Discipline: Mathematics and Statistics
Alejandra Gutierrez - Philander Smith College
The ‘hot hand’ phenomenon has been greatly discussed. Being ‘hot’ is defined as having successes on the majority attempts at goal in a designated time frame. As a part of the discussion about the ‘hot hand’ phenomenon, some research has emerged investigating the statistical significance of perceived high performance in bowling. This research has been limited to cases where the data had to be collapsed to two categories, one representing only a success characterized by a strike and one representing a failure characterized by a non-strike. This limitation results in an inaccurate portrayal of high performance in that it suggests that high performance is only characterized by a strike. We overcome this limitation and make available more complete results for the general sports enthusiast and the Professional Bowlers Association (PBA) league. This could potentially aid professional bowlers and the PBA league in a more accurate assessment of athlete’s performances. We assume that bowling data follows a multi-state, higher-order Markovian model, which allows us to collapse the data into three categories: high performance, average performance, and poor performance. We extract data from the PBA website and compute the multiple window scan statistic associated with perceived above avaerage performances. Then we use the exact distribution of the multiple window scan statistics to obtain the probability that under a particular set of conditions, an observed cluster is statistically significant. From this, our goal is to separate above average performance clusters that may appear intuitively significant from those that could have happened by random chance. For the practically impressive clusters observed, we found that while the clusters were practically impressive, statistically they could have happened by random chance. In future work, we will consider dependency and look at more bowlers over longer periods of time to determine if there is non-randomness in success clusters under these varied conditions.
Funder Acknowledgement(s): This research is based upon work supported by the National Science Foundation under Award No. DMS-1148695 and DMS-1359016 with the latter being an MAA funded activity.
Faculty Advisor: Deidra A. Coleman, email@example.com
Role: All of the research was conducted by me under the direction of my mentor. Specifically, I worked on extracting the data from the Professional Bowlers Association website using R code to perform data scraping. I then created code to prepare the extracted data for analysis and computed the multiple window scan statistics for each bowler. I created the measurable definitions of performance classifications into high, average, or poor. The graphs that will be presented was developed by me along with the table of findings.