"But for the most part, those studies always show that the variance in the real-life performance is identical to the variance that would be expected if nothing was operating except the normal randomization"
Ah...so variance in real life is somewhat random. Holy cow? Of course it is. Hot streaks do come up randomly. You can't control it...or they would be streaks. A Boston 3B named Boggs felt that by eating chicken before every game he could have more control over his "randomness"(or so I've read). If you slipped him a mickey and gave him turkey nuggets instead, would his performance have suffered? Probably not...you can't control "hot" like that.
Streaks come and go, randomly, surely But random comes and goes in the middle of such streaks. For example, a guy who is a .300 career hitter, but has hit .450 for the past 3 weeks, is certainly more likely to get a hit in his next AB than the .300 career hitter who is hitting .150 over that period.
Wanna bet on it?
In a coin flip proposition the coin has no control over the result. In a hitting proposition the batter certainly does.
moe
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We don't think that Bill will object to our excerpting one paragraph from his subscription article, the "Hot Hand Question" ...
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Suppose that you take a player’s statistics, and re-organize his at bats at random. . . .or suppose that you take his Start-a-Madic, ASPC or Ethan Allen’s magic spinning wheel game card and recreate a thousand at bats for him. You will find, absolutely and without question, that there is just as much up and down variation in the random performance as in the player’s actual record. This has been studied hundreds of times. There is a very good web site devoted to the issue, the Hot Hand Web Site (http://thehothand.blogspot.com, maintained by Texas Tech professor Alan Reifman.) I don’t want to overstate the study; the Hot Hand phenomenon has been studied hundreds of times by dozens of different researchers, and occasionally, one of us thinks we possibly have found some tiny and elusive difference between the "actual" and simulated data. But for the most part, those studies always show that the variance in the real-life performance is identical to the variance that would be expected if nothing was operating except the normal randomization.
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(1) Okay, this is true, that a Strat-O-Matic card will show as much variance as a real player would. A real player's variance is not wider than the variance of normal randomization.
(2) But does the conclusion follow?! I don't believe that it does. Just because Effect A is not larger than Effect B, can we conclude that Effects A and B have the same CAUSES? A person's skin can turn red from a Niacin flush, and can turn red from being embarrassed. Supposing the skin turns red to the same degree in both cases. Do we conclude inevitably that the red skin is being caused by the same thing?
An imaginary S-O-M player hits in 9 games in a row due to throws of the dice. A real MLB player hits in 9 games in a row due to his having his timing in rhythm, his wife being nice to him, and his eating chicken instead of Oreo Double Stufs. Why would the 9 games in a row factor --- > necessarily imply the same cause, just because they happen to occur to the same extent?
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James cast his investigation in terms of the question --- > if a player's performance can go up or down ... by how many standard deviations can it go?
I would suggest ONE standard deviation, just as a first guess. Here's what I wrote there...
A really stimulating investigation of the subject ... I especially like the question, How many standard deviations can skill deflect? In tournament chess, 200 rating points equate to an SD, and it's well accepted that players can (with difficulty) sustain a "hot streak" of just about 1 SD "over their heads" for a few months at a time. They can (very easily) sustain play 1-2 SD's below their ability ... :- )
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I think there is an esoteric point that we overlook here, in our zeal (as sabermetricians) to conclude that Random Is Random and we can capture human imperfections with stats.
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The story goes about a stats professor who challenged each of his students to write out 100-trial coin flips by hand, "inventing" the sequences, and then to actually flip coins and record those. The students shuffled them. Then the professor would casually sort through the pile, tossing the real trials into one pile and the "invented" coin flip records into another pile -- and being right almost every time.
This was because REAL COIN FLIP SEQUENCES ARE MUCH MORE RANDOM THAN WE'D EXPECT. The real records would routinely have 7-heads sequences in them, but the students would always limit their streaks to two and three...
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It's only an analogy, but the human mind (and its expectations; the "petty confidence") affects human performance.
It's very likely that Strat-O-Matic cards "should" have hot streaks of (say) magnitude 7 .... and that real humans "should" have hot streaks of magnitude 3 ... and that when you witness humans having hot streaks of magnitude 6-7, this actually IS a reflection of the fact that they are having remarkable hot streaks and cold streaks.
Or not :- )
Jeff
Comments
"In form." Simply, it's playing above your average level of play, that's my understanding anyway. Players have described it as things just going right, passes hitting team mates perfectly in stride, receiving passes in control, scoring goals off of shins. On the other hand, being out of form means things just don't work, whether a perfectly set up shot going just wide, or passes being just that little bit too far out in front.
In my own experience playing pickup soccer, I have been what I would consider "in form" once. For someone of my skill level that means I don't turn the ball over, and score a couple goals a game (which is unheard of). It lasted for probably three weeks, and afterwards I wouldn't say I lost the talent, just returned to my normal "grit, hustle and defense" game.
I think it is partly "random," but it also has a to do with a great deal of playing/practice, self-confidence, things just feeling right. So much goes into soccer, baseball, a shot in basketball, that it can't simply be explained away with "statistical variation." Maybe luck, if by luck you mean things happening that you don't understand, or can't explain thoroughly with science or math.
Granted, soccer is far more free flowing and seems more emotional than baseball, but I think the analogy is a good one.
By the way, I love this site. Definitely my go to source for M's news, and the occasional Seahawks article.
First off, I don't get how the coin flipping analogy supports the notion of hot streaks. Tango read your comment and actually took it to mean you were arguing the opposite of your actual position. He thought you were pointing out how bad people are at recognizing randomness which might wrongly lead them to think if they flipped 7 heads in a row it meant they were doing something to influence the results. http://tangotiger.com/index.php/site/article/bill-james-on-looking-for-r...
Second, your final paragraph goes right past my head. Why would humans be expected to have LESS randomness than a robot in any circumstance? If humans were perfectly consistent in their performance (never hot or cold), I don't see how they could possibly have less variance than a Strato card. Pure randomness is the floor, so any thing that matches pure randomness must be purely random.
I have to agree with Tango here. When it comes to humans there is always some degree of skill involved so there is no point in asking if a particular skill exists or not. The question should always be how big the skill is. If that skill is so small that it is almost imperceptible, then it it isn't worth making a big deal about. You almost certainly won't be able to tell at any moment whether a particular string of outcomes is because of luck or skill based on results only (and claims of a player being "hot" are almost always focused on results, not anything the player is actually doing different).