# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

8
PLAYER WIN AVERAGES

Anyone associated with a baseball, football, or basketball team would probably say that a player's objective is to help his team win games. Therefore, it seems reasonable to measure how much a professional athlete's efforts help his team win or cause his team to lose games. As we will see in later chapters, for basketball and football this is a very difficult task. For baseball, however, Eldon Mills and Harlan Mills (Player Win Averages) came up with a simple yet elegant way to measure how a baseball player changes the chance that his team will win a game. To illustrate the method, consider perhaps the most famous hit in baseball history: Bobby Thompson's home run in the 1951 playoffs. Thompson came to bat for the New York Giants in the bottom of the ninth inning of the deciding game of the 1951 playoff against the Brooklyn Dodgers. The Giants were down 4–2 and had runners on second and third with one out. Assuming the two teams were of equal ability, we can calculate that at this point (more on this later1) the Giants had a 30.1% chance of winning. Thompson hit his historic home run and the Giants won. Of course, the Giants now had a 100% chance of winning. So how can we measure the credit Thompson should be given for this batterpitcher interaction? At the start of the game we assume each team has a 50% chance of winning. The metric we track at all points in time is (my team's chance of winning) — (opponent's chance of winning).

Let's call this metric Winning Probability Difference (WINDIFF). At the start of a game, WINDIFF = 50 — 50 = 0. After each game event (batter outcome, stolen base, pickoff, and so forth) the batter and pitcher receive credit equal to how they change the value of WINDIFF.

1 The most complete list of game- winning probabilities based on game margin, inning, out
situation, and runners on base is in Tango, Lichtman, and Dolphin, The Book, chapter 1.

-71-

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