Decision-making in Baseball
Baseball is a great game to analyze from game theory perspective because of the scale of strategic decisions that are continuously made on the fields and each play. In every play, there are various players (baseball players, coaches, team managers and owners) with different goals and payoffs, and thousands of pitch-by-pitch decisions are made in course of an at-bat, inning, game, and season. Major League Baseball, one of the four major professional sports leagues of North America, is the most suitable platform for analysis because statistical information is tracked for almost every single complexion of the game. In the following paper, we choose to inspect one at-bat decision of a single game in detail as a microcosm of the strategies occurring in daily baseball.
Major League Baseball is the highest level of play in North American professional baseball. The regular season includes 162 games for each team and is concluded by advancing five teams from each league (American League and National League) to the "postseason", or play-off, where the winner is laurelled after the World Series. The Tigers/ Red Sox game (American League Champion Series Game 2) on October 13, 2013 is chosen to be analyzed in details by applying game theory.
The winner of ALCS (win 4 out of 7 games) will go to the World Series. Tigers have been into World Series for 12 times and Red Sox, 11 times since 1901. As attending World Series is one of the most honorable for players, managers, and even fans, every decision in every play in every game in play-off would be much more important than in regular season.
October 18, 2013: ALCS #2
Tigers' pitcher didn't allow a hit until the sixth and left after seven with a 5-1 lead. The upcoming reliever (pitcher who is not a starter) made a miserable condition, bases are loaded against the tie-run batter, David Ortiz. The primary players involved in this at-bat were:
#34 David Ortiz, Designated hitter - Career Stats: .287 BA, .381 OBP, .549 SLG i
#12 Mike Napoli, Infielder - Career Stats: .286 BA, .340 OBP, .449 SLG
#62 Al Alburquerque, Pitcher, Reliever - Career Stats: 10-3, 2.98 ERA, 1.297 WHIP
#53 Jo Benoit, Pitcher, Reliever - Career Stats: 44-35, 4.11 ERA, 1.285 WHIP
#21 Fred Porcello, Pitcher, Reliever - Career Stats: 61-50, 4.51 ERA, 1.389 WHIP
Game Tree: which pitcher should manager use to face Ortiz
For our game tree we looked at the scenario the Tigers faced at the bottom of eight with two outs, bases loaded, and Ortiz at the plate. We analyzed each strategy from this point forward by examining the option for Tigers' manager, Leyland, as well as for the Red Sox and then by looking forward and reasoning back to determine the optimal strategy for Tigers.
In first part, to make it simpler, we will use career stats which have large sample sets as our references. Also, we will construct the payoff by using batter's BA (batting average,...