Game Theory Final Project Barry Bonds: To Walk or Not to Walk December 17, 2005 The Strategerists Yang Xiao, Irwin Chiu, Naoise O'Loughlin-Irwin, John Osvald Mighty Barry at the Plate The outlook wasn't brilliant for the ‘Frisco nine that day, The score stood four to two, with but one inning more to play. And then when Snow died at first, and Durham did the same, A pall-like silence fell upon the patrons of the game. A straggling few got up to go in deep despair. The rest clung to that hope which springs eternal in the human breast. They thought, "if only Barry could but get a whack at that. We'd put up even money now, with Barry at the bat." But Tucker preceded Barry, as did also Ledee; and the former was a hoodoo, while the latter was a cake. So upon that stricken multitude, grim melancholy sat; for there seemed but little chance of Barry getting to the bat. But Tucker let drive a single, to the wonderment of all. And Ledee, the much despised, tore the cover off the ball. And when the dust had lifted, and men saw what had occurred, there was Ricky safe at second and Tucker a-hugging third. Then from forty thousand throats and more there rose a lusty yell; it rumbled through the valley, it rattled in the dell; it pounded through on the mountain and recoiled upon the flat; for Barry, mighty Barry, was advancing to the bat. There was ease in Barry’s manner as he stepped into his place, there was pride in Barry’s bearing and a smile lit Barry’s face. And when, responding to the cheers, he lightly doffed his hat, no stranger in the crowd could doubt t'was Barry at the bat. Eighty thousand eyes were on him as he rubbed his hands with dirt. Forty thousand tongues applauded when he wiped them on his shirt. Then, while the writhing pitcher ground the ball into his hip, defiance flashed in Barry's eye, a sneer curled Barry's lip. And now the leather-covered sphere came hurtling through the air, and Barry stood a-watching it in haughty grandeur there. Close by the sturdy batsman the ball unheeded sped -- "That ain't my style," said Barry. "Ball one!" the umpire said. From the benches, black with people, there went up a muffled roar, like the beating of the storm waves on a stern and distant shore. "Kill him! Kill the picther!" shouted someone on the stand, and it's likely they'd have killed him had not Barry raised his hand. With a smile of Christian charity, great Barry's visage shone, he stilled the rising tumult, he bade the game go on. He signaled to the pitcher, and once more the dun sphere flew, but Barry still ignored it, and the umpire said, "Ball two!" 2 "Fraud!" cried the maddened thousands, and echo answered "Fraud!" But one scornful look from Barry and the audience was awed. They saw his face grow stern and cold, they saw his muscles strain, and they knew that Barry wouldn't let that ball go by again. The sneer has fled from Barry's lip, the teeth are clenched in hate. He pounds, with cruel violence, his bat upon the plate. And now the pitcher holds the ball, and now he lets it go, and now the air is shattered by the force of Barry's blow. Oh, somewhere in this favored land the sun is shining bright. The band is playing somewhere, and somewhere hearts are light. And, somewhere men are laughing, and little children shout, but there is no joy in McCovey Cove - mighty Barry has been intentionally walked with two on and two outs. -By Ernest Lawrence Thayer & the Strategerists Even Barry Bonds’ most ardent detractors must admit one simple fact: the man can hit home runs. In fact, Bonds set the record for most home runs in a season at 73 in 2001, claiming one of the most sought after records in baseball. At the same time he posted impressive batting stats, batting .328, .370 and .340 in 2001, 2002 and 2003 respectively. In 2002 he broke another long-standing single season record: intentional walks. According to this statistic, no batter had been as feared at the plate since Willie McCovey in 1965, whose opponents favored walking over pitching 45 times. During 2002, Bonds’ opponents took this option 68 times. In 2004 Bonds posted yet another impressive record – one that absolutely obliterated his previous mark. Although his batting statistics had held steady over the past three years, (and most, in fact, would hold steady in 2004), Bonds was intentionally walked a staggering 120 times, almost twice his previous mark. Bonds’ performance over the years leading up to 2004 does not justify this increase – his batting average, at bats, RBIs and home runs moved very little. If Bonds himself wasn’t the cause of this reaction by opposing managers, what were they reacting to? 3 We will examine several possible solutions as we apply a game theory approach to the problem. We must first consider Bonds’ supporting cast. If Bonds is walked, the player up to bat after him will bat with a man on base, and depending on the number of outs in the inning, so will subsequent players. If the average competency of the players batting after Bonds decreased dramatically from 2003-2004, the intentional walk option could become more attractive to managers. It is likely that there is no one single explanation for this phenomenon, rather, it will be a combination of factors. We must also consider the possibility that Bonds performance was in fact improving, which caused opponents to react, or adversely, opponent’s pitching may have decreased in proficiency from the previous year. It should also be noted that Bonds is one of the most unpopular players in history, and most in baseball do not want to see him break the career home run record he is currently chasing… could this lead opposing managers to act irrationally? If they are playing a dominated strategy, what was the likely effect on the team? We will explore these possibilities by applying game theory to the problem. First, we will look forward and reason back by examining the results from 2001-2003, when Bonds was intentionally walked less, to the results from 2004, when Bonds was walked more. Was this strategy successful for opposing managers? What was the statistical expected value decision they faced, and were they acting rationally? Following a statistical analysis, we will then explore outside factors that might have affected managers’ decisions, and compare them to our statistical analysis to decipher why this strategy was so widely deployed in 2004. 4 When does it make sense to intentionally walk Bonds? “You walk Barry. Just walk him.” – Greg Maddux “I became a good pitcher when I stopped trying to make them miss the ball and started making them try to hit it.” -- Sandy Koufax For a manager attempting to make the decision of whether or not to walk Barry Bonds, several variables are analyzed within his mental model of the game: how much of a lead does the team have, how many outs are there, how many men are on base, how good is my pitcher on the mound, etc. We will attempt to simplify the model within a manager’s head down to one key statistic – minimizing runs scored. As we analyze this model, there are certainly situations where it is wise to intentionally walk Bonds. For example, it is wise to walk Bonds whenever there are runners in scoring position and first base is open with two outs. Because of Bonds’ higher batting average and the high likelihood of a runner on second or third base scoring on any hit, a manager protecting a slim lead would be wise to walk Bonds to force a teammate with a lower batting average to drive in the runs. In addition, walking him actually creates force outs at bases as well as sets up the potential double play that would net the team two outs. In some baseball situations, an intentional walk is a dominated strategy. For example, walking Bonds when the bases are loaded is clearly not preferred if it walks in the tying run. A walk issued when runners are on first and second with one out or less is also not preferable. This places a runner on third who can score on a sacrifice fly or a particular ground out and increases the chances of someone scoring. 5 We will eliminate these dominant and dominated strategies as obvious choices for the manager. We will examine some non-intuitive situations such as having a person on first with one or less outs in which it is unclear if the strategy of intentionally walking Bonds is the best course of action. To determine this, we will look at the expected runs scored using the history of Giants’ outcomes from 2001 – 2003. We will examine whether a) Bonds was walked or not and b) how many runs the Giants scored as a result. From these findings, we should be able to come up with an expected number of runs scored dependent on whether the opponent walks Bonds. If the opposing manager is rational and has a good understanding of baseball statistics, they will choose the course of action in which the expected runs are minimized. In the next page, we provide an analysis of the Giants’ past history of runs scored as a result of a walk issued to Bonds.