The problem of shot selection in basketball

In basketball, every time the offense produces a shot opportunity the player with the ball must decide whether the shot is worth taking. In this paper, I explore the question of when a team should shoot and when they should pass up the shot by considering a simple theoretical model of the shot selection process, in which the quality of shot opportunities generated by the offense is assumed to fall randomly within a uniform distribution. I derive an answer to the question "how likely must the shot be to go in before the player should take it?", and show that this "lower cutoff" for shot quality $f$ depends crucially on the number $n$ of shot opportunities remaining (say, before the shot clock expires), with larger $n$ demanding that only higher-quality shots should be taken. The function $f(n)$ is also derived in the presence of a finite turnover rate and used to predict the shooting rate of an optimal-shooting team as a function of time. This prediction is compared to observed shooting rates from the National Basketball Association (NBA), and the comparison suggests that NBA players tend to wait too long before shooting and undervalue the probability of committing a turnover.Comment: 7 pages, 2 figures; comparison to NBA data adde

Assessing Inclusion Behaviors and Impact of Inclusion within the Fleet

NPS NRP Executive SummaryThis project supports the Navy’s efforts to promote diversity and inclusion (D&I), which are recognized as strategic imperatives that give the Navy a warfighting advantage against our adversaries. The study utilizes both quantitative and qualitative approaches to understand the major contributing factors to an inclusive and diverse command, accomplishing four research objectives: (1) developing metrics to assess behaviors of inclusion within the fleet; (2) assessing inclusion behaviors within the fleet using the developed metrics; (3) determining the most impactful D&I competencies for building inclusion; and (4) identifying command practices that contribute to greater acceptance of diversity. We develop and introduce a survey instrument to assess Personal Inclusion Factors (individuals’ feelings of being personally included within their command) and Command Core Inclusion Competencies (individuals’ beliefs about how their commands demonstrate practices that promote diversity and inclusion) suitable for a Navy context. The instrument captures best practices and validated metrics for promoting and assessing D&I in organizations and tailors them to the Navy and Sailors’ work. We fielded this survey to 489 active-duty Navy personnel (enlisted and officers) asking them to report on both their current and past commands. We find that females across all race/ethnicities on average report lower feelings of inclusion and rate commands lower on Core Command Inclusion Competencies than their male counterparts. This gender difference is stronger for sea versus shore commands. Participants also answered open-ended questions about the competencies that they believed were most important for promoting D&I in the fleet. "Inclusive leadership" emerged as a dominant theme; in particular, participants felt most included in commands where leadership valued their perspectives and ideas and where Sailors felt heard on a day-in, day-out basis.N1 - Manpower, Personnel, Training & EducationThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

Assessing Inclusion Behaviors and Impact of Inclusion within the Fleet

NPS NRP Project PosterThis project supports the Navy’s efforts to promote diversity and inclusion (D&I), which are recognized as strategic imperatives that give the Navy a warfighting advantage against our adversaries. The study utilizes both quantitative and qualitative approaches to understand the major contributing factors to an inclusive and diverse command, accomplishing four research objectives: (1) developing metrics to assess behaviors of inclusion within the fleet; (2) assessing inclusion behaviors within the fleet using the developed metrics; (3) determining the most impactful D&I competencies for building inclusion; and (4) identifying command practices that contribute to greater acceptance of diversity. We develop and introduce a survey instrument to assess Personal Inclusion Factors (individuals’ feelings of being personally included within their command) and Command Core Inclusion Competencies (individuals’ beliefs about how their commands demonstrate practices that promote diversity and inclusion) suitable for a Navy context. The instrument captures best practices and validated metrics for promoting and assessing D&I in organizations and tailors them to the Navy and Sailors’ work. We fielded this survey to 489 active-duty Navy personnel (enlisted and officers) asking them to report on both their current and past commands. We find that females across all race/ethnicities on average report lower feelings of inclusion and rate commands lower on Core Command Inclusion Competencies than their male counterparts. This gender difference is stronger for sea versus shore commands. Participants also answered open-ended questions about the competencies that they believed were most important for promoting D&I in the fleet. "Inclusive leadership" emerged as a dominant theme; in particular, participants felt most included in commands where leadership valued their perspectives and ideas and where Sailors felt heard on a day-in, day-out basis.N1 - Manpower, Personnel, Training & EducationThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

The Hot (Invisible?) Hand: Can Time Sequence Patterns of Success/Failure in Sports Be Modeled as Repeated Random Independent Trials?

The long lasting debate initiated by Gilovich, Vallone and Tversky in is revisited: does a “hot hand” phenomenon exist in sports? Hereby we come back to one of the cases analyzed by the original study, but with a much larger data set: all free throws taken during five regular seasons () of the National Basketball Association (NBA). Evidence supporting the existence of the “hot hand” phenomenon is provided. However, while statistical traces of this phenomenon are observed in the data, an open question still remains: are these non random patterns a result of “success breeds success” and “failure breeds failure” mechanisms or simply “better” and “worse” periods? Although free throws data is not adequate to answer this question in a definite way, we speculate based on it, that the latter is the dominant cause behind the appearance of the “hot hand” phenomenon in the data

A cognitive forcing tool to mitigate cognitive bias:A randomised control trial

Abstract Background Cognitive bias is an important source of diagnostic error yet is a challenging area to understand and teach. Our aim was to determine whether a cognitive forcing tool can reduce the rates of error in clinical decision making. A secondary objective was to understand the process by which this effect might occur. Methods We hypothesised that using a cognitive forcing tool would reduce diagnostic error rates. To test this hypothesis, a novel online case-based approach was used to conduct a single blinded randomized clinical trial conducted from January 2017 to September 2018. In addition, a qualitative series of “think aloud” interviews were conducted with 20 doctors from a UK teaching hospital in 2018. The primary outcome was the diagnostic error rate when solving bias inducing clinical vignettes. A volunteer sample of medical professionals from across the UK, Republic of Ireland and North America. They ranged in seniority from medical student to Attending Physician. Results Seventy six participants were included in the study. The data showed doctors of all grades routinely made errors related to cognitive bias. There was no difference in error rates between groups (mean 2.8 cases correct in intervention vs 3.1 in control group, 95% CI -0.94 – 0.45 P = 0.49). The qualitative protocol revealed that the cognitive forcing strategy was well received and a produced a subjectively positive impact on doctors’ accuracy and thoughtfulness in clinical cases. Conclusions The quantitative data failed to show an improvement in accuracy despite a positive qualitative experience. There is insufficient evidence to recommend this tool in clinical practice, however the qualitative data suggests such an approach has some merit and face validity to users

The Epistemic Status of Processing Fluency as Source for Judgments of Truth

This article combines findings from cognitive psychology on the role of processing fluency in truth judgments with epistemological theory on justification of belief. We first review evidence that repeated exposure to a statement increases the subjective ease with which that statement is processed. This increased processing fluency, in turn, increases the probability that the statement is judged to be true. The basic question discussed here is whether the use of processing fluency as a cue to truth is epistemically justified. In the present analysis, based on Bayes’ Theorem, we adopt the reliable-process account of justification presented by Goldman (1986) and show that fluency is a reliable cue to truth, under the assumption that the majority of statements one has been exposed to are true. In the final section, we broaden the scope of this analysis and discuss how processing fluency as a potentially universal cue to judged truth may contribute to cultural differences in commonsense beliefs

Author Correction: A consensus-based transparency checklist.

An amendment to this paper has been published and can be accessed via a link at the top of the paper

Applying strategies from libertarian paternalism to decision making for prostate specific antigen (PSA) screening

<p>Abstract</p> <p>Background</p> <p>Despite the recent publication of results from two randomized clinical trials, prostate specific antigen (PSA) screening for prostate cancer remains a controversial issue. There is lack of agreement across studies that PSA screening significantly reduces prostate cancer mortality. In spite of these facts, the widespread use of PSA testing in the United States leads to overdetection and overtreatment of clinically indolent prostate cancer, and its associated harms of incontinence and impotence.</p> <p>Discussion</p> <p>Given the inconclusive results from clinical trials and incongruent PSA screening guidelines, the decision to screen for prostate cancer with PSA testing is an uncertain one for patients and health care providers. Screening guidelines from some health organizations recommend an informed decision making (IDM) or shared decision making (SDM) approach for deciding on PSA screening. These approaches aim to empower patients to choose among the available options by making them active participants in the decision making process. By increasing involvement of patients in the clinical decision-making process, IDM/SDM places more of the responsibility for a complex decision on the patient. Research suggests, however, that patients are not well-informed of the harms and benefits associated with prostate cancer screening and are also subject to an assortment of biases, emotion, fears, and irrational thought that interferes with making an informed decision. In response, the IDM/SDM approaches can be augmented with strategies from the philosophy of libertarian paternalism (LP) to improve decision making. LP uses the insights of behavioural economics to help people better make better choices. Some of the main strategies of LP applicable to PSA decision making are a default decision rule, framing of decision aids, and timing of the decision. In this paper, we propose that applying strategies from libertarian paternalism can help with PSA screening decision-making.</p> <p>Summary</p> <p>Our proposal to augment IDM and SDM approaches with libertarian paternalism strategies is intended to guide patients toward a better decision about testing while maintaining personal freedom of choice. While PSA screening remains controversial and evidence conflicting, a libertarian-paternalism influenced approach to decision making can help prevent the overdiagnosis and overtreatment of prostate cancer.</p

Context-dependent preferences in starlings: linking ecology, foraging and choice

Foraging animals typically encounter opportunities that they either pursue or skip, but occasionally meet several alternatives simultaneously. Behavioural ecologists predict preferences using absolute properties of each option, while decision theorists focus on relative evaluations at the time of choice. We use European starlings (Sturnus vulgaris) to integrate ecological reasoning with decision models, linking and testing hypotheses for value acquisition and choice mechanism. We hypothesise that options' values depend jointly on absolute attributes, learning context, and subject's state. In simultaneous choices, preference could result either from comparing subjective values using deliberation time, or from processing each alternative independently, without relative comparisons. The combination of the value acquisition hypothesis and independent processing at choice time has been called the Sequential Choice Model. We test this model with options equated in absolute properties to exclude the possibility of preference being built at the time of choice. Starlings learned to obtain food by responding to four stimuli in two contexts. In context [AB], they encountered options A5 or B10 in random alternation; in context [CD], they met C10 or D20. Delay to food is denoted, in seconds, by the suffixes. Observed latency to respond (Li) to each option alone (our measure of value) ranked thus: LA≈LC<LB<<LD, consistently with value being sensitive to both delay and learning context. We then introduced simultaneous presentations of A5 vs. C10 and B10 vs. C10, using latencies in no-choice tests to predict sign and strength of preference in pairings. Starlings preferred A5 over C10 and C10 over B10. There was no detectable evaluation time, and preference magnitude was predictable from latency differentials. This implies that value reflects learning rather than choice context, that preferences are not constructed by relative judgements at the time of choice, and that mechanisms adapted for sequential decisions are effective to predict choice behaviour.This work was supported by Biotechnology and Biological Sciences Research Council (BBSRC) Grant BB/G007144/1 to AK www.bbsrc.ac.uk; TM was supported by a Doctoral Grant from the Portuguese Foundation for Science and Technology (FCT) www.fct.pt/index.phtml.en. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Implicit Essentialism: Genetic Concepts Are Implicitly Associated with Fate Concepts

Genetic essentialism is the tendency for people to think in more essentialist ways upon encountering genetic concepts. The current studies assessed whether genetic essentialist biases would also be evident at the automatic level. In two studies, using different versions of the Implicit Association Test [1], we found that participants were faster to categorize when genes and fate were linked, compared to when these two concepts were kept separate and opposing. In addition to the wealth of past findings of genetic essentialism with explicit and deliberative measures, these biases appear to be also evident with implicit measure