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|Ch. 1||Who's the best hitter? : averages||1|
|Ch. 2||But which team are you betting on? : odds & probabilities||15|
|Ch. 3||Will you win the lottery? : expectations||29|
|Ch. 4||What would Pete Rose do? : professional betting||49|
|Ch. 5||Will the Yankees win if Steinbrenner is gone? : conditional probabilities||69|
|Ch. 6||How long should the World Series last? : repeated tries||81|
|Ch. 7||When should you stop betting? : double-or-nothing||101|
|Ch. 8||What about streaks? : statistics||123|
|App. 1||Now a word from our statisticians||153|
|App. 2||The binomial theorem||169|
When I was six, my father gave me a bright red scorebook that opened my heart to the game of baseball.
—Doris Kearns Goodwin, writer and historian
My daughters first came to the ballpark when they were so young, they couldn't even track what was going on. Their first understanding of baseball was that innings were amounts of time between dinner (after the 3rd inning) and Fudgesicles (after the 6th). The next insight was that when the ball sailed over the fence, that was a good thing—people stood up and cheered; and the billboard cow, advertising a local dairy, nodded her pressboard head in approval. By the time the girls were nine and six, they were following the plays and learning to keep score.
Some of their questions were naive: "Dad, how come everyone is yelling 'Go Die, Ump? '"
"That's 'Good Eye, Ump,' dear, and we're being sarcastic."
"Dad, what's sarcastic?"
Other questions invited a discussion: "Dad, how come people are yelling 'Yer Due! '?"
"Well, that requires looking at batting averages. That guy's batting average is 290 and that means that, until recently, he's been getting hits about 29 percent of the time. But, in the past week, he's had very few hits, so it seems like he's overdue for some hits. One could question that logic because —"
"Thanks, Dad. Would you like some Cracker Jacks?"
Even in the olden days of my youth, baseball reached all parts of the United States and also other countries, especially Japan and Latin America. However, in America, Major League baseball was regarded as the ultimate level of baseball.
In those ancient days before satellite communications,the Major Leagues were physically restricted to the Northeast and Midwest, a relatively small part of the country. From 1903 to 1952 there were sixteen of these teams located in ten cities in the parallelogram with corners at Chicago, Boston, Washington, DC, and St. Louis.
Many baseball fans and baseball writers from this era grew up in big cities like New York, Chicago, Philadelphia, Detroit, and Boston, so they experienced Major League baseball first-hand. Or at least they were able to follow the regular season by listening to the radio. For example, many baseball fans in the South listened to St. Louis Cardinals' games on the radio. My situation was quite different.
I grew up in Utah, which seemed about as remote from the center of baseball action as a kid could get. I was aware of the brazenly named "World Series." But, for a long time, I didn't even wonder how the teams got to be in the World Series. It seemed like being in New York was a big advantage, if not a requirement, though teams like the Cleveland Indians made cameo appearances. I didn't question this any more than I would have questioned how my parents came to be married or that Roosevelt and Stalin came to be world leaders. It had always been so. Even out in Utah, cool teachers would let their classes listen to the World Series on the radio; my cool teacher was a young lady who taught history. Thanks, Miss Lake.
The real professional baseball team in my home town was our local Salt Lake City Bees, a team in the class C Pioneer League. This league included teams like the Idaho Falls Russets (think potatoes) and the Billings Mustangs (think horses, not cars). I attended many games and I listened to all the other games on my radio, carefully hidden under the bed covers when necessary. I remember recalculating hitters' batting averages—long division with a pencil!—and then checking the Salt Lake Tribune the next morning to see if I'd done them right.
Hub Kittle was the pitcher-manager of the Bees. He was a legend in the minor leagues for decades. On August 27, 1980, as a minor league pitching coach, he took the mound for Springfield (Illinois) versus Iowa, teams in the American Association. He was six months past his 63rd birthday and was the oldest player ever in organized baseball. He retired the Iowa batters in the first inning on two flies and a groundout; he threw one pitch in the second inning before leaving the game.
The most interesting ballplayer for the Bees was the catcher, Gus Triandos. He was nicknamed "Tremendous Triandos" because of his rather solid build. He was powerful, but not swift. Indeed, he was the only Major League player to play over 1000 games, mostly with Baltimore, and end up with a perfect stolen-base record, 1 for 1. In addition, he holds the Major League record with 1,206 consecutive games without being caught stealing. In one inconsequential game, near the end of a season, he decided to amble from first base to second base. The catcher was so surprised that he did not throw. (Uncontested stolen bases counted in those days.)
The Salt Lake City Bees, and the World Series via radio, were not enough to satiate my appetite for baseball. My favorite board game was All-Star Baseball, a game designed to simulate real baseball. This was a precomputer nonelectronic game that modeled the hitting of well-known ballplayers of the 1940s, including Cleveland shortstop and manager Lou Boudreau, Yankee center fielder Joe DiMaggio, the Pittsburgh slugger Ralph Kiner, St. Louis Cardinal Stan Musial, Brooklyn infielder Jackie Robinson and the Boston outfielder Ted Williams. Some pitchers were included, like Cleveland pitcher Bob Feller. For each such player, there was a cardboard disk that was to be placed over a spinner; see the samples on page vi. The edge of the disk was marked off with coded possible outcomes like Home Run, Triple, Double, Base on Balls, Strike Out, Ground Out, and Fly Out. There were two versions of the Single, the little single on which any runners advanced one base and the big single on which any runners advanced two bases. For example, the regions 1, 5, 9, and 10 represented Home Runs, Triples, Bases on Balls, and Strike Outs. The regions of these outcomes were proportional to the baseball player's real lifetime performances. Thus sluggers like Ted Williams and Ralph Kiner had relatively large regions for Home Runs, while the pitcher Bob Feller had large regions for Strikeouts and other ways to make outs. All of the players had miniscule regions for Triples.
The idea of the game was to create a couple of teams and then have them play, at-bat by at-bat, until the game was completed. Each hitter's at-bat was determined by flipping the spinner, using the disk for that player. The bigger the Home Run region on the disk, the more likely it was that the spinner would land on Home Run! Two players could create a team, or one could play both teams by oneself. I learned about, and got a good feel for, probability by playing this game over and over. And over.
The probabilities on the cards were for players' entire careers and did not take into account who the opposing pitchers were, strategies used by both teams, the size and shape of the ballparks, and many other factors that affect hitters' performances. As we shall see in this book, probababilistic analyses become more realistic and valuable when more such factors are taken into account. In fact, later versions of the game, All-Star Baseball, took into account some basic strategies of the game as well as the batters' lifetime records.
Thanks to baseball, I became comfortable with, and reasonably proficient at, elementary probability. When I later encountered probability as a formal concept, I found it completely intuitive. This contrasts vividly with how many people feel about probability, so I credit the game for my good intuition. As I think about it, I realize that my first statistical observation was the positive correlation, a word I didn't know then, between home runs and strikeouts of the players; sluggers tend to strike out more.
Like other baseball fans, I've had different kinds of encounters with baseball: listening to the games on the radio, attending minor league games, later watching games on TV, reading baseball summaries in the newspaper, and of course my fantasies with my board game. In all of these encounters, I was bombarded with statistics like players' batting averages. Why? Do these statistics tell me exactly what to expect? Is baseball predictable? The short answer is: No, past performance does not predict future results in the short run as any baseball fan and some wise financial investors know. Nevertheless, we appreciate the statistics because they do give us an idea of what to expect. Moreover, in the long run, there are patterns. In fact, there would be patterns even if the players were robots with the same skills but no memory. Probability and statistics are tools that allow us to compare players' performances with how they would do if they were robots. This helps us decide whether their recent changes in performance are due to real changes or just to randomness.
My family and I were big Eugene Emeralds baseball fans in the 1970s. During the 1970-1971 seasons, the Emeralds were the AAA farm team, in the Pacific Coast League, for the Philadelphia Phillies. Near the beginning of the second game of an Emeralds' double-header, a certain batter from the opposing team came to the plate. I stood up, handed my scorebook to my wife, and said, "Here. Hold this. I'm going to get a foul ball." In the next moment, the ball bounced off a wall and into my mitt just as I expected. My family was duly impressed, but I had noticed that during the first game all of this guy's foul balls had been going to the same part of the stands above where we were sitting. So I positioned myself in the appropriate place. That was the only foul ball I ever recovered at a professional ballgame. Even though this event may have given my family the impression that baseball is perfectly predictable, it generally isn't.
One day at the ballpark, we were sitting near a fellow from Philadelphia and his son. He explained that he was on a business trip, but that he had brought his 13-year-old son so that he could see a minor league baseball game. I paled and stammered, "I'm 39 years old and I've never been to a Major League game!" My young daughters promptly planned a trip to Candlestick Park in San Francisco, the nearest Major League park. I've now been to games in about 15 different Major League ballparks. We still follow the Eugene Emeralds, which has been an A-level farm team for several Major League teams. And my daughters have even made me become a Seattle Mariners fan.
I'm a mathematician, and for thirty years I taught probability and elementary statistics at a college. I love probability and baseball. I enjoy casual gambling at casinos, especially blackjack, but I know enough about my long-term expectations, as I'll explain in Chapter 7, to avoid investing much time or money in this. Some examples in the book involve roulette and the lottery, but I take a close look at gambling on baseball in Chapter 4.Odds are a natural tool for gamblers but are something of a step-child of probability, so I had only casual encounters with odds over the years. In my journey through the garden of probability, with a baseball mitt on my hand, I went from probability to odds, but I'm convinced that most baseball fans are more comfortable with odds than with probability. You'll know intuitively many of the concepts discussed in this book. I will make the concepts more precise and then use them to explain some results in probability that have interesting applications to baseball. Probability is a wonderful window into the workings of baseball, gambling, and, sometimes it seems to me, life itself.
Posted January 23, 2012
Posted January 23, 2011
Posted December 27, 2009
No text was provided for this review.