## Popular obsessions

These are real-world topics which (in more polite terms) attract more attention and argument than they deserve. A separate page discusses fantasy obsessions.

### Math topics

On the mathematical side, the Monty Hall problem and Benford's Law are, in basic form, simple and well explained in the Wikipedia pages, but attract unnecessarily convoluted explanations.

### Inane media comparisons for the chance of winning the lottery

This is a pet personal peeve. In early 2016 the Powerball lottery prize reached the record level of almost 1.6 billion dollars. A single ticket has a 1 in 292 million chance of winning. I often get contacted by journalists on such occasions, because there will be many short news articles comparing this chance to a list of asserted chances of other unlikely events. The link above shows three such lists. As well as the dubious accuracy of some figures there, and the fact that those other chances depend very substantially on individual behavior, the conceptual problem is that these other activities are hardly comparable to "buying one lottery ticket". If one must seek comparisons, a sensible alternative is to standardize on a one in a million chance. Buying 6 Powerball tickets every week for a year adds up to about a 1 in a million chance to win once. To compare to another "ordinary" activity, this is similar to the chance of you being killed in your next 200 mile automobile trip.

### The mystique of card counting

The popular history of blackjack card counting makes a great story, parts of which are actually true. But like other adventure stories, it is not so advisable to try it yourself. After quite considerable effort you might become competent enough to make a small profit, and after more effort you might start to make a noticeable profit. And then (in most places) be banned from casinos. To me there are two take-away lessons here. First, if an occupation in which you sit in an enclosed room and focus intensely on a repetitive activity appeals to you, then more worthwhile occupations are available -- air traffic controller, for instance. Second, I suspect that the casino industry has actually benefitted from the existence of card counting raising the profile of blackjack amongst the general public and thereby attracting more players; they have no reason to crack down on minor players.

### The mystique of outstandingly successful investors

Logic says that, because most stock market investment is via professional management (I'll write mutual funds, for simplicity) which charge a fee to investors, the average return to investors over all such funds must be essentially the overall market average, minus the average fee. Despite academics, and index fund groups such as Vanguard, emphasizing this fundamental and empirically verifiable truth since the 1970s, it has taken a long time for passive investment to become commonplace. One of several reasons is surely "wishful thinking" by investors who believe (or, more likely, are sold the belief) that they can somehow pick a better-than-average fund.

This relates to the mystique of outstandingly successful investors, exemplified by Peter Lynch in mutual funds, Jim Simons in hedge funds, and Warren Buffett's holding company. There are two issues in thinking about such people. With tens of thousands of managers, some "by chance" will do better, and a few will be very lucky. In order to judge whether the best performers did better than what could be expected by chance for the best, one would need to know funds' risk profiles, and to take account of effects such as survivorship bias. I do not know any convincing analysis. But for the sake of argument let us stipulate that indeed a handful of managers have indeed been demonstrably better than explainable as luck. That would be interesting as a fact about human ability. But does it help you? By analogy, let us imagine that there are a few struggling young artists whose work can be bought cheaply today but will be very valuable in 20 years; how do we identify these particular artists? There is a lot of data showing that, within the bulk of fund managers, there is little correlation between performance in successive years, and simply looking at the best performers over the last 5 or 10 years is not enough to identify the special handful. You can see for yourself by playing This online simulation game by my STAT 157 students Yixin Shen and Dodo Qian.

### Hot hands -- phenomenon or fallacy?

An interest in extremes and records is a common human trait -- I imagine there is some psychological research on why this is so -- and in the context of sports people pay attention to streaks of successes of some type. Alan Reifman's 2011 book Hot Hand: The Statistics Behind Sports' Greatest Streaks and his blog contain many examples. The "hot hand" phenomenon originally referred to successive attempts by a player within a game (shots in basketball being the prime example) being successful. Many players believe that sometimes they are "in the zone" and for a period of time perform better than usual. If true, one could in principle detect it by looking at long streaks and comparing observed lengths with what would be expected "just by chance" for that player's skill level.

Now a priori this a reasonable question worthy of statistical study. But there have been many studies, some of which find no evidence of this "hot hand" and others find a small but statistically significant effect. So a posteriori we may confidently conclude that the effect is at most small and so the bottom line is

it doesn't matter whether it's real or not.