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Resampling Baseball Probability Theory


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Resampling Baseball Probability Theory

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Resampling Baseball Probability Theory

  1. 1. Resampling Baseball 1Resampling Baseball Probability Theory by Edgardo Donovan RES 600 – Dr. Yufeng Tu Module 2 – Case Analysis Monday, November 3, 2008
  2. 2. Resampling Baseball 2 Resampling Baseball Probability Theory So can a statistical approach ever accurately yield the chances of a seven-game world series? The beauty of modeling probabilities is that refinements can be made. But maybe statisticians will have to wait for 1000 years of World Series results to fully and accurately model the probabilities of different game lengths in the Fall Classic. In the meantime, math fans and baseball fans marvel alike at the nuances of baseball--the "game of inches"--that make seven- game World Series so frequent.. BEN STEIN Inside Science News Service (ISNS), 2003 tatistics involving the official games of Major League Baseball are fascinating because in part they rely on an evenhanded static set of regulations which interact with an unpredictable human athletic element. This often leads to results that seems to deviate fromstandard probability expectations. Resampling techniques are one of the most effectiveways to streamline and properly place extreme data variances involving probability inbaseball within a proper context. Whereas certain types of research are designed to best measure levels of risk(Kierulff) and to predict success/failure outcomes in the realm of competitive humanaffairs (Lomax), Ben Stein and Kenneth Chang in the their respective works entitled “Are7-Game World Series More Common than Expected?” and “A 7-Game World Series isUnusually Common” take on different views regarding the roles of the human element andstraight probability in the game of baseball. Stein argues that baseball deviates fromstraight probability in its tendency to have seven-game World Series Championships
  3. 3. Resampling Baseball 3because of game and players nuances. Chang states that when one analyzes World Seriesall-time results the average probability of seven-game World Series Championships is notmuch more than the standard 31.5% probability hence reaffirming his faith inmathematics. Although Stein is correct in acknowledging the unpredictable variant humanelement in baseball influence on standard probability, Chang is correctly shows howresampling will streamline data variances over time. Whereas tests of statistical significancesometimes tell us virtually nothing about the importance of a research result (Gall), resamplinginvolves numerous repeated samples within the same body of usually small data in anattempt to define the characteristics of the data universally. Only recently has this beeneasier to do. Resampling can possibly involve hundreds of thousands of calculations andwas less prevalent when personal computing technology was in its infancy and still ratherexpensive. Organizations promoting resampling, such as the ones represented, believe that resampling eliminates a lot of the complexity inherent intraditional research methods. They argue that rather than attempting to extend a series ofparametric and non-parametric tests from a small sample to better understand greaterphenomena is inferior compared to resampling which enables analysis of the totality ofmost sorts of data. Resampling has become increasingly popular as a tool used for testingmediation because it does not require the normality assumption to be met, and because it
  4. 4. Resampling Baseball 4can be effectively utilized with smaller sample sizes under 20 units (Wikipedia). One ofthe challenges of traditional research, which emphasizes formal hypotheses andsignificance testing of null hypotheses, is that extreme data variances in the majority ofcases are not desired and can take away from the overall research model applicability.Resampling smoothes out the degree of data variance. It computes the same groups of datasometimes hundreds and even thousands of times. The end result is a more streamlinedrepresentation of results. By eliminating the need towards ensuring that prospective datasets will confine themselves within an acceptable results range, resampling mediationrenders research less complex. This can be an attractive approach for those who areseeking to accurately universally define a full range of possible results. Resampling is practical in few mono-dimensional areas such as the game ofbaseball where data set behavior patterns can be universally defined within a handful ofparameters. Chong Ho Yu in his 2003 research titled “Resampling Methods: Concepts,Applications, and Justification”, states that the obstacles in computing resources andmathematical logic have been removed and that perhaps now researchers will pay moreattention to philosophical justification of re-sampling. In making a case for his argument Yu brings up the “Monte Carlo Simulation”where researchers make up data and draw conclusions based on many possible scenarios.The name "Monte Carlo" comes from an analogy to the gambling houses on the FrenchRiviera. Years ago some gamblers studied how they could maximize their chances ofwinning by using simulations to check the probability of occurrence for each possible case
  5. 5. Resampling Baseball 5in games of chance. The forerunner of gaming statistical analysis geared towardsimproving the success of players was actually pioneered by Ed Thorpe in his acclaimed1962 book “Beat the Dealer”. He devised a somewhat successful statistical methodologybased on resampling designed towards that end. The contextual basis of his method wasthe game of Blackjack which provided a contained small statistical data set in the form of adeck or two of un-shuffled cards. His methodology provided “hit” or “stay” indicators basedon what cards had already been dealt and the probability of desirable cards appearing. Thismethod is also known as card-counting and was heralded as a breakthrough but ceased towork once casinos caught on and started to involve 3 or more decks of continuouslyshuffled cards into the game. The added level of complexity eliminated the previous 1%advantage of the card-counter and turned the odds back in overwhelming favor of thehouse. Other experts added to the critique of resampling vis-à-vis card counting by pointingto the chance of a three-of-a-kind hand. They recognized that that event does not happenvery often, and it would take many hands from an un-shuffled deck of cards to estimate itsprobability (Simon). Resampling may work fine in small mono-dimensional controlled data setenvironments but ceases in its efficacy once multidimensional or “complex” variables areadded to the equation. The attempt to define multidimensional complex phenomena is thebasis for most scientific research and it is hard to imagine one being successful in thatendeavor if the choice to ignore complexity is made.
  6. 6. Resampling Baseball 6 The sport of baseball in comparison is less complex than counting cards in anattempt to overturn the odds at a four deck Casino blackjack table. The endeavor ofcalculating batting and pitching averages per different innings is much less complex andeven-handed lending itself to resampling. Although the human element does provide avariance of sorts from straight probability resampling can streamline its effect. One of the reasons for resampling’s continued popularity is that it appeals to thatfacet of the human psyche that longs to render the surrounding world less mysterious,more discernable, and less unpredictable so that it can be managed more effectively(Levin). The game of baseball as it is played in the United States is not immune to thisphenomenon. The pursuit of statistical analysis in baseball games is so engrained inAmerican psyche that all sorts of descriptive statistics are displayed during games. Fans areleft to ponder whether the portrayed statistical information represents positive or negativeindicators for their team. There may be a more promising future for resampling in the area of game-theoryand sports analysis in baseball. The latter is an accepted technique utilized to measure thelikelihood of outcomes concerning issues related to mono-dimensional environments.There are potential extensions of game-theory techniques based on resampling in the areasof corporate risk management and military war gaming as well. Although the latter two stillinvolve complex environments, resampling can be used to better define gain/losspropositions as long as they are done in a highly contextualized micro-level. For example, amilitary campaign may attempt to war-game a specific number of similarly modeled
  7. 7. Resampling Baseball 7aircraft without taking into account other impacting factors such as air superiority, anti-aircraft resources, weather variances, proximity to support bases, pilot ability, etc. In theinvestment world, one could attempt to resample scenarios based on the past performanceof stocks in relation to mono-dimensional variations of inflation, interest rates, etc. Statistics involving the official games of Major League Baseball are fascinatingbecause in part they rely on an evenhanded static set of regulations which interact with anunpredictable human athletic element. This often leads to results that seems to deviatefrom standard probability expectations. Resampling techniques are one of the mosteffective ways to streamline and properly place extreme data variances involvingprobability in baseball within a proper context.
  8. 8. Resampling Baseball 8 BibliographyAnonymous. (2008). Bootstrapping (statistics). Retrieved on 11 August 2008 from (2008). Resampling stats. Retrieved on 11 August 2008 from, Kenneth. (2002). Baseball: A 7-game world series is unusually common. New YorkTimes, 22 October, 2002, p.6Gall, M.D. (2001). Figuring out the importance of research results: statistical significanceversus practical significance. University of Oregon.Howell, David. (2008). Resampling statistics: randomization and the bootstrap. University ofVermontKierulff, H. (1971). Probabilistic Forecasting for Contractors. ManagementLevin, Joel. (1998). What if there were no more bickering about statistical significance tests?Research in the Schools. Vol. 5, No. 2, 43-53.Lomax, K.S.. (1954). Business failures: another example of the analysis of failure data.Journal of the American Statistical Association. Vol. 49, No. 268 pp. 847-852Simon, Julian. (2008). Why the formal method in statistics is usually theoretically inferior.Retrieved on 11 August 2008 from
  9. 9. Resampling Baseball 9Stein, Ben. (2003). Are 7-game world series more common than expected? Inside ScienceNews Service (ISNS), 17 October, 2003, update 20 October, 2003Yu, Chong Ho. (2003). Resampling methods: concepts, applications, and justification.practical assessment, research & evaluation, 8(19). Retrieved September 10, 2008 from