–Arts and letters for the modern age–

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–Arts and Letters for the Modern Age–

Whose Hot Hand? Which Fallacy?

by | Mar 20, 2023

There’s always a little light-hearted ribbing around the office or among friends over March Madness betting pools. But basketball-related disputes are sometimes more enduring. Statisticians and researchers have been passionately divided for decades over the mere issue of shooting a basketball. To paraphrase David Foster Wallace on behind-the-scenes rifts in lexicography, this is the seamy underbelly of sports analytics. The question is whether a thing called “the hot hand” exists or if it’s just a cognitive illusion on the part of basketball fans, coaches, players. 

The topic started in academic circles but, going by the name “hot hand fallacy,” eventually made its way into the public square. Notable examples include a 2013 article in the New York Times by David Brooks in which he stated that the notion of being in a “groove” had been debunked by expert attention to data. In an ostensibly motivational speech, Larry Summers got the Harvard basketball team to admit that they believed in the hot hand, and then revealed that they were under an illusion. If you saw the movie The Big Short, you saw the Nobel Prize winning economist Richard Thaler, sitting alongside Selena Gomez at a craps table, diagnosing a misguided belief in basketball known as “the hot hand.” 

The urtext of hot hand skepticism is a 1985 paper by Thomas Gilovich, Robert Vallone, and Amos Tversky (GVT) called “The Hot Hand in Basketball: On the Misperception of Random Sequences.” The paper purportedly showed that there’s no such thing as a hot hand in basketball. When people watching a basketball game say, “pass Curry the ball, he’s on fire!” GVT concluded that these normie sports fans are confused about what’s really happening on the floor. Contrary to the normies, Curry was not really on fire. People just tend to over-detect and reify patterns. 

I am on the side of the normies. I deny that this ambitious claim was ever fully demonstrated, statistically or otherwise. 

Nowadays, one can be in the statistical cognoscenti and take either position. It wasn’t always this way. GVT were credited with disproving the hot hand for many years.     

The philosopher Quassim Cassam declared that basketball coaches who cling to the belief in the hot hand lack intellectual character, lumping them in with conspiracy theorists for having a similar vice. The latest research has found better results for the optimists by further contextualizing factors GVT didn’t, such as shot difficulty, tightness of defense, etc. GVT’s research was much more one-dimensional, and in incorporating only the data points of hits and misses along one dimension, the research was strongly indirect and “dichotomous.” 

A player might have this set of hits and misses during a game: HMHMMHHMMH. Strings of random numbers (also called H’s and M’s for convenience) can also appear this way. But what if a player’s last ten shots show the pattern HMMHHHHHHH? This looks like a hot streak, but the trouble is that even here random number strings can also exhibit this behavior. GVT concluded that the data does not support the belief that a player who hits a shot has a better than random chance of hitting the next shot. GVT had previously asked 100 basketball fans if the hot hand, in order to count as such, would be distinct from random chance and if the chances of a shot after a hit should have a higher-than-average chance of success. The people who employ the term natively – the fans – agreed to these conditions of valid use, and that valid use was not detectable in the data. Therefore, there is no hot hand. QED. 

Even as the experts are now divided, my argument will not rely on any statistical insights that are newer than GVT’s initial findings and it would have the same merit or lack thereof whether or not the experts still agreed. This is a dive into qualitative, not quantitative reasoning. I’ll assume GVT were correct in what they demonstrated, narrowly limited to the numbers, for argument’s sake. Any further statistical methods that contradict or reinterpret GVT in favor of the hot hand will be a perk. 

This clarification is necessary to highlight the fact that the fallacy that’s gone unnoticed so far is not the hot hand, but equivocation. A more specific form of equivocation has been named and called out in recent years with increasing frequency – the motte-and-bailey. A motte-and-bailey fallacy is committed when one asserts a stronger and more difficult to defend version of an argument but retreats to a weaker and easier to defend version when challenged on the stronger claim. Weaker claims are generally easier to defend. They’re efficient, but they’re not as sexy. Boldness gets people talking. The problem is it gets people talking past one another. 

A serious problem of definition began early, when 100 fans agreed that random chance must be distinct from the hot hand. I’d like to ask these fans a couple questions myself. I might ask “Are you aware that random strings of data points also cluster at times, as if in a hot streak of some sort but again, are actually random?” I might also ask survey participants if they’re confident that even a past tense reference to a player having the hot hand requires real time increased chances of each shot going in after a hit, such as “wow, he had the hot hand that game!” This would be an obviously routine invocation of the hot hand in everyday discourse, and one that doesn’t require increased chances of shot success after any and every successful shot. If the answers I elicited complicated the GVT’s definition, it wouldn’t be the first time survey participants were wishy-washy. People often react differently when asked to evaluate The Affordable Care Act vs Obamacare.

It’s important to concede that GTV did successfully demonstrate some weaker, but still interesting claims. What they showed would be enough to make any workaday researcher proud. First, they showed that genuine hot streaks in basketball almost certainly happen with less frequency than is traditionally supposed. They also showed that a random basketball fan’s perception of spotting a hot streak in real time is not statistically reliable. A player who hits a shot is not necessarily more likely to hit subsequent shots, free from all other contexts. 

That would have been fine, if not for all the pop-intellectual showboating. What the showboating inadvertently calls attention to is the fact that GVT made the highly questionable assumption that by homing in on a common use among others, they had a legitimate claim on the common use. GVT gestured toward magnanimity by conceding that other uses might exist, but then asserted that the common use of the main varying notions all fall under their definition, marginalizing other uses without linguistic curiosity or investigation. If some other non-trivial uses exist with the linguistic family resemblance of “hot hand” that aren’t implicated by GVT’s work, then it’s much less interesting when philosophers admonish normies to stop believing in the phenomenon or when economists make cameos in movies to lecture that a cognitive illusion is afoot. 

The skeptical argument gains its popular cachet by labeling the allegedly debunked phenomenon by a common and complex term, ‘the hot hand’. Widening what GVT called the common use to match the real-life use can be done preliminarily from the armchair. The use GVT gave their attention to is what I’ll call the “match-kindling thesis,” in keeping with the temperature and fire metaphor. This view holds that shots made in basketball act as a kind of ignitor match, which can eventually start a fire, as in “he’s on fire!” If this view is true, then it should be detectable in the data and distinguishable from random chance. GVT at least dealt this view a significant blow. Making this usage explicit, it means that any successful shot or two should result in an increased chance of the next shot being successful. But this doesn’t exhaust every common and legitimate use of “hot hand.”

I’ll compare the match-kindling thesis to what I’ll call the “flow thesis.” In this context, “flow” is a synonym of groove, and it doesn’t assert that any successful shot is a sufficient condition to “ignite” flow and it needn’t be a generally distributed potentiality of the external world, like combustibility. “Flow” and “groove” refer to a state of roughly maximal coordination of the body that is best suited to the physical activity at hand. This is a common notion, but the psychologist Mihaly Csikszentmihalyi also wrote a book about it called, Flow: The Psychology of Optimal Experience. Csikszentmihalyi describes flow as a “state in which people are so involved in an activity that nothing else seems to matter.” The key piece I’m emphasizing is not necessarily a participant’s utter consumption in an activity, but a certain level of unconscious coordination of the body, usually after a sufficient level of skill is consciously achieved. The utter consumption Csikszentmihalyi describes is a sufficient, but not a necessary condition for common uses of “flow” and “groove.” 

Contra GVT, there is no linguistic constraint on “hot hand” successfully referring to a flow state as one of the main common uses of the term. The factors contributing to whether a player goes into or out of a flow state, so far as GVT’s one-dimensional data are concerned, could partly be due to whether enough muscle memory had kicked in from practice, whether or not a player’s circadian rhythms were disturbed, whether a player was hung over, whether the layout of a gym was more orienting than another, etc. Nothing here indicates that any particular hit or miss of a shot determines the chances of the next shot for better or worse, at least not as a characteristic of single shots generally. 

To decide that the full common use of the hot hand was debunked by GVT’s work would implicitly rely on eliminativist or at the very least strongly behaviorist reasoning. Let me explain what I mean. When it comes to AI, which employs statistical methods to perform its impressive work, many researchers believe that if a computer program can pass the Turing Test, then it counts as conscious. In other words, all it takes to be conscious is the exhibition of a kind of behavior — it amounts to nothing more than that. It’s not that an AI would then be viewed as having deep internal thoughts and desires, as much as that thoughts and desires in human beings would be knocked off their epistemic pedestal, insofar as they’re called upon for explanations of human behavior. Similarly, GVT believes that since you can explain player performance as within the realm of random chance, hot hands must not be real, but are simply an erroneous label that people apply to behavior when they don’t understand probability. 

This kind of reasoning, when generalized, would simply entail full-blown behaviorism: there would simply be no point in adverting to mental phenomena to explain human behavior, even when it comes to something as modest as the role of the mental in physical coordination. Instead, all you would need to do is see how statistically likely some behavior was. If it was within a normal statistical distribution of behavior for people in general (or for that person in particular), then there would be nothing left to explain. It is not necessarily that behaviorist views are assumed here to be off limits, but they’re specific and unusual enough to call for open articulation in cases where they play a supporting role in a chain of reasoning.

In other words, let’s say you’re reluctant to accept that an AI that’s powered by statistical methods and passes the Turning test would by definition possess something equivalent to human consciousness, where human consciousness would then only be understood statistically. This is even worse, because at least such an AI would have to exhibit the full outward range of a human behavior, as opposed to GVT’s one-dimensional and context-weak data. If GVT’s kind of indirect, surface data is by itself enough to debunk the hot hand phenomenon, then presumably any technique that could statistically mirror human activity would also place that human activity under serious suspicion, relegating it to the “folk” realm of intellectual prestige.  

However, in the realm of explicit reasoning, it’s not that the hot hand skeptics deny that skill is involved in making shots. What they believe instead is that skill is only ever manifested in discrete shots, separate from others. Further, they believe that the common use of “hot hand” must involve something in the family resemblance to the gambler’s fallacy. The gambler’s fallacy leans on the belief that a random outcome will be “due” in a particular instance, because the lack of that outcome in the past has made it more likely to occur in the present. In this way, the gambler’s fallacy is like the negative sibling of the hot hand, in the minds of the skeptics. The gambler’s fallacy relies on recent absence to predict a “due” outcome, while the hot hand fallacy relies on recent presence to predict a “hot” one. The two fallacies are joined by failing to appreciate the alleged statistical independence of discrete instances. 

If strong statistical independence is right, then flow states cannot have the effect of leading a player to hit many shots in a row because in such a scenario the consecutive successful shots would be linked by the flow state. In other words, flow states cannot exist. But strictly speaking, without relying on an implicit assist from behaviorist reasoning, whether or not GVT’s work successfully debunks the hot hand (i.e., flow states) is underdetermined. That is, the findings are consistent with more than one main explanation: that a flow state is being experienced, on the one hand, or on the other that each shot is independent of another, never running together in flow states. 

Underdetermination is a highly involved philosophical concept, but we don’t need to dive in too deep. Facing an underdetermined outcome is perfectly illustrated in the Stanford Encyclopedia of Philosophy. It happens when “… the evidence available to us at a given time may be insufficient to determine what beliefs we should hold in response to it. In a textbook example, if all I know is that you spent $10 on apples and oranges and that apples cost $1 while oranges cost $2, then I know that you did not buy six oranges, but I do not know whether you bought one orange and eight apples, two oranges and six apples, and so on.” As the philosopher Steven D. Hales wrote of hot hand skepticism, “the critics have to assume an error theory,” (emphasis added). 

But without announcing or perhaps even noticing it explicitly, GVT focused most of their attention on the match-kindling thesis, not the flow thesis. In the context of the match-kindling thesis, whether GVT’s skepticism wins out or if subsequent research overturns it, no such problem of underdetermination arises in either case. In the hands of David Brooks, Quassim Cassam, and Richard Thaler, however, the informal invocation of “hot hand” implicates the flow thesis through common usage, as the layperson is entitled to incorporate normal meaning in the wild to understand what terms mean when invoked informally. This sets up the bailey, which if made explicit would be “the flow thesis was debunked by GVT.” This is the harder position to defend. The difficulty in defending this position then gives way during argumentation to the motte, which if stated explicitly would be “the match-kindling thesis was debunked by GVT.” This is the easier position to defend. 

Still, even the more recent studies that found the hot hand have not all found exceptionally strong or frequent effects from a lay sport fan’s perspective, so hope in the hot hand might be dim, even if technically alive. But here, on behalf of the normies and the jocks, an important distinction needs to be drawn between “frequent” and “common.” In this context, frequency is a characteristic of the data sets under consideration, but the concept doesn’t necessarily consider absolute occurrence. That is to say, if something is common it is found often, while still possibly being infrequent within its set.

Think of all the basketball games that take place on a regular basis, both formally and informally. There are pickup games at varying skill levels, YMCA and health club leagues, summer leagues, high school games, college games, pro games outside the United States, and finally the NBA. The opportunity for hot streaks to take place, even if infrequent, is enormous. In other words, that something is uncommon in its own narrow context, (e.g., relative to all other shots under consideration), doesn’t necessarily make it absolutely rare in the wider context of the real world, which is the number of times observed and experienced in total.

My contention is that in this context of both lived and watched experience, the normie belief in the flow thesis, and therefore the hot hand, enjoys the default entitlement. That is to say, at first glance, all other things equal, short of strong evidence to the contrary, the belief in flow states needs no extra justification. It needs no extra justification any more than that you can swing your arms when walking in such a way that eventually becomes second nature, or that when you swing a hammer for extended periods of time that you can get “in the groove” during certain periods of work. It is indeed continuous with normal bodily coordination, even while involving more specialized movements. 

The flow thesis could still suffer from scrutiny of data, hypothetically. This would involve a lot more information, something aspiring much more closely to sufficient comprehensive intelligibility than what GVT presented. For example, the belief could eventually lose its entitlement if no study ever found that hot streaks were more likely regardless of how granular and contextualized the study. In this scenario, the evidence would have to be elusive even after incorporating direct extensive footage and detailed analysis of bodily movements from shooters in basketball games, and to the extent possible, information from brain imaging. The hot hand could then become like invisible gremlins that actually make the mechanical components of a car go but leave no trace of their work behind. Depending on how the gremlins are conceived, they can be completely shielded from epistemic disconfirmation. 

But my view is that the flow thesis starts with a roughly equal level of parsimony to GVT’s skeptical thesis, unlike the invisible gremlins. Parsimony is often equated with Occam’s Razor, the view that entities should not be multiplied needlessly, a stance in favor of metaphysical frugality, insofar as possible. Profligate theses get cut; frugal ones stay around. Entities like the gremlins were killed by their lack of parsimony, while three-point shooters in flow states live on. Some say they live their best lives when the games are most important, when it’s all on the line. It’s all there in March, in the NCAA tournament. You might notice a player or two who can’t seem to miss, and that could lead to a rapturous outcome the experts wouldn’t have predicted. With that surprising outcome, hoop dreams will be dashed or fulfilled. It’s madness. I still believe.