Is the point you only consider measuring success in the case of an initial success? Thus you are conditioning on data with at least one success contained within it and have biased data?
TL;DR; if you count proportion of 1s and 0s in a random binary string (of a bounded length) after each 1, then you'll get <50% for 1s for the obvious reason, that you always skip the first 1.
Unsurprising, as the 50% expectation is only obvious for infinite sequences. All kinds of statistical correlations happen if you start adding arbitrary preconditions to finite sequences.
> We observe that the canonical study in the influential hot hand fallacy literature [2],Gilovich, Vallone, and Tversky(1985), along with replications, have mistakenly employed a biased selection procedure that is analogous to Jack’s. Upon conducting a de-biased analysis, we find that the longstanding conclusions of the canonical study are reversed.
> [2] The hot hand fallacy has been given considerable weight as a candidate explanation for various puzzles and behavioral anomalies identified in the domains of financial markets, sports wagering, casino gambling,and lotteries (Arkes(2011),Avery and Chevalier(1999),Barberis and Thaler(2003),Brown and Sauer(1993),Camerer(1989),Croson and Sundali(2005),De Bondt(1993),Long et al.(1991),Durham, Hertzel, and Martin(2005),Galbo-Jørgensen, Suetens, and Tyran(2016),Guryan and Kearney(2008),Kahneman andRiepe(1998),Lee and Smith(2002),Loh and Warachka(2012),Malkiel(2011),Narayanan and Manchanda(2012),Paul and Weinbach(2005),Rabin and Vayanos(2010),Sinkey and Logan(2013),Smith, Levere, and Kurtzman(2009),Sundali and Croson(2006),Xu and Harvey(2014),Yuan, Sun, and Siu(2014))
Their claim is that people do apply "arbitrary preconditions" in the analysis of various situations.
No, you won't. See Table 1 in the paper, for 3 coin flips.
You get exactly 50%, as expected because the probabilities are independent.
But when you only look at streaks, you find that the 1s are clustered in the streaks! Thus, if you average across many sequences (aka games) and weight per-series instead of per-1, you underweight the successes that occur in sequences with longer streaks and more 1s, giving an average-of-averages that is less than 0.5.
Why the researchers insist on averaging across sequences, I don't know.
A rich guys later success is predicated on their early success, but over time we begin to understand the laws were arbitrarily written under bias of the initial success, not that one individual is so uniquely qualified we should coddle their fee fees forever.
Now there’s a political platform embedded in math I can get behind.
This is a good mathematical analysis. But here's another way of looking at it: the hot hand fallacy is stating that every shot is strictly independent. You don't have good days and bad days, every day is exactly average. Which is ridiculous, especially in the negative direction:
- A player could be sick
- A player could have an minor injury they are playing through
- A player could have not eaten properly before the game
- A player could have been practicing a new shooting form and not quite adjusted properly yet
If you can have bad days, by definition all the other days are good days even if they are only "normal" days.
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[ 2.4 ms ] story [ 31.2 ms ] threadUnsurprising, as the 50% expectation is only obvious for infinite sequences. All kinds of statistical correlations happen if you start adding arbitrary preconditions to finite sequences.
> We observe that the canonical study in the influential hot hand fallacy literature [2],Gilovich, Vallone, and Tversky(1985), along with replications, have mistakenly employed a biased selection procedure that is analogous to Jack’s. Upon conducting a de-biased analysis, we find that the longstanding conclusions of the canonical study are reversed.
> [2] The hot hand fallacy has been given considerable weight as a candidate explanation for various puzzles and behavioral anomalies identified in the domains of financial markets, sports wagering, casino gambling,and lotteries (Arkes(2011),Avery and Chevalier(1999),Barberis and Thaler(2003),Brown and Sauer(1993),Camerer(1989),Croson and Sundali(2005),De Bondt(1993),Long et al.(1991),Durham, Hertzel, and Martin(2005),Galbo-Jørgensen, Suetens, and Tyran(2016),Guryan and Kearney(2008),Kahneman andRiepe(1998),Lee and Smith(2002),Loh and Warachka(2012),Malkiel(2011),Narayanan and Manchanda(2012),Paul and Weinbach(2005),Rabin and Vayanos(2010),Sinkey and Logan(2013),Smith, Levere, and Kurtzman(2009),Sundali and Croson(2006),Xu and Harvey(2014),Yuan, Sun, and Siu(2014))
Their claim is that people do apply "arbitrary preconditions" in the analysis of various situations.
You get exactly 50%, as expected because the probabilities are independent.
But when you only look at streaks, you find that the 1s are clustered in the streaks! Thus, if you average across many sequences (aka games) and weight per-series instead of per-1, you underweight the successes that occur in sequences with longer streaks and more 1s, giving an average-of-averages that is less than 0.5.
Why the researchers insist on averaging across sequences, I don't know.
Now there’s a political platform embedded in math I can get behind.
http://www.jellyjuke.com/a-conceptual-explanation-of-the-hot...
- A player could be sick
- A player could have an minor injury they are playing through
- A player could have not eaten properly before the game
- A player could have been practicing a new shooting form and not quite adjusted properly yet
If you can have bad days, by definition all the other days are good days even if they are only "normal" days.