Oh no, not at all! Say it isn't so; I'm crushed! Surely, pure stats must reveal nothing but absolute truth without regard for any fundamentals inherent in what is being measured:Quote:QFIT"There are three kinds of lies: lies, damned lies, and statistics." --Benjamin Disraeli

One must be extremely careful when presenting stats as misapplication of statistical theory can result in absurdity.

Spurious Correlations

Quote:Tylervigen @SpuriousCorrelations

US spending on science, space, and technology

--correlates with--

Suicides by hanging, strangulation and suffocation

Number of people who drowned by falling into a pool

--correlates with--

Films Nicolas Cage appeared in

Per capita cheese consumption

--correlates with--

Number of people who died by becoming tangled in their bedsheets

...<MORE>...

Quote:DrawingDeadNumber of people who drowned by falling into a pool

--correlates with--

Films Nicolas Cage appeared in

Well, everyone knows that one is a valid correlation.

Using a decision tree or similar. There are only 14 times (of the 16 potential "4" flip outcomes) that one or more heads can occur in first 3 spots in any 4 flip sequence. Thus we disregard TTTT and TTTH. Agreed?

In the remaining 14 scenarios that are eligible to have a head following a head only approx 40% do so.

https://sinews.siam.org/Portals/SiNews2/EasyDNNNews/thumbs/383/117HotHandsTable.JPG

***For this particular example*** Thus a head = 50% is not true statement once we measure all instances that meet the qualifier of how often does a "head follow a head when one or more of the first 3 flips is a head".

It's the taking of TTTT and TTTH out the equation is why we end up with a shortfall of measurable tails.

**Anyhow the only good of this type of insight (it seems) is that the researchers found that those who could hit free throws near their typical ft% even after several makes in a row actually are showing evidence of a hot hand; just like 50% heads isn't expected under the above coin flip restriction, but if found (it wasn't) it'd defy probable expectation

One post you say a head followed by a head is less than 50%. In the next post you say all flips are 50/50. Which is it?

Look at the bottom of this image:

Notice the sum is 12 HHs and there are 24 H's in the first 3. What is 12/24? Hint: it's 0.5 AKA 50%.

The chart shows that the "head after heads" unweighted average after a "conditional sequence" (ie when one or more head occurs in the first 3 positions) is approx. 40.5% (hence the number in the "HH percentage "column).

Maybe read the original article and the academic paper https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2627354 that started all this.

Or the other links the article contained in this thread.

And yes, of course, we all agree a fair coin is 50/50 for any random flip. That was never in dispute.

***I'm here more to learn than teach that's for sure. I, and apparently others on the Internet, think this is interesting. I have no motives other than discourse.

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 40.5% figure is simply wrong. I read the piles of sh** sources you keep posting (I have no idea why). It's wrong. That's it.

Better yet, can you show how the figure is ~40% and not 50%?

Here is an online argument I've found between a hedge fund guy and a stats prof. over these exact issues. http://andrewgelman.com/2016/02/18/miller-and-sanjurjo-share-5-tips-on-how-to-hit-the-zeitgeist-jackpot/

And here is the chart again below for those who want to interpret/explain further (maybe not needed).

Quote:RS......you CANNOT be serious.

The 40.5% figure is simply wrong. I read the piles of sh** sources you keep posting (I have no idea why). It's wrong. That's it.

Better yet, can you show how the figure is ~40% and not 50%?

HHHH : 1 means that for every time there was an H is the first 3 spots an H followed it 100% of the time. Thus 1 = 100% in this example.

HHHT: 2/3rd means 2 out of the 3 times or 66.666666%..... the qualifying H was followed by another H.

The .40 is the approx 40.5% probability after all the qualifying events were assessed.

Quote:DrawingDeadI think there's a simple one syllable word for what's been going on here, not with all that much subtlety and pretty much up in flashing neon lights, and not just in this thread... but I don't think I'm allowed to say it.

I think the word you refer to is 'Troll'

I know forum rule one forbids 'All personal insults' and I've seen cases where the accusation 'Troll' has been deemed to be such a personal insult. I don't agree with that implied extension to the rule, but hey, I don't set the rules or their interpretation.

So, Like DD, I will not accuse the OP of being a troll. I will not attack the writer, I will attack the writing:-

Every link, chart, table and bit of narrative that I've seen from the OP has been absurdly wrong and unsupportable. He refuses to desist in posting abject stupidity.

So, I'm going to block the OP, so as to no longer see his posts.

I also block Trolls..