The Hot Hand in Basketball: An Analysis of the Thinking

Zarar explains his sabbatical, AND the hot hand.

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Ed’s Note: I’m taking the year off from RR to do my MBA at Rotman. Is it worth it? Ask me in a year – I’ll be writing a brutally honest post about it which will become a must-read for anyone ever taking the program. For now, though, here’s a paper I submitted for a course called Business Problem Solving: A Model-Based Approach, which focused on thinking biases when analyzing day-to-day and business issues. Of course, I picked basketball. Special thanks to Blake Murphy for the editing.

Introduction

The NBA defines clutch scoring as points scored with under five minutes left in a game with the score difference being five points or less.  The degree to which teams maximize  points-per-possession during this critical stretch is usually the difference between winning and losing, with coaches having to make key decisions during this time.  One such decision is whether to let a player who has the “hot hand” continue shooting the ball, in hopes his recent hot streak will continue, or to look for alternate sources for offense, perhaps towards players who the defense is paying less attention to.  

This paper will not attempt to prove or disprove the hot hand theory.  It will assume it to be a valid basketball strategy, and explore the thinking behind utilizing the hot hand versus other available options.  It will understand the claims of the theory, examine its beliefs and implications, and comment on the quality of the thinking that supports it.  An alternate model will be presented, one which encourages action opposite to the one prescribed by the hot hand, and it will undergo similar analysis.  Based on the analysis, steps which will improve the way we think about clutch scoring will be described, which will hopefully yield better offensive decision-making processes.

Model Identification

The hot hand in basketball is a widely subscribed to theory which encourages players who are having strong shooting games to continue shooting.  Coaches adopting this strategy expect to increase the points-per-possession yield by ensuring that the in-form player is shooting the ball as much as possible, with the belief that feeding the hot hand will be productive.  For example, NBA players having hot shooting games are often encouraged to shoot more with the belief that their high in-game shooting percentage results in a greater chance of them hitting their next shot, regardless of how much lower their season or career shooting percentage is.

An opposing view to this model is the belief that feeding the hot hand will be counterproductive.  This view sees the in-form player attracting greater defensive attention, resulting in them attempting lower percentage shots, while taking away better shooting opportunities from teammates who have lesser defensive attention.  For example, a player who has made 8 of the 10 shots he’s attempted is likely to attract greater defensive attention resulting in tighter spaces, narrower passing lanes, and better shot contests, making the attempted shot of lower quality.  In addition, as defense is a zero-sum affair, there is an opportunity cost: the increased defensive attention towards the player would have left someone else with poorer defensive coverage more open, and thus given them a better shot which was never realized.  In this model, providing the in-form player with more shot attempts will result in a lower points-per-possession yield.  

The Productive Hot Hand

This section will disaggregate the hot hand theory by identifying the type of thinking that proponents of this model will likely hold, including players, coaches, and analysts.  It will attempt to identify the sources that inform the model and led to its creation, while reflecting on why the model has persisted over the years despite statistical evidence to the contrary.  An assessment of the thinking behind the hot hand theory will also be discussed.

Disaggregation

Proponents of the hot hand theory are likely to believe that:

  • Confidence in one’s shooting ability is a large determinant of whether the shot is successful
  • Making successive shots gives the player a right to take the next shot
  • Distinct periods of successes (hot streaks) and failures (cold streaks) are expected\

Confidence in one’s shooting ability is a large determinant whether the shot is successful

An important element of the hot hand theory is the belief that when a player “feels good” about himself, he is likely to succeed.  Confidence is seen as the intangible element that fuels on-court success, especially shooting.  At times confidence and self-belief are seen as a greater component of success than physical attributes.  Dante Exum, a point guard for the Utah Jazz, gave prominence to the role of confidence when recovering from a knee injury, hinting that despite his knee being deemed physically healed, the priority was him believing that his knee was ready:

“[Gaining confidence] was the biggest thing that we were trying to work on throughout this whole rehab.  Definitely in the later stages, when it got to that point where I was starting to play again, it was just about getting the confidence back in the knee and the ability to play again.” (Taylor, 2016)

In the case of the hot hand theory, this confidence arises from a player seeing his shot go in.

Making successive shots gives the player a right to take the next shot

At the crux of the hot hand theory is the belief that success breeds success.  If a player has made a few shots in a row, he deserves to take the next shot as he has the highest probability of making it.  Possessions are seen as the currency of basketball, and shot attempts are an indication of how important a player is to the team as the cost of a shot attempt is generally a possession.  For example, most NBA teams’ leading player also averages the highest number of shot attempts.  However, when a lesser player is having a successful stretch, coaches and analysts will often call to “ride out” the hot hand as the in-form player has demonstrated a right to take the next shot, regardless of what the pecking order in the team is.

Distinct periods of successes (hot streaks) and failures (cold streaks) are expected

Proponents of the hot hand expect a player to go through prolonged stretches of success and failure.  If a hot hand exists, then so does a cold one which sees a player go through poor shooting stretches.  From a coach’s perspective, these periods are often seen as the norm. Toronto Raptors head coach, Dwane Casey, when commenting on Patrick Patterson’s struggles, hinted at the remedy being to simply ‘get out’ the cold stretch:

“Shooters never forget how to shoot, it’s like riding a bike, so he’s got to keep shooting it….that’s the stretch he’s going through, get it out now and be ready to come out next week when it’s for real and be ready to hit those shots.” (Wolstat, 2015)

The idea that a player will generally not shoot his career field goal percentage throughout the season, but will go through a balancing cycle of hot and cold streaks is a belief that many coaches and analysts hold true.

Analysis

Confidence in one’s shooting ability is a large determinant of whether the shot is successful

This type of thinking deemphasizes a player’s physical attributes including strength, stamina, and shooting motion, which are generally the same when he’s going through a cold or hot spell.  Instead, it focuses on how much self-belief and confidence the player possesses at the time when the shot is released as a determinant of success.  This thinking is not just limited to basketball players, but other sports as well.  Extending this beyond the sporting landscape, intangible attributes like confidence and self-belief are seen as a driver of success in physical feats.

This thinking can be critiqued as overestimating the amount of information one needs to predict success (or failure).  There is an inherent recency bias of making future decisions based on a smaller, more vivid, set of information.  The deemphasis of base rates in favor of recent trends is the general principle behind this thinking.  Even though confidence is arguably a positive trait, this can be problematic as it can lead to overplacement of one’s abilities to the point where a person may think that their abilities are superior to their peers.  However, when looked at objectively, they may not be.

Making successive shots gives the player a right to take the next shot

The essence of this belief is that making shots is part of a feedback loop that can increase the chance of future success, and thus, the player experiencing success should have a chance to replicate it.  The thinking can be extended beyond the basketball court and into everyday life: Success is important, and the actions that caused success need to be replicated to achieve more success, regardless of existing plans.  It may be irrelevant what the fourth-quarter strategy was for a team at the start of the quarter – if a player unexpectedly “heats up,” efforts will be made to maximize the output.  If a person deals with two stockbrokers and one of them picks three winning stocks in a row, his recommendation will be given greater weight, regardless of whether the other has a better overall record of picking stocks. There is a tendency to not think deeply about what enabled the actions to have caused success, but instead to rely on heuristics and easy explanations of what can be complex systems.

This is a form of reinforcing feedback as described in Peter Senge’s The Fifth Discipline, where successful outcomes are supplying reinforcing feedback which are seen to accelerate a positive trend.  The question is not whether the thinking is right or wrong, but whether it is applicable in the context.  Related to this thinking is the “snowball effect” where a person performs an action which yields a positive result.  The ensuing success is attributed primarily to the person, which in turn gives them further authority to perform more actions.  The cycle continues until the person is seen as infallible until they, arguably inevitably, are met with failure or regression.  The incorrect attribution of success can be a fatal flaw in this thinking.

Distinct periods of successes (hot streaks) and failures (cold streaks) are expected

The insensitivity to base rates is the undercurrent that drives the thinking behind the hot hand.  Instead of viewing a player’s shot-making ability as a continuum that adheres to base rates, analysts often tend to view them in hot and cold streaks.  This thinking can be prone to a clustering illusion where successful clusters of events dominate the thinking instead of the larger sample size, which may be more evenly distributed. Similarly, it can be that recent negative events can overshadow an otherwise impressive record.

Gilovich, 1985, shows that there is no evidence of a positive correlation between outcome of successive shots, and that the hot hand is a fallacy. However, the desire to ascribe and explain success or failure is a very strong human tendency (in this case, why a player is making shots).  The ability to assign a cause to an effect can be seen as valuable, and this can promote lazy thinking relying on easily accessible models, regardless of their truth content.  It is very easy to explain a string of unfortunate events as “having a bad week” or alternately, a string of positive ones as, “must be his day.”

The Counterproductive Hot Hand

This section will disaggregate the theory that belief in the hot hand is counterproductive.  It will identify the type of thinking that proponents of this belief likely hold.  It will attempt to identify the sources that inform the model and led to its creation, while reflecting on why there is strong support for this model, including from the author.  An assessment of the thinking behind the theory will also be discussed.

Disaggregation

Proponents of the counterproductive hot hand (CHH) are likely to also believe that:

  • Self-belief can lead to overconfidence, and underestimation of shot difficulty
  • The better a player is shooting, the more defensive attention he receives, thus reducing efficacy
  • The more a player is involved in the game, the more the defense learns about them, and is thus able to devise better strategies

Self-belief can lead to overconfidence, and underestimation of shot difficulty

It is reasonable to suggest that when a player is having a strong shooting game, their confidence about their shooting ability increases.  The feeling that this is “my night” increases, and this leads them to believe that they can make more difficult shots than what they are generally capable of.  Consider a player who shoots well from the 18-23 foot range, but shoots poorly from more than 23 feet.  During the middle of a strong shooting game, their thinking starts to evolve and they feel that they have a high chance of making any shot due to this being an exceptional evening.  In this scenario, they would start taking shots from the 23+ feet range (which are more easily on offer by the defense), thus reducing their statistical chances of success.  They underestimate the difficulty of making a shot which they have a track record of being poor at.  

The better a player is shooting, the greater the defensive attention received, thus reducing efficacy

One of the changes seen in clutch time play is the increased attention paid to players who are having strong performances.  Coaches plan on mitigating threats from proven performers by sending double-teams in the form of weak-side help, trapping, etc.  In situations like this, if the strong-performing player insists on shooting, the quality of the shot they will attempt can be argued to be poor, as they have received the most defensive attention.  Proponents of CHH would reason that the greater the defensive attention received, the worse the likelihood of scoring,

The more a player is involved in the game, the more the defense learns about them, and is thus able to devise better strategies

NBA defenses tighten in the fourth quarter, with a higher degree of game planning including offense/defense substitutions, situational play-calling, higher use of timeouts, etc.  These tactical changes are based on game flow, player performances, injuries, and a host of other factors.  The reasoning that the involvement of a player in a game is proportional to the quality of strategies devised against them, is a logical one as coaches with an opportunity to evaluate players for a longer duration will be able to gather more information, and use that information to devise more effective strategies.  The NBA’s introduction of SportVU technologies focused on positioning, movement, and tendencies, giving the coaching staff real-time insights which can be applied immediately.  If a player has a high number of touches and is involved in the game, there will be more information available to use against them.

Analysis

Self-belief can lead to overconfidence, and underestimation of shot difficulty

This thinking can be generalized as self-belief potentially leading to overconfidence, which can lead to an underestimation of how difficult a task is.  Related to the recency bias described when discussing confidence earlier, in this thought process, a person’s increasing belief in their own abilities leads them to think that they possess all the necessary information to make informed choices, even if those choices are regarding situations they have not encountered.  In the basketball sense, a player who has hit three spot-up mid-range jumpers in a row, may feel strongly about his chances of hitting a pull-up three in transition.  This would happen despite the latter being a completely different type of shot, and one that his recent experience would not help him in.  Having unwarranted confidence can also result in a confirmation bias where one disregards poor results and focuses primarily on positive ones, thus incorrectly reinforcing self-belief.

There is an element of luck and ability at play in most situations.  When luck or variance are confused with ability, it can lead to individuals giving their knowledge and abilities more credit than what is due.  NBA analysts who subscribe to this viewpoint often encourage players to play within their assigned role on the team, and “not try to do too much.”  This thinking is founded in the belief that a person’s specialized role exists for a very strong reason, and deviations from it can be risky and lead to loss.  Alternatively, it could be argued that this risk-averse thinking has an opportunity cost, i.e., the true potential or value of the person is never realized as they are limited to the bounds of their role.

The better a player is shooting, the greater the defensive attention received, thus reducing efficacy

This is a popular thought process in the NBA: A player who has been hurting your team all night requires additional attention in clutch time so that the damage can be minimized.  NBA stars such as LeBron James, Stephen Curry, and James Harden are frequently double-teamed with the goal of minimizing the points a team concedes.  Proponents of CHH will argue that in these situations, it is desirable for the defending team to force these stars to take contested shot attempts, instead of passing to players who are less covered by the defense.  

In stark contrast to this belief is one that suggests that talent is the ultimate differentiator, and that there is little a team can do to stop the effectiveness of these players.  Proponents of this thinking view sending greater defensive resources as a form of irrational escalation of commitment, as more resources are being allocated to a failing course of action.

In a broader sense, this thinking can be framed as: The better someone is performing, the more the opposition is focused on limiting them.  The question that needs to be asked is whether it is worth limiting them.  Individual production on a team, whether it be in basketball, software development, or manufacturing, may not be indicative of the broader success of the initiative.  Without considering the bigger picture and understanding the root cause of the issue at hand, it may be wasteful to allocate valuable resources to the “problem.”

The more a player is involved in the game, the more the defense learns about them, and is thus able to devise better strategies

It can be reasoned that in order to develop effective countermeasures to a problem, a strong understanding of the problem needs to be gained.  Underpinning this thinking is the belief that as available information grows, strategies developed using that information are more effective.  This is a logical thought process and there are plenty of examples where this heuristic holds true.  For example, transportation planning relies on commuter and transit data to plan out schedules, and the more data available, the more effective the schedule.  The assumption that this thinking process makes is that there is, 1) a scalable way to transform data into relevant information, and that, 2) the increasing information gained will improve and not deteriorate our strategies.  

There may be situations where gathering as much information as possible is beneficial, but there also may be situations where it is better to act early with incomplete information, learn from the experience, and apply those learnings in the next iteration.  From a basketball sense, this thinking assumes that the more a coaching staff sees a player during a game (i.e., gather data), the better they will be able to stop them in clutch time (i.e., create and apply a strategy).  This thinking, though sound in reasoning, may be incorrect if the player is difficult to analyze (e.g., has a high degree of relative skill which cannot be accounted for in a strategy).

Thinking Improvements

Both models tend to overvalue current trends over a larger sample size as they acknowledge the effects of the hot hand.  The difference is that proponents of the productive hot hand advocate for the in-form player to shoot, and supporters of CHH advocate for the player to draw attention and pass to other options for fear that shooting is a poorer option due to increased defensive attention.  The schools of thought agree that the focal point of the possession should be the player, it is only the usage and action of the player which is in question.  As discussed, there exist several biases in both ways of thinking ranging from overestimation of one’s abilities to base rates insensitivity.  However, a structural flaw in the thinking behind both models is that they do not sufficiently consider the change in the player’s quality of decision-making that is likely to occur over time.  The models assume that the person in question will make good decisions in the future (whether it be shooting, passing, or cutting) as they had in the past, i.e., the quality of decision-making is constant.  If this underlying assumption is incorrect, then the models fail to produce the scoring throughput, since the in-form player is the key constraint in both models.  As Goldratt, 2004, explained when discussing the Theory of Constraints, the constraint (in-form player) is what limits throughput (points) in a system, and the constraint in most systems changes. Neither model’s thinking accommodates for this change and instead is influenced by biases which reinforce the questionable proposition that the in-form player is the constraint that needs to be actively utilized.

The weakness in thinking has to be addressed at two levels.  First, as discussed above, the tendency to exaggerate the effect of a dynamic and changing entity needs to be acknowledged.  Second, this entity needs to be seen, not as the cause of the the effects, but as an effect itself, with the cause being the rest of the domain.  As illustrated by Senge, 1990, this manner of thinking does not see the player as the central figure causing the key action on the court (as our analysis showed, this is prone to biases), but acknowledges that his behaviour is the result of the underlying structure, whether he acknowledges that or not.  Particularly, his hot streak has been enabled by the underlying structure, not because of individual actions.  The structure is causing the player behaviour and if that structure is still resulting in high quality decision-making by the player, then he will increase value. If the structure is reducing the quality of the decisions of a player, then that player will reduce value.  An analysis of how the underlying structure influences the player is beyond the scope of this discussion, but it remains the key area which both models fail to explore.  

It is often difficult to measure the effect of independent variables on a dependent variable, especially in complex nondeterministic systems such as basketball.  Theoretically, determining how a person’s decision-making is influenced by a variety of factors is very valuable and can lead to excellent analysis of how late-game possessions should be run.  In a practical sense, it is infeasible to measure these effects, though technology like SportVU is catching up.  As a starting point for a change in thinking, the focus should be shifted away from the person and their ingrained biases, to the outside world which indiscriminately acts on the person.

References

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