“Hot Hand” on Strike: Bowling Data Indicates Correlation to Recent Past Results, Not Causality
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{"title"=>"\"Hot hand\" on strike: Bowling data indicates correlation to recent past results, not causality", "type"=>"journal", "authors"=>[{"first_name"=>"Gur", "last_name"=>"Yaari", "scopus_author_id"=>"9839244400"}, {"first_name"=>"Gil", "last_name"=>"David", "scopus_author_id"=>"42661244700"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"sgr"=>"84855800954", "pmid"=>"22253898", "doi"=>"10.1371/journal.pone.0030112", "pui"=>"364087495", "isbn"=>"1932-6203", "issn"=>"19326203", "scopus"=>"2-s2.0-84855800954"}, "id"=>"6fae1bc5-8c45-3d97-a34e-63e519d3ecc1", "abstract"=>"Recently, the \"hot hand\" phenomenon regained interest due to the availability and accessibility of large scale data sets from the world of sports. In support of common wisdom and in contrast to the original conclusions of the seminal paper about this phenomenon by Gilovich, Vallone and Tversky in 1985, solid evidences were supplied in favor of the existence of this phenomenon in different kinds of data. This came after almost three decades of ongoing debates whether the \"hot hand\" phenomenon in sport is real or just a mis-perception of human subjects of completely random patterns present in reality. However, although this phenomenon was shown to exist in different sports data including basketball free throws and bowling strike rates, a somehow deeper question remained unanswered: are these non random patterns results of causal, short term, feedback mechanisms or simply time fluctuations of athletes performance. In this paper, we analyze large amounts of data from the Professional Bowling Association(PBA). We studied the results of the top 100 players in terms of the number of available records (summed into more than 450,000 frames). By using permutation approach and dividing the analysis into different aggregation levels we were able to supply evidence for the existence of the \"hot hand\" phenomenon in the data, in agreement with previous studies. Moreover, by using this approach, we were able to demonstrate that there are, indeed, significant fluctuations from game to game for the same player but there is no clustering of successes (strikes) and failures (non strikes) within each game. Thus we were lead to the conclusion that bowling results show correlation to recent past results but they are not influenced by them in a causal manner.", "link"=>"http://www.mendeley.com/research/hot-hand-strike-bowling-data-indicates-correlation-recent-past-results-not-causality", "reader_count"=>24, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>3, "Researcher"=>6, "Student > Ph. D. Student"=>4, "Student > Postgraduate"=>1, "Student > Master"=>3, "Other"=>2, "Student > Bachelor"=>4, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>3, "Researcher"=>6, "Student > Ph. D. Student"=>4, "Student > Postgraduate"=>1, "Student > Master"=>3, "Other"=>2, "Student > Bachelor"=>4, "Professor"=>1}, "reader_count_by_subject_area"=>{"Mathematics"=>2, "Agricultural and Biological Sciences"=>3, "Neuroscience"=>1, "Sports and Recreations"=>4, "Physics and Astronomy"=>1, "Psychology"=>4, "Social Sciences"=>3, "Computer Science"=>6}, "reader_count_by_subdiscipline"=>{"Neuroscience"=>{"Neuroscience"=>1}, "Social Sciences"=>{"Social Sciences"=>3}, "Sports and Recreations"=>{"Sports and Recreations"=>4}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Psychology"=>{"Psychology"=>4}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>3}, "Computer Science"=>{"Computer Science"=>6}, "Mathematics"=>{"Mathematics"=>2}}, "reader_count_by_country"=>{"Romania"=>1, "Belgium"=>1, "United Kingdom"=>1, "Portugal"=>1}, "group_count"=>0}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/352552"], "description"=>"<div><p>Recently, the “hot hand” phenomenon regained interest due to the availability and accessibility of large scale data sets from the world of sports. In support of common wisdom and in contrast to the original conclusions of the seminal paper about this phenomenon by Gilovich, Vallone and Tversky in 1985, solid evidences were supplied in favor of the existence of this phenomenon in different kinds of data. This came after almost three decades of ongoing debates whether the “hot hand” phenomenon in sport is real or just a mis-perception of human subjects of completely random patterns present in reality. However, although this phenomenon was shown to exist in different sports data including basketball free throws and bowling strike rates, a somehow deeper question remained unanswered: are these non random patterns results of causal, short term, feedback mechanisms or simply time fluctuations of athletes performance. In this paper, we analyze large amounts of data from the Professional Bowling Association(PBA). We studied the results of the top 100 players in terms of the number of available records (summed into more than 450,000 frames). By using permutation approach and dividing the analysis into different aggregation levels we were able to supply evidence for the existence of the “hot hand” phenomenon in the data, in agreement with previous studies. Moreover, by using this approach, we were able to demonstrate that there are, indeed, significant fluctuations from game to game for the same player but there is no clustering of successes (strikes) and failures (non strikes) within each game. Thus we were lead to the conclusion that bowling results show correlation to recent past results but they are not influenced by them in a causal manner.</p> </div>", "links"=>[], "tags"=>["bowling", "indicates", "causality"], "article_id"=>129687, "categories"=>["Physics", "Mathematics"], "users"=>["Gur Yaari", "Gil David"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0030112"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Hot_Hand_on_Strike_Bowling_Data_Indicates_Correlation_to_Recent_Past_Results_Not_Causality/129687", "title"=>"“Hot Hand” on Strike: Bowling Data Indicates Correlation to Recent Past Results, Not Causality", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-01-12 02:41:27"}
  • {"files"=>["https://ndownloader.figshare.com/files/692654"], "description"=>"<p>The top four rows of the top table show a typical scoring box of a bowling game. The fifth row is our way of transforming this information into a binary sequence of success/failure (strike/non strike) for each frame. This series is broken into (ten in this case) ordered pairs of consecutive results, which in turn populate the bottom contingency table. From this table one can use the hypergeometric distribution to obtain an expectation (mean) and variance for the upper left cell . The final step is to calculate a value for this table based on the expectations and the observed value.</p>", "links"=>[], "tags"=>["physics", "mathematics"], "article_id"=>363109, "categories"=>["Physics", "Mathematics"], "users"=>["Gur Yaari", "Gil David"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0030112.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Example_of_calculating_for_one_game_/363109", "title"=>"Example of calculating for one game.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-01-12 00:51:49"}
  • {"files"=>["https://ndownloader.figshare.com/files/692733"], "description"=>"<p>On the upper left we show how for binary sequence (a game) we calculate (see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030112#pone-0030112-g001\" target=\"_blank\">figure 1</a>) which are averaged to obtain . On the upper right we show how for each binary sequence we make a random permutations of it (R) and then calculate the corresponding . For each realization (R) we calculate , save this value and repeat these steps many times (100,000). On the bottom plot we show a typical distribution of (in this case it is for player number 11534, Walter Ray Williams Jr who happen to show negative correlation to previous roll); since this distribution is very close to a normal distribution we can take advantage of it and measure the deviation of the observed value () from the expected one () in units of the standard deviation (). If the observed value falls into the right of the mean (red area), it means the player has a “Hot hand” tendency while if the observed value falls in to the left of the mean (blue area), it mean the player has “Cold hand” (“anti hot hand”). The resulting reflects the statistical significance of this observation.</p>", "links"=>[], "tags"=>["physics", "mathematics"], "article_id"=>363183, "categories"=>["Physics", "Mathematics"], "users"=>["Gur Yaari", "Gil David"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0030112.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Example_of_calculating_for_one_player_/363183", "title"=>"Example of calculating for one player.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-01-12 00:53:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/692861"], "description"=>"<p>ROC curves are calculated for different values of and following the stochastic simulations described in the text. The left column refers to while the right column refers to . The different rows correspond to different aggregation levels of the test (games, tournaments, seasons and career: G/T/S/C). One sees how the presented method starts to show impressive power for very small values of . However, aggregation levels of T/S/C detect streakiness for while in aggregation level G, it is not detected as designed.</p>", "links"=>[], "tags"=>["validation", "stochastic"], "article_id"=>363322, "categories"=>["Physics", "Mathematics"], "users"=>["Gur Yaari", "Gil David"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0030112.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Method_validation_with_stochastic_simulations_/363322", "title"=>"Method validation with stochastic simulations.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-01-12 00:55:22"}
  • {"files"=>["https://ndownloader.figshare.com/files/693040"], "description"=>"<p>The top 50 players (in terms of number of available games in the last 9 seasons) are ordered according their . In this plot, , , and are presented. The shaded areas reflect the alpha threshold and the same value corrected for multiple tests (100 here). Panel a is for all games exist in the data, panel b is round 16 and above only.</p>", "links"=>[], "tags"=>["deviation", "null", "aggregation"], "article_id"=>363494, "categories"=>["Physics", "Mathematics"], "users"=>["Gur Yaari", "Gil David"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0030112.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Significance_of_deviation_from_NULL_hypothesis_for_different_aggregation_levels_/363494", "title"=>"Significance of deviation from NULL hypothesis for different aggregation levels.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-01-12 00:58:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/693152"], "description"=>"<p>Box plot of the mean probability of success of each player for the different frames in a bowling game. The increase in the mean (black solid line) success rate of all players between frame 1 and frame 3 is evident. A paired Mann-Whitney test (two sided) between frame 1 and frame 5 yields a very low P value of ( between frame 1 and 3). The dashed line spans the mean success rate of all of the players while the blue rectangle spans the middle 50% quantiles.</p>", "links"=>[], "tags"=>["rates", "100"], "article_id"=>363602, "categories"=>["Physics", "Mathematics"], "users"=>["Gur Yaari", "Gil David"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0030112.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Success_rates_by_frame_for_the_top_100_players_/363602", "title"=>"Success rates by frame for the top 100 players.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-01-12 01:00:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/693210"], "description"=>"<p>Panels A–B: The conditional probability for a strike in the 9th (green) and 10th (red) frames given the number of strikes in the first 8 frames is plotted. The 95% confidence intervals shown are calculated using bayesian framework with Jeffreys prior (see <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030112#pone.0030112-Agresti3\" target=\"_blank\">[33]</a>). Data is shown for two individuals with the most identifiable patterns. The numbers at the title of each panel represents the player's code according to the supporting information S1. Dashed lines represent the base probability of success for each player in the corresponding frame and dotted lines show the linear fits results. Panels C and D show the distribution of slopes () and obtained from the fits of all players respectively.</p>", "links"=>[], "tags"=>["physics", "mathematics"], "article_id"=>363669, "categories"=>["Physics", "Mathematics"], "users"=>["Gur Yaari", "Gil David"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0030112.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Gaining_prediction_power_/363669", "title"=>"Gaining prediction power.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-01-12 01:01:09"}

PMC Usage Stats | Further Information

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  • {"unique-ip"=>"14", "full-text"=>"13", "pdf"=>"2", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"5", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2017", "month"=>"12"}
  • {"unique-ip"=>"20", "full-text"=>"27", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"2", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"1"}
  • {"unique-ip"=>"2", "full-text"=>"2", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"3", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"2"}
  • {"unique-ip"=>"35", "full-text"=>"42", "pdf"=>"0", "abstract"=>"0", "scanned-summary"=>"0", "scanned-page-browse"=>"0", "figure"=>"23", "supp-data"=>"0", "cited-by"=>"0", "year"=>"2018", "month"=>"3"}

Relative Metric

{"start_date"=>"2012-01-01T00:00:00Z", "end_date"=>"2012-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences/Behavior", "average_usage"=>[354, 559, 676, 770, 854, 949, 1040, 1128, 1220, 1295, 1364, 1439, 1511, 1580, 1636, 1693, 1753, 1808, 1882, 1944, 2019, 2070, 2120, 2176, 2247]}, {"subject_area"=>"/Physical sciences", "average_usage"=>[304, 506, 616, 712, 799, 879, 968, 1052, 1134, 1212, 1284, 1357, 1427, 1494, 1557, 1621, 1689, 1756, 1823, 1883, 1944, 1997, 2056, 2118, 2171]}]}
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