for streaky shooting at all -- it's just a normal distribution.

The rest of the book is a great read, too. I use it in my "Science and Pseudoscience" seminar every year.

[soon2bepro]

I find it ridiculous to claim that there are no times when you're playing better and worse. Of course there are, in ANY game. (well, any game at which you can't play perfect at *most* times, like you would at tic-tac-toe)

However, feeling good about your game is not a scientifical evidence, it's just how you feel. So you may want to think twice about it before raising the stakes just because you feel like playing

[moorobot]

I'm well versed in stats and have a faith in them and I am afraid to tell you that, as far as I know, statistics as a science cannot distingusih between 1 and 2. Logic might be able to, but the numbers won't tell you this. Physiologically, I think it is quite clear that at some points you will "feel better" in terms of having better reflexes, no stomachaches etc. It is not exactly random, their are some ways of helping a little in predicting it i.e. drug consumption, diet.
It does not follow, however, that you or anyone else will know in advance whether you will be a better player on day X. First, there is a luck (SD, etc.). Secondly, our states of being change quickly.
-J.D. Drew, rich and oft-injured MLB outfielder, once stated that sometimes he felt terrible and hit well that day and other days couldn't hit at all when he felt great. Joe Carter and more recently Geoff Jenkins had the best stretches of their careers when an injury forced them to keep their weight back and avoid pulling pitches that they usually pulled but should be hitting the other way. The injusries of these people stops them from doing what they shouldn't be doing usually but are, and it takes what would normally be a phsyical defect for an otherwise omniscent being with perfect discipline, and turns it into a benefit for a fallible person. this is an example of human beings not having the knowledge to know in advance or why they perform better at sporting events. It is not "random when the hot hand will start and when it will end", strictly speaking, but we can't predict it in any logical sense in any case because we do not know everything about everyone, including ourselves; we are not omniscent but we are complicated. Joe Carter (et al.) circa june 1986 is not exactly equal to Joe Carter in august 1986, hence this situation is not exactly equal to some dice rolling a bunch of times, every time you roll the dice you are rolling the same thing (essentially) exactly; everytime a pool or baseball player picks up a piece of wood and tries to hit a ball, the human being is not the exact same thing.
-All of this said, statistics have done a lot better at predicting results in sports then scouting/any other methods. So while forecasts of sports are not facts about the sport, they are better at performing a pragmatic function than anything else, and we have no reason to believe in hot streaks, clutch hitting etc. and we shouldn't believe in something we have no reason to believe in. 2+2 is always equal to four, but human beings that are equal to X one day are equal to Y another day.

[Copernicus]

You can look at athletic performance as having an underlying mean and standard deviation plus an element of "noise".

The noise are those factors that add or detract from the normal probaibility distribution of performance, be they physical (fatigue vs being fresh, nagging injuries vs total health) or mental (you just met the love of your life vs your wife just caught you with her sister).

Noise will tend to cancel out statistically over a series of performances (eg a season, half season...some statistically relevant period) and the underlying distribution becomes observable over a group of those series. The underlying distribution is the composite of "talent" and a random element ("it (substitute your favorite sport) is a game of inches")...the wind blows a homerun foul, a shot going wide gets deflected past the goalie etc)

One of the best examples of this is "sophomore slump". When you observe rookies, the normal distribution of outcomes will, with some probability, have one of those rookies perfomrig at, say, +2 SD from his mean. It is likeley that that rookie of the year will perform closer to his mean level the following year, and it appears he has slumped, when in fact he actually "over delivered" in his rookie year. In fact I would expect that an apparent slump is more likely for star rookies than consistent performace at that level. Conversely, a disappointing or average rookie season might be expected to improve if the initial assessment of talent wasnt off base.

A similar line of reasoning might apply to the SI cover "jinx". A fall off from the level of performance that landed an athlete the cover story can be expected to revert to the mean performance, looking like SI caused it.

[mosta]

These replies are very good. The two thoughts I have at the moment are 1. the distinction I was trying to make is only meaningful if the state of heightened performance persists over some stretch (versus being on or off turn by turn (makes the purported distinction meaningless)). and that is exactly what the statistical studies are looking for. 2. could the research be skewed by focusing on professional or otherwise high-level athletes? they are so well trained and practiced and coached that there will probalby be very little variation in their mechanics. with me however, I played pool for years without ever using a mirror or a video camera or a coach. I improved and sometimes I found and overcame problems. but realistically, I had no real idea what I was doing. on one of my good days I may have just happened to settle into a well aligned posture, whereas I was all crooked the day before. and the day before I felt it was wrong, but couldn't tell how, and may have only made it worse trying to figure out what to do.

someone should use me as a research subject.

thanks for the insights.

[Copernicus]

[ QUOTE ]

These replies are very good. The two thoughts I have at the moment are 1. the distinction I was trying to make is only meaningful if the state of heightened performance persists over some stretch (versus being on or off turn by turn (makes the purported distinction meaningless)). and that is exactly what the statistical studies are looking for. 2. could the research be skewed by focusing on professional or otherwise high-level athletes? they are so well trained and practiced and coached that there will probalby be very little variation in their mechanics. with me however, I played pool for years without ever using a mirror or a video camera or a coach. I improved and sometimes I found and overcame problems. but realistically, I had no real idea what I was doing. on one of my good days I may have just happened to settle into a well aligned posture, whereas I was all crooked the day before. and the day before I felt it was wrong, but couldn't tell how, and may have only made it worse trying to figure out what to do.

someone should use me as a research subject.

thanks for the insights.

[/ QUOTE ]

I dont think any study would be skewed by observing pros. There are considerable differences in mechanics in almost any sport. For example, the position I know best is hockey goaltending. It should have been obvious to anyone who understands goaltending mechanics that JS Giguere's amazing run in the Stanley Cup playoffs a few years back was many standard deviations beyond his normal performance. His positioning is good, but his movement is poor, his rebound control is non-exisistent and so on. Yet he managed to frustrate the Western teams all the way through the playoffs. Then it turned around in the Finals, which were really a contest of which goalie was going to play worse, Brodeur or Giguere.