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• W2489969778 abstract "Sporting events generate many interesting probability questions. In probability counterintuitive results are common and even experienced mathematicians can make mistakes in problems that sound simple on the surface. In this article we examine two sports applications in which probability questions have results that may come as a surprise to sports fans and mathematicians alike. The first concerns the chances of rare events in sporting contests, with recent examples from baseball and football. The second considers the merits of longer playoff series in sports like major league baseball and professional basketball, where a set of games is used to determine who advances in a post-season tournament. Problem 1: Rare Events One of the most appealing aspects of watching sports events is the possibility that a viewer may see something especially noteworthy, perhaps even unprecedented. Sports fans who have the good fortune to be in attendance when something spectacular happens have vivid memories and wonderful stories. Baseball fans love to describe the time they saw a no-hitter, a player hit for the cycle, a triple play, or some other rare event. A typical response to such descriptions is, “Wow, what are the chances of that?” Those of us who love sports and math frequently are asked, “What are the chances of ...?” It may be easy to come up with a quick estimate of the probability, but first guesses are often wrong, sometimes off by orders of magnitude! Making estimates of the probability of rare events can be difficult. Checking the answer may be hard because the events are sometimes so unusual that we often do not have enough historical instances to get a sense of the probability. A problem of this type for sports fans occurs in the first round of the annual Division I men’s basketball tournament of the National Collegiate Athletic Association. Since 1985 when the tournament field expanded to 64 (now 65) teams, a 16th seed has yet to beat a top-ranked first seed. The probability of a 16th seed winning a first round game is not zero, but it is small and we have no past history to inform us. We look at examples of streaks in a baseball game and a football season as a way to explain some of the difficulties that occur when thinking about rare events. Example 1: Four homers in a row On April 22, 2007 the Boston Red Sox had a remarkable third inning against the New York Yankees. Red Sox slugger Manny Ramirez came to the plate with two out and nobody on and launched a home run. Then J. D. Drew, Mike Lowell, and Jason Varitek followed Ramirez and each of them hit a home run. Such a back to back to back to back event is rare indeed as this was" @default.
• W2489969778 created "2016-08-23" @default.
• W2489969778 creator A5070018635 @default.
• W2489969778 date "2010-01-01" @default.
• W2489969778 modified "2023-09-28" @default.
• W2489969778 title "Surprising Streaks and Playoff Parity: Probability Problems in a Sports Context" @default.
• W2489969778 doi "https://doi.org/10.5948/upo9781614442004.003" @default.
• W2489969778 hasPublicationYear "2010" @default.
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