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The hot (invisible?) hand: can time sequence patterns of success/failure in sports be modeled as repeated random independent trials?

ABSTRACT: The long lasting debate initiated by Gilovich, Vallone and Tversky in [Formula: see text] 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 ([Formula: see text]) 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.

SUBMITTER: Yaari G

PROVIDER: S-EPMC3187751 | biostudies-literature | 2011

REPOSITORIES: biostudies-literature

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The hot (invisible?) hand: can time sequence patterns of success/failure in sports be modeled as repeated random independent trials?

Yaari Gur G Eisenmann Shmuel S

PloS one 20111005 10

The long lasting debate initiated by Gilovich, Vallone and Tversky in [Formula: see text] 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 ([Formula: see text]) of the National Basketball Association (NBA). Evidence supporting the existence of the "hot hand" phenomenon is provided. However, while statistical traces of this phenomeno ...[more]

PMID: 21998630

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Project description:BackgroundMultiple-period parallel group randomized trials (GRTs) analyzed with linear mixed models can represent time in mean models as continuous or categorical. If time is continuous, random effects are traditionally group- and member-level deviations from condition-specific slopes and intercepts and are referred to as random coefficients (RC) analytic models. If time is categorical, random effects are traditionally group- and member-level deviations from time-specific condition means and are referred to as repeated measures ANOVA (RM-ANOVA) analytic models. Longstanding guidance recommends the use of RC over RM-ANOVA for parallel GRTs with more than two periods because RC exhibited nominal type I error rates for both time parameterizations while RM-ANOVA exhibited inflated type I error rates when applied to data generated using the RC model. However, this recommendation was developed assuming a variance components covariance matrix for the RM-ANOVA, using only cross-sectional data, and explicitly modeling time × group variation. Left unanswered were how well RM-ANOVA with an unstructured covariance would perform on data generated according to the RC mechanism, if similar patterns would be observed in cohort data, and the impact of not modeling time × group variation if such variation was present in the data-generating model.MethodsContinuous outcomes for cohort and cross-sectional parallel GRT data were simulated according to RM-ANOVA and RC mechanisms at five total time periods. All simulations assumed time × group variation. We varied the number of groups, group size, and intra-cluster correlation. Analytic models using RC, RM-ANOVA, RM-ANOVA with unstructured covariance, and a Saturated random effects structure were applied to the data. All analytic models specified time × group random effects. The analytic models were then reapplied without specifying random effects for time × group.ResultsResults indicated the RC and saturated analytic models maintained the nominal type I error rate in all data sets, RM-ANOVA with an unstructured covariance did not avoid type I error rate inflation when applied to cohort RC data, and analytic models omitting time-varying group random effects when such variation exists in the data were prone to substantial type I error inflation unless the residual error variance is high relative to the time × group variance.ConclusionThe time × group RC and saturated analytic models are recommended as the default for multiple period parallel GRTs.

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The hot (invisible?) hand: can time sequence patterns of success/failure in sports be modeled as repeated random independent trials?

Publications

The hot (invisible?) hand: can time sequence patterns of success/failure in sports be modeled as repeated random independent trials?

Similar Datasets

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