
Surprised by the hot hand fallacy? a truth in the law of small numbers - bookofjoe
https://onlinelibrary.wiley.com/doi/abs/10.3982/ECTA14943?mod=article_inline
======
neonate
[https://sci-hub.tw/https://doi.org/10.3982/ECTA14943](https://sci-
hub.tw/https://doi.org/10.3982/ECTA14943)

------
jellyjuke
Here's something I wrote that I feel gives an intuitive explanation:

[http://www.jellyjuke.com/a-conceptual-explanation-of-the-
hot...](http://www.jellyjuke.com/a-conceptual-explanation-of-the-hot-hand-
fallacy.html)

~~~
alwaysdoit
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.

------
lostmsu
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.

~~~
abdullahkhalids
From the paper

> 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.

------
fullshark
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?

~~~
srtjstjsj
No, the point is about a subtlety in the way averages of averages are
calculated, and how that introduces weighting biases.

------
kroep93nd
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.

