Heard this research paper mentioned on a podcast. They implied it is credible. I don't understand how. I looked it up and still can't believe it. (the math proofs are beyond my limited capabilities)

Excerpt:

JACK THE RESEARCHER TAKES A COIN from his pocket and decides to flip it, say, one hundred times. As he is curious about what outcome typically follows a heads, whenever he flips a heads he commits to writing down the outcome of the next flip on the scrap of paper next to him. Upon completing the one hundred flips, Jack of course expects the proportion of heads written on the scrap of paper to be one-half. Shockingly, Jack is wrong. For a fair coin, the expected proportion of heads is smaller than one-half.

Link to paper:

https://papers.ssrn.com/sol3/papers....act_id=2627354

I think that all will be clear once you read this paper, which is related to the one you posted:



https://papers.ssrn.com/sol3/papers....act_id=2627354

I believe this is the same Miller-Sanjurjo paper we analyzed in linked thread a few years ago.

https://forumserver.twoplustwo.com/4...heads-1562992/

I just bumped it for convenience.


PairTheBoard

Thank you!

It just occurred to me that there's a similarity between what they do in this paper and gerrymandering, although it's not an exact analogy.

But, consider a State with two political parties A and B. Exactly half the voters vote for A and half for B. How is it possible that in every election for state legislators A wins nearly all of the seats? Gerrymandering. In district 1 party B has a 99% majority while in districts 2,3,4,...,n party A has a 51% majority. A 50-50 split in total votes results in an n to 1 split in legislators because the 99% majority in district 1 counts no more toward the Legislature than any of the many 51% majorities in the other districts.

Similarly, in this paper the HHHH quartet with 3 hothand heads counts no more toward the paper's "probability" of hothand heads than the TTHH quartet with only 1 hothand head. The paper's method of counting hothand heads amounts to effectively gerrymandering the data.


PairTheBoard

...so when black comes my next bet should be red?

That is the entire point of the paper. Research on hot hands, up to that paper, were making that mistake

Not sure I understand what you're saying. I find it hard to believe that hot hand research looked at quartets of shots like this paper does with coin flips. The easy way to test for hot hands would just be to look at every shot made in a season and see if the next shot was made. When that's done with coins it's 50-50.

However, if hot hand research only looked at quartets of shots with at least one made shot in the first 3 and then randomly picked one of the made shots in the first 3 of that quartet to see if the next shot was made AND found ONLY the same frequency made as the player's average, then the paper would be relevant because the paper shows the frequency should go down (at least for a 50% shooter). Under that scenario, if hot hand researchers found the frequency was just average and concluded no hot hand effect then the paper would tell them they were making the wrong conclusion. The conclusion for finding no reduction in frequency with such a gerrymandered sampling technique should be that there is a hot hand effect. I can't believe researchers only used this or similar sampling techniques before this paper though. It seems unnecessarily dumb.


PairTheBoard

The research didn't look at quartets of shots, but the effect still exists if you use more than 3, or 4, or 5, or 6 or 199. It simply becomes a smaller effect. You will note that the above sentence is basically a paraphrase of the abstract of the paper.

The easiest method to test your ideas about the research up to the point of the paper would be to look at the research up to that point. As with most papers, they likely cited the previous research.

You'd be surprised at the state of statistical analysis of time-series data currently. Most of it is done poorly without seemingly a care in the world for avoiding silly pitfalls

I know practically nothing about how they have carried out hot hand research. You seem to know something about it. Can you describe the specifics of a method they have used where the paper is relevant and would significantly inform the results?


PairTheBoard

I am pretty sure that we (smp) discussed it the last go-around about this specific paper. If I remember correctly, at least one of us was willing to actually read the paper, and that person was also willing to quote the relevant part(s) of the paper that discussed the research you are asking me to find within the paper that has been linked to several times in this iteration of the discussion of the paper.

I don't believe that person was me, since it doesn't seem like something I would do. But you never know.

It is possible that I am remembering another discussion of the paper (the one we are talking about) though, in which case it is still the case that the paper does supply citations for research that was done without taking into account or correcting for the statistical artifact that the paper is about.

Perhaps someone more industrious than me will reread the paper and copy and paste the relevant passages. Of course, this person could just state that the relevant passages begin just after the first paragraph of the introduction and let you work it out from there, if they were feeling slightly under the weather upon realizing that they were being asked to read a paper for someone else.

It looks like I misjudged this paper based on the Wall Street Journal's story on it. Evidently the authors were making a legitimate point.

Here is the abstract of the paper:
-------------------------------------
Abstract
We prove that a subtle but substantial bias exists in a standard measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data. The magnitude of this novel form of selection bias generally decreases as the sequence gets longer, but increases in streak length, and remains substantial for a range of sequence lengths often used in empirical work. The bias has important implications for the literature that investigates incorrect beliefs in sequential decision making---most notably the Hot Hand Fallacy and the Gambler's Fallacy. Upon correcting for the bias, the conclusions of prominent studies in the hot hand fallacy literature are reversed. The bias also provides a novel structural explanation for how belief in the law of small numbers can persist in the face of experience.
===================

Unfortunately, I can't download the paper without creating an account with SSRN which I'd rather not do. I'll take Brian's word for it that they do a good job. I'd still like to see an example though.

This "Law of Small Numbers" is something I've seen before but never really understood. I get the idea now.

From Google:
"Law of Small Numbers Definition The law of small numbers refers to the incorrect belief held by experts and laypeople alike that small samples ought to resemble the population from which they are drawn. Although this is true of large samples, it isn't for small ones."


PairTheBoard

As I posted above, I bumped that thread for our reading convenience. I reread the thread and I think everyone responded to the the Wall Street Journal story on the paper rather than the actual paper. So no examples of actual hot hand research that this paper addresses. Only attempts to explain where the bias comes from when getting the counter intuitive 40% chance for Heads using the quartet subdivisions of data.


PairTheBoard

Gilovich, Vallone and Tversky (1985)

Also, get a free subscription to ssrn. Saying you don't want to is silly. Kind of like saying that you don't want to read free research articles.

PairTheBoard