PSU STAT 497 - Probability Models Schwertman 1999 (6 pages)

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Probability Models Schwertman 1999



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Probability Models Schwertman 1999

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Penn State University
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Stat 497 - Special Topics
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Can the NCAA Basketball Tournament Seeding be Used to Predict Margin of Victory Tyler Smith Neil C Schwertman The American Statistician Vol 53 No 2 May 1999 pp 94 98 Stable URL http links jstor org sici sici 0003 1305 28199905 2953 3A2 3C94 3ACTNBTS 3E2 0 CO 3B2 Y The American Statistician is currently published by American Statistical Association Your use of the JSTOR archive indicates your acceptance of JSTOR s Terms and Conditions of Use available at http www jstor org about terms html JSTOR s Terms and Conditions of Use provides in part that unless you have obtained prior permission you may not download an entire issue of a journal or multiple copies of articles and you may use content in the JSTOR archive only for your personal non commercial use Please contact the publisher regarding any further use of this work Publisher contact information may be obtained at http www jstor org journals astata html Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission The JSTOR Archive is a trusted digital repository providing for long term preservation and access to leading academic journals and scholarly literature from around the world The Archive is supported by libraries scholarly societies publishers and foundations It is an initiative of JSTOR a not for profit organization with a mission to help the scholarly community take advantage of advances in technology For more information regarding JSTOR please contact support jstor org http www jstor org Wed Jan 2 12 49 02 2008 Can the NCAA Basketball Tournament Seeding be Used to Predict Margin of Victory Tyler SMITHand Neil C SCHWERTMAN Following the announcement by the NCAA of the seeding and placement of men s basketball teams in the regional tournaments there is often much discussion among basketball afficionados of the fairness A statistical analysis of simple regression models for the tournament games shows that indeed there is a strong association between the seed positions of the teams and the actual margin of victory in fact fairly reliable prediction models of actual margin of victory in tournament games can be achieved based primarily on the seed numbers alone KEY WORDS Nonlinear effects Press Regression 1 INTRODUCTION One of the most popular and publicized collegiate competitions is the NCAA Men s Basketball tournament which many call March Madness Several previous studies of this tournament by Schwertman McCready and Howard 1991 Schwertman Schenk and Holbrook 1996 and Carlin 1996 have focused on models for predicting the probability of each seed winning the regional tournament Carlin 1996 used very basic regression models to predict probability of winning using seed positions and computer rankings such as the SAGARIN ratings as the independent variables In this article however rather than focusing on the probability of winning a contest we concentrate on building somewhat more complex regression models using the information provided by seed positions for accurately predicting the actual margin of victory In this study of the NCAA regional men s basketball tournament our primary objective is to determine using no more than second order regression models if I seed positions alone provide sufficient information to accurately predict margin of victory 2 the difference in seed positions is sufficient to provide accurate predictions of margin of victory and 3 there is evidence that the NCAA selection committee does a good job of seeding the tournament To organize the NCAA men s basketball tournament each spring the NCAA selection committee designs four regional 16 team single elimination basketball tournaments for Division 1 A The committee not only selects the teams although certain conference and conference tournament Tyler Smith is Statistician Data Analyst Department of Statistics University of Kentucky Lexington KY 40506 Neil C Schwertman is Professor of Statistics Department of Mathematics and Statistics California State University Chico CA 95929 0525 94 Tlze American Statisticiarz May 1999 Vol 53 No 2 champions are included automatically but also seeds the teams based upon a consensus of team strength The committee attempts to have the corresponding seeds across regional tournaments approximately equal in strength The format for each regional tournament is given in Figure 1 where the number 1 seed strongest team plays the number 16 seed weakest team the number 2 seed second strongest plays the number 15 seed second weakest and so on In the first round at least the stronger teams lower seed numbers have a definite advantage as they are paired with the weaker teams higher seed numbers If there are no upsets this same advantage occurs in the second and subsequent rounds Of course upsets usually occur and may result in a middle level team playing a much weaker team than the top seed is playing Incidentally in the 56 regional tournaments using the 16 team format only during the first year 1985 eastern regional were there no upsets i e the lower seed number defeated the higher seed number in all 15 games 2 THE MODELS Because simple models for predicting the dependent variable margin of victory are more understandable and provide a clearer picture of the relationship between the dependent and independent variables only basic regression models of no more than second order were considered The dependent variable for our models is the actual margin of victory for the team with lower seed number with a negative sign if an upset occurs that is if the team with higher seed number wins Our goal is to use only seed positions or functions of seed positions in linear regression models to predict the margin of victory Therefore the independent variables for the models are yearly trend and the lower and higher seed numbers zl and z2 respectively or functions of x1 and 2 2 One function of x1 and 2 2 which Schwertman McCready and Howard 1991 and Schwertman Schenk and Holbrook 1996 found quite effective in predicting the winner in each contest is a nonlinear transformation of seed number based on the normal distribution The same transformation was used to determine if this procedure was also effective for predicting margin of victory In total 60 models 30 using raw seed numbers and 30 using this nonlinear scoring transformation of seed numbers were evaluated For each set of predictors models with and without the intercept term and with and without a


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