Explanation of the Hot Hand from Stigler, from Dan Grossman

2015-09-30 · Dan Grossman, Victor Niederhoffer
Original source

Can this be explained in words so that a reader like me can understand it? The question arises: how to explain this to a normal person not a statistician?

"The ‘Hot Hand’ Debate Gets Flipped on Its Head: A new paper shows how a simple coin toss may prove that basketball players really can get hot"

Prof. Stigler ?

Steve Stigler writes in:

Here's one take.
It comes from averaging relative frequencies over different numbers of trials.
Here are the possibilities for n=4 and the relative frequency of H following directly after H:

HHHH 3/3=1
HHHT 2/3=.67
HHTH 1/2=.5
HTHH 1/2=.5
THHH 2/2=1
HHTT 1/2=.5
HTHT 0/2=0
THHT 1/2=.5
HTTH 0/1=0
THTH 0/1=0
TTHH 1/1=1
HTTT 0/1=0
THTT 0/1=0
TTHT 0/1=0
TTTH 0/0 undefined
TTTT 0/0 undefined
Total rel freq = 5.67; average over the 14 cases that give data = 5.67/14= .40
Even though the number of successes is 12 out of 24 cases of looking at a
result after a H.

Victor Niederhoffer adds:

But isn't there a conditional probability explanation for this from normal statistics of bayesian or just conditional nature. Seems like a simple math team problem.