Hot Hand... You Betcha!

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"Gödel's Lost Letter" tackled the "hot-hand fallacy" recently:

https://rjlipton.wordpress.com/2015/10/12/is-the-hot-hand-fallacy-a-fallacy/

 I have to confess to tiring a bit of this whole debate: there IS such a thing as being 'in the groove' or 'in the zone' or 'on your game' or 'HAVING A HOT HAND' (IMHO) and everyone who has ever played basketball or tennis or golf or bowling or any number of other sports KNOWS it (there are times we ought not downplay people's personal experience in favor of slapping dry stats and randomness onto situations that are exceedingly difficult to analyze, and where uncontrolled variables abound -- reminds me of what is routinely done in epidemiology... don't get me started).

A lot depends on simply how you define "hot hand" and what units of time are considered... i.e., does someone have a hot-hand for a game, or for a 13-min. stretch of a game. And in the case of the basketball "hot-hand" the stats often look at 2-4 shots in a row to predict the next shot, when larger samples, probably 5-10 shots minimum, need to be considered, because the variables are so-o-o many -- also, if you make 4-5 layups in a row it probably means nothing; but if you repeatedly put in shots from the far corner, the 3-point-range, and while being double-teamed (i.e, lower-percentage shots) that begins to mean something, yet I've never seen "shot-type" or shot-circumstances taken into consideration.

Any athlete will have experienced that rare feeling when their health/nutrition/sleep/physiology/physical prowess/movement/mood/psychology/whatever all seem to coalesce to yield an excellent performance, where they can be depended upon, more than other teammates, for crucial plays. Not every instance that looks like a "hot-hand" of course, to the outside observer, may be one, but I'm a believer ;-) that it does exist on occasion (and am old enough to recall Wilt Chamberlain's 100-point effort in 1962, including a phenomenal 28 out of 32 free throws! And a 'hot' Michael Jordan's winning shot for the 1982 NCAA championship, or Christian Laettner's 1992 championship shot, and on and on).
I s'pose next the statisticians will try to tell me that Reggie Jackson was NOT really ever "Mr. October" for the NY Yankees! ;-)  DON'T even go there!!

Sports performance is clearly in part a function of skill and experience (and psychology), which can vary from day-to-day (even moment-to-moment) for a given individual. A 'hot-hand-like fallacy' is more likely to hold sway in something like gambling where outcomes are more strictly governed by "chance," not skill, and a perceived "streak" may not be real (even in gambling though, it is possible that tiny, almost imperceptible clues, trends, properties, signals, are picked up by the experienced gambler at times that raise his/her performance on certain games).

Anyway, while I'm merely banking on common sense here (admittedly, a dangerous medium), there are statisticians who have also found technical flaws with the 'hot-hand fallacy' argument (see Gelman, for example, here), and therefore speak of the 'fallacy of the hot-hand fallacy' to which, of course, their detractors can respond with the fallacy of the fallacy of the hot-hand fallacy... but then, I find their arguments fallacious.

Now, excuse me while I go shoot some baskets, while I'm feeling kinda hot (...under the collar).

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ADDENDUM ==> the above post was written a few days back and pre-scheduled for Sunday-posting. Lo-and-behold, just yesterday, science writer George Johnson had a piece in the NY Times on, of all things, the hot-hand fallacy!:

http://tinyurl.com/ndstbp8

As indicated above I consider the "hot-hand fallacy" and "gambler's fallacy" two very different subjects and levels of complexity; referencing them together is mixing apples and oranges a bit (though I understand why both show up in such discussion).
Like most articles, this one fails to take into account the intrinsic oversimplifications of hot-hand analyses, and again treats the hot-hand as something spectators observe, rather than something an athlete 'feels' or experiences.
I wish this whole area would just move along now as not worthy of further exploration (...but am sure it won't).

Still Legal... Torturing Data

Review of "Standard Deviations" by Gary Smith

"Lying with statistics is a time-honored con. In Standard Deviations, economics professor Gary Smith walks us through the various tricks and traps people use to back up their own crackpot theories. Today, data is so plentiful that researchers spend precious little time distinguishing between goo, meaningful indicators, and total nonsense. Not only do others use data to fool us, we fool ourselves."
-- from the back cover of the book

This is one fun read! And a volume that hasn't received enough attention. It's 300 pages of easy-to-follow, enlightening, illustrative (and non-technical) material, that is actually very important, as a veritable romp through the mined landscape of troublesome statistics, be they from mass media, academia, or from scientists themselves!

Gary Smith's book came out in 2014 at a time when I felt overdosed on popular statistics treatments, so I didn't give it much attention. It's now out in paperback and had I read it earlier it would've been on my "best books" list of 2014. It adds to the growing arsenal of work critiquing our statistical naivete. The phrase "lies, damned lies, and statistics," coined well over a century ago, has never been truer than today.

Smith himself is an economist, but he draws examples for this statistics salad from every nook-and-cranny of life; sports, Wall Street and finance, gambling/lotteries, advertising, medicine, research, ESP, etc. The book offers example after example after example of statistical tomfoolery, shenanigans, trickiness, and plain honest mistakes. If you've read much in this genre, many of Smith's examples will be familiar, even time-worn, but still his firehose spray of cases is well organized, impressive, fun, AND educational.

Various important themes run through the book:

1)  One major theme is how humans are pre-wired to look for and find patterns in their observations... and how easily that can lead them astray. As he writes at one point, "data clusters are everywhere, even in random data." Patterns need to be mitigated by common sense... if a pattern just doesn't make sense, then don't believe it, but look for other confounding variables, or sheer coincidence. The use of 'common sense' and reason in tandem with data, permeates these pages. A theory without good data to back it up isn't worth much, but so too, provocative data without a good theory to explain it is dubious -- data and theory ought go together like hand and glove.

2)  Graphs and visual displays are often a source of bias or distortion -- always check the labeling and scaling/spacing of axes or other depictions. Don't assume that data are collected, analyzed, or reported accurately.

3)  It's not always the data as presented that is a problem... it can also be the data that ISN'T presented -- either it was never collected, or it was collected, but for reasons not spelled out, then deleted from presentation. And what is missing may be more important than what is shown.

4)  "Regression to the mean" is the subject of another whole chapter, emphasizing that extreme or outlying data, performances, or events, often tend to revert to closer-to-the-mean values over time.

Of course sometimes a research study may actually be good, but the popular press reporting of it is flawed or oversimplified -- details and nuances being stripped away for the sake of time or space.

One reviewer faults Smith for being "relentlessly negative." That may be an overstatement, but even if true, I view it as a positive!... the book essentially says, 'Look here, and here, and over there, and at this here; at all these examples of the misuse of data leading us astray.' And THIS is a message we need to hear MORE, not less of, in today's data-saturated lives!

One thing I like about the book is that Smith doesn't mince his words. While he has positive things to say about such heavyweights as Daniel Kahneman and Dan Ariely, he doesn't hesitate to criticize other popular writers, including the authors of "Freakonomics," or a sociologist named David Phillips, or "The Motley Fool" writers, when they have erred. Some may find him too dismissive in a few instances where the issues aren't altogether settled, but I like his blunt, critical approach.
He also disparages some of the common arguments for the famous 'man with two children' probability paradox, which has a number of variations, and has been extensively debated (Smith gives the answer as 1/2 probability, not 1/3, as many do).

Each chapter ends with a short paragraph summary of the main points, and the final chapter of the book also summarizes the essence of each previous chapter. In short, and without being too redundant, Smith drives home the essential ideas he wants you to come away with from the plethora of examples provided.
Bottom-line, it isn't just difficult, but virtually impossible, to take into account all the 'confounding' factors that may affect a scientific study and its reportage, so a watchful, skeptical eye is in order.

One of my beefs with self-described 'skeptics' is how much time they spend on what I call 'low-hanging fruit'... astrology, ESP, UFOs, homeopathy, etc. while giving a light touch to articles in scientific journals that are weak, poorly-done, poorly reported, or even fraudulent. Excellent science is hard to do, but we ought at least be holding out for "good" science.  I HOPE a book like Smith's helps inculcate a greater wariness of assumed reputable scientific evidence. The "evidence" of "evidence-based science" (perhaps better-called 'publish-or-perish-science'!) is often incomplete or skewed, and considerably more subjective, biased, or based on ill assumptions, than acknowledged; it is rarely incontrovertible, and yet all-too-often escapes keen examination (especially via a broken peer-review process).
Professor John Ioannidis is famous for concluding that 'most research findings are false'. I'm more comfortable simply saying that most research findings are oversimplified, potentially-misleading, and ill-contrived, yet too-easily lapped-up by both uncritical skeptics and the public. The main defense against this state-of-affairs is an educated, on-guard citizenry (and more open-source peer review)... and Smith's book is a diligent effort toward that goal.
In the end, this isn't only a fun book; it's actually a highly important treatise!

Statistics Is Suddenly Sexy!

As someone who last took a statistics course 35 years ago, I could never have foreseen the popular rage that statistics and data-crunching would become in current times (I still recall, and wrote about, my introduction to statistics as a youngster in a museum, though I didn't know it as such back then). And I haven't yet read Nate Silver's huge bestseller "The Signal and The Noise" -- I assume it is good and probably has a strong Bayesian tilt. But I love the volume I've just finished reading (which doesn't even mention Bayes): "Naked Statistics" from Charles Wheelan -- it's likely the best, most palatable introduction to statistics for layfolks I've ever seen. Not at all overly-technical, in fact sprinkled with fun and humor, and full of real-world examples (not abstractions) of statistical thinking in our day-to-day lives.

The book has a very nice progression of topic areas from means and medians and 'descriptive statistics,' through probability, correlation, the central limit theorem, hypothesis-testing, and on to regression analysis, but always with an emphasis on understanding underlying concepts, not specific empirical formulas or computation.
The author's focus is constantly on educating the reader as to why a basic understanding of statistics is vital self-defense in today's firehose world of information, journalism, science claims, and headlines. Clear examples are drawn from health reporting/diagnosis, gambling, Wall Street and the economic meltdown, polling, sports, business, and other everyday encounters (as well as including a very good chapter on the classic "Monty Hall Problem").
Some reviewers call Wheelan's approach "intuitive," which can be dangerous in so much as applied statistics and definitely probability can actually be very counter-intuitive at times, but again, this book is only dealing in the basics.
The one major drawback of the volume is that, as indicated above, there is no discussion of Bayesian analysis, which is sort of the 'golden boy' of much current statistical talk, that readers will miss out on.

 My favorite chapter may be Chapter 6, describing how a probabilistic "Value at Risk" financial model from "overconfident math geeks" nearly brought down "the global financial system," but every single chapter is simultaneously intelligent and entertaining (...makes me want to read more of Wheelan).

The NY Times has a review from Abigail Zuger who rightly calls the book, "sparkling and intensely readable":

http://www.nytimes.com/2013/01/29/science/naked-statistics-by-charles-wheelan-review.html?_r=0

Zuger, an M.D., actually refers to it as, "the most important health book of the year... even though it’s not primarily about health," and then continues,
"...his multiple real world examples illustrating exactly why even the most reluctant mathophobe is well advised to achieve a personal understanding of the statistical underpinnings of life, whether that individual is watching football on the couch, picking a school for the children or jiggling anxiously in a hospital admitting office."

Wheelan incidentally, wrote a prior bestseller, entitled "Naked Economics," which I suspect is equally good if you care to brush up on that field of study.

As long as we're talking stats, some other recent pieces worth mentioning:

Another blogger believes, "All journalists should be required to pass a course in basic statistics before they are let loose on the unsuspecting public" and argues so here:

http://learnandteachstatistics.wordpress.com/2013/01/28/journalists/

Meanwhile, Evelyn Lamb and Hilda Bastian are two bloggers who presented last week at the Science Online Conference in North Carolina (THE premier annual digital science communication gathering). Theirs was one of the few math sessions, and entitled: "Public Statistics: Blogging With Numbers":

http://scio13.wikispaces.com/Session+2G

Lamb wrote an introductory piece to the session for her Scientific American blog here:

http://blogs.scientificamerican.com/roots-of-unity/2013/01/27/statistics-in-public/

...and Bastian covers statistics with a light touch at her blog here:

http://statistically-funny.blogspot.com/

Finally, statistician William Briggs recently had Twitter attention tossed his way for an older provocative piece he did called, "Statistics is Not Math" in which he argues that "Statistics is not math; neither is probability... Statistics rightly belongs to epistemology, the philosophy of how we know what we know." (be sure and read the interesting comments as well):

http://wmbriggs.com/blog/?p=3169

Many people have recently made the case that statistics, in some form, should be part of the core math curriculum for ALL secondary students, and be a basic part of math literacy. Read the above books and links and you'll be on your way to having it covered. In fact, seriously, I think Wheelan's book (or something like it) ought be mandatory reading for all engaged citizenry!

In a 3-minute TEDTalk below Arthur Benjamin argues the case for required secondary statistics education:

And I'll close out with this example of probably how NOT to use statistics from another (tongue-in-cheek) 7-min. TEDTalk: