Examining a Sunk Cost Effect in the Managerial Decisions of Major League Baseball

Transcription

1 Haverford College Economics Department Examining a Sunk Cost Effect in the Managerial Decisions of Major League Baseball Patrice Harkins Spring 2011 Professor Richard Ball

2 Table of Contents Abstract..3 I. INTRODUCTION...4 II. LITERATURE REVIEW...8 III. DATA AND METHODOLOGY...17 IV. ANALYSIS.22 V. RESULTS.26 VI. CONCLUSIONS 31 BIBLIOGRAPHY APPENDIX 2

3 Abstract This paper investigates the existence of a sunk cost effect in the decision making processes of the Major League Baseball clubs management. This study builds on previous research, which points to an influence of these prior investment costs on decisions in the National Basketball Association. Since in a drafting system team franchises only can make a one player selection per round, the draft order represents a tangible cost to teams both in opportunities forgone and the financial investment of salary contracts. If a sunk cost effect is present, then a franchise will keep a player regardless of the player's performance because of the prior investment made in the player. Using OLS, Logit, and survival analysis models, 7681 players were analyzed over 20 draft years, Findings showed that a player s overall draft pick had a significant effect on games played and number of at bats. The higher (lower numerically) a player was drafted; the greater was the probability that the player would reach the Major Leagues. Additionally, survival analysis results showed that low draft picks made it to the Major League teams quicker. 3

4 I. Introduction Since the early twentieth century, baseball has been considered our nation's pastime. Our professional sports leagues account for a large part of our economic and social life, and thus are an important topic to investigate academically. In particular, professional baseball is a prime example of a sport that has grown tremendously; therefore, the baseball industry is an excellent place to gain academic insight. Although baseball has largely been profitable from its conception, over the past century, baseball has transformed into a colossal money making entity. In 2007, overall revenues generated by the Major League Baseball (MLB)-connected businesses were estimated to exceed $6 billion (Zimbalist, 2010). By 2008, the MLB surpassed its previous revenue levels reaching $6.8 billion, rivaling the profits of the National Football League (NFL) for the first time in decades (Kercheval, 2008). From tickets, to player s salaries, to endorsements, each year millions of dollars are invested into baseball franchises because of their potential to accrue such substantial profit. These professional sports leagues provide a unique environment to test hypotheses about decision making and rationality, specifically sunk costs. Furthermore, sports offer an overwhelming amount of accessible and testable data. Given that the primary goal of a manager is to maximize the success of a team through the acquisition of talented players, each year franchise managers are confronted with the role of predicting which amateur players will turn into all-star successes. In an effort to promote competitive balance between teams and comparable profits, most of our professional sports leagues have instituted a reverse-order draft. This means that a manager is constrained to decide one draft pick per round from a pool of possible headliners or duds, a daunting task. Thus, the management of baseball franchises must make decisions based on the incomplete information they have, which makes the construction of 4

5 a successful team essentially a guessing game. The draft order combines all available information about an amateur player s performance and is the principal employed by decisionmakers in basing expected potential and profitability of a player. A player s overall draft position can be considered analogous to price in a well-established market. It is an ordinal rather than a cardinal measure of expected value and should reflect all publicly available information about the player s prospects or chance of success (Spurr, 2000). The draft picks are decided through numerous people and institutions, but based mainly from the judgments of scouts who also face information asymmetry and directly observe only a fraction of the available pool of talent and often for just a few games. There is a great deal of uncertainty. Although this lack of complete knowledge is nearly equal across the different baseball clubs, it doesn t diminish the degree of risk that management undertakes by signing draft picks. In comparison to the managers of both professional football and basketball, baseball managers assume a greater degree of uncertainty in decision making. Unlike the draft picks of both the National Basketball Association (NBA) and the National Football League (NFL), most of the draftees in baseball most likely will not produce value for their teams for years, if at all due to the great degree of talent and chance necessary to reach the highest levels (Aberle, 2010). With over 1000 selections made each year, the vast majority of these players never even make it to the Majors, while the success rate for the draftees of basketball and football is virtually 100% (Spurr, 2000). According to analysis of the first-round draft picks in baseball from 1965 to 1985 conducted by Spurr (2000), only 320 of a total of 506 players, or 63%, eventually reached the Major Leagues. Furthermore, according to survey data conducted by Callis (2003), one of every four first-round picks ultimately makes a nontrivial contribution to a Major League team, and a mere 1 in 20 becomes a star. Only 8% of the players drafted in the first 10 rounds typically 5

6 develop into big league regulars, and few beat the odds. The odds are 3 to 1 against a first round pick, 9 to 1 against a second rounder, and 15 to 1 against a third round pick (Burger and Walters, 2009). Of those players that make it to the Majors, many develop for several years in the Minor Leagues, forcing managers to project their roster years in advance and use a more strategic, long term thought process in draft decisions, which could be the reason why a sunk cost effect might occur. The reasoning behind this argument relies completely on the time frame. When drafted players are considered for promotion to the Majors or to be traded after months or years in an organization, the amount of investment already made in them both in money and time becomes relevant to whether a player should play more, play less, be demoted, promoted or get cut from the organization. What results from the draft are profound differences in ability and consequently in compensation the higher the draft pick numerically. In recent years, players salaries and signing bonuses have skyrocketed, which makes each draft pick decision a huge investment since draft number is primarily the way to assign value to a player s contract. Bonuses of over a million dollars became commonplace in the 1990s for players selected at the very top of the draft. Median signing bonuses for first round choices have increased from 225,000 in 1990 to 1.78 million in 2000 a compound growth rate of 23 percent (Staudohar, Lowenthal, and Lima, 2006). These multimillion dollar decisions are reinforced by franchises management desires to win on the field as well as maximize wealth. However, it is not certain that these investments will pay off. For example, the number one draft pick of the 1990 rule four amateur draft, Todd Van Poppel, was signed for a record of 1.2 million dollars, and considered the next big player. He was drafted right out of high school and was rushed through the Minors. He lasted 11 years in the Majors, but did not reach all-star status and was traded 6 times. The following year, first draft 6

7 pick Brien Taylor was signed by the Yankees for a new record of 1.55 million. Not only did he never make it to the Majors, but he wasn t released from the Yankees organization until 7 years after being drafted (Real Clear Sports, 2011). In summary, the returns are uncertain for the players and long deferred (Burger and Walters, 2009), yet the costs are significantly large for highly drafted players. Overall, it is the type of environment where the acknowledgement of sunk costs could arise. The purpose of this thesis is to discover if there is any evidence in the data that supports that draft order is a significant predictor of games played to demonstrate that there is a sunk cost effect in the managerial decision making process of the MLB franchises. Using a previous study conducted by Staw and Hoang (1995) as a model and survival analysis, I hypothesize that the highest drafted players in the MLB will be more likely to survive in baseball longer and make it to the Major Leagues regardless of their overall performance as a result of a sunk cost effect in managerial decision making. 7

8 II. Literature Review Economic theory implies that a rational decision-maker should ignore sunk costs because they are incurred and cannot be recovered, thus should not be considered in subsequent decisions. Economics concentrates strongly on these assumptions about behavior. Despite the fact that the irrelevance of sunk costs is considered a basic principle of economics, studies have shown that individuals do not always ignore sunk costs. Many behavioral economists and psychologists have shown interest in the reasons behind this paradox of human behavior and have studied this sunk cost fallacy in a number of contexts. A majority of the literature on the sunk cost and escalation of commitment effect have been conducted in laboratory settings (Arkes & Blumer, 1985; Frisch, 1993; Philips, Battalio, & Kogut, 1991). In these experiments, the subjects are presented with scenarios where funds have previously been invested in a project. These prior works on sunk costs were designed to show empirically that a decision-maker might continue to commit to an unsuccessful project because of the investment already placed within the course of action. Arkes and Blumer s (1985) radarblank plane experiment is frequently cited by sunk cost literature. In this classical study, subjects were presented with a scenario in which millions of dollars had been invested in a plane that would be undetectable by radar, yet during the development process of this plane a competitor had produced a superior plane. A large majority of subjects (87%) responded that they would continue with the venture when the project was described as already 90% completed. On the other hand, very few subjects chose to invest the millions in a scenario in which the project had not begun. In addition, Arkes and Blumer (1985) used a field study to demonstrate that customers who initially paid more for a season subscription to a theater series attended more 8

9 plays during the next 6 months as a result of their higher sunk cost in the season tickets versus those who had bought a regular ticket. In some environments reacting to sunk costs can be considered rational, as McAfee, Mialon, and Mialon (2010) argued in their study. The researchers argued that agents may rationally react to sunk costs because of informational content, reputation concerns, or financial and time constraints. With their models, McAfee, Mialon and Mialon (2010) claim that it is rational to ignore sunk costs only in situations in which past investments are not informative, reputation concerns are unimportant, and budget constraints are salient. Our professional sports Leagues design seems to qualify as one of the environments where decision makers should react to sunk costs. The returns on investment decisions made in professional sports are highly uncertain as I have discussed in detail, so acknowledging prior investments can be considered rational. The MLB drafting system permits team franchises to make one player selection during each round. Therefore, every year Major League teams invest millions of dollars in contracts to sign draftees on which returns are unforseeable. It is not guaranteed that a player will meet their expected potential, and following the draft, the player s cost has already been incurred. Salary contracts are based roughly in line with draft order, such that players drafted earlier expect to be paid substantially more than those taken later in the draft. Therefore, the draft order of players represents an explicit cost to teams. The draft order also represents a set of opportunities foregone, since choosing any particular player means passing over other qualified candidates. The fact that resources have already been committed to such a player leads to a situation where escalation may arise. A team may over-use a player relative to his value, if a large previous investment has been made. Although it is expected that performance is the primary determinant to keep or trade a player, if sunk costs have an influential role in 9

10 decision making, then the draft pick might be a significant predictor of a franchise retaining a player even after controlling for performance. Further research in other field settings points to the escalation phenomenon, particularly in the National Basketball Association (Staw & Hoang, 1995; Camerer & Weber, 1999). Staw and Hoang's (1995) study of the NBA was one of the first comprehensive inspections of the sunk-cost effect in a real world scenario, and it demonstrated significant sunk cost effects on personnel decisions. The study was interested in observing if the amount of investment an NBA franchise had made in a player affected playing time received and duration of the player's stint with the organization. One would expect that a franchise would play their most effective players, yet if the sunk cost effect is present in managerial decisions, then the highly drafted player would play more and stay longer regardless of performance. Using performance statistics of players and the draft order of players for the first and second round NBA drafts, Staw and Hoang (1995) hypothesized that if sunk costs influence decision making, then draft order will be a predictor of playing time even after the effects of on-court performance have been controlled. In order to determine the success of a player, the researchers created an index composed of total number of points scored in a season, assists, steals, shots blocked, rebounds, personal fouls, free-throw percentage, field-goal percentage, and 3-point field goal percentage. The dependent variable was the number of minutes a player played in the regular season. In order to control for playing time, Staw and Hoang (1995) divided the statistics mentioned by the total number of minutes played that season. The researchers decided that to avoid confounding a player's performance with his position and reduce multicollinearity they should factor analyze. Multicollinearity refers to the presence of a correlation between two or more of the explanatory variables in a regression. The consequences 10

11 of multicollinearity are that variance and covariance will be wider, which make it difficult to reach a statistical decision for the null and alternative hypothesis. A wider confidence interval may lead the researcher to accept the null hypothesis when it should be rejected. In the presence of multicollinearity, the standard errors of the affected coefficients tend to be large, and it can lead to difficulty interpreting the regression coefficients. It can represent a serious issue in survival analysis because of the time-varying component of this type of analysis. The process of factor analysis brings intercorrelated variables together under more general, underlying variables. After Staw and Hoang (1995) used factor analyzation to reduce the effects of multicollinearity, it became clear that three factors determine the performance statistics of both guards and forwards. These factors were scoring, toughness, and quickness. Scoring included field-goal percentage, points per minute, and free-throw percentage. Toughness was comprised of rebounds per minute and blocks per minute. Quickness was composed of assists per minute and steals per minute. The study standardized each of these component measures by summing them and dividing by the total number of items in the factor, which created an index with a mean of zero and a standard deviation of 1. Other control variables that could have an effect on performance were included such as injury, being traded, team's winning percentage, and a dummy variable for position. The first of their regressions tested the significance of performance on games played. They found that draft order was a significant predictor of minutes played over the entire 5 year period studied, and the effect was beyond those of performance, trade, or injury. The next regression focused on a player's survival in the league because the decision to cut someone is 11

12 similar to the decision to play or bench a player and would be based on sunk costs as well. The model they constructed used the hazard rate 1 as a linear function of time expressed as: r(t)= exp[α + β 1 X + β 2 X(t) + γ(t) where r(t) is the hazard rate, α is a constant, X is the vector of time-constant variables like draft number, X(t) is the vector of time-dependent variables, and t is the time variable of career length. The same control variables were used from the first regression with the inclusion of player's team record because poorly performing teams might be more likely to change their roster. Lastly, Staw and Hoang (1995) used a regression with a hazard rate in this regression to measure the probability of the player's first trade. They discovered that a first-round pick would stay in the league 3.3 years longer than a player drafted in the second round. Also, draft order had a significant, positive effect on the hazard rate for being traded. Moving from the first-round to the second-round of the draft increased a player's chances of being traded by a shocking 72%. The results also demonstrated that players were less likely to be traded if they were on winning teams. Similarly, in Camerer and Weber's (1999) re-examination of Staw and Hoang's (1995) study, they found results that indicated that draft order had an effect on playing time. Their reexamination posed additional questions to strengthen the evidence of a sunk cost, or escalation effect. For example, their study highlighted that there are a number of counterarguments to why a high draft-pick might play more that do not consider sunk costs as the reasoning. Hence, they found it important to delve deeper and overturn these arguments through a re-analysis of NBA statistical data from the first and second rounds of the drafts. One such argument is 1 The hazard rate is interpreted roughly as the probability of the event of being cut occurring in a time interval t to t + Δ, given that the individual was at risk of being cut at time t 12

13 that it is possible that a higher draft pick receives more playing time because teams are trying to determine the true value of their investment; however, they claimed that this argument cannot explain the results that Staw and Hoang (1995) found in 2 or more years after the draft. It is unlikely that a franchise would still assess its investment after two years of observing the player's performance. Another such argument is that coaches and general managers play early drafted players more to validate their choices or to avoid admitting to mistake, yet administrative decisions are usually made interactively between owners, management, and coaches. As a result, they argued that a coach or general manager alone would not feel the need to vindicate himself and bias a high draft-pick's playing time. Camerer and Weber also expanded upon Staw and Hoang s (1995) study by including a draft x trade interaction variable. By employing an interaction variable of draft pick and the trade control variable, these researchers were able to see if the sunk cost was carried over to the new team even if it was not the team who made the original investment. This touches upon an important point. If escalation arises out of the draft as a commitment of resources, then when a player is traded to a new team, the new team should not inherit the escalation motives of the first team. When a player is traded to a new team, does the effect of draft number disappear? Even with the inclusion of this additional control variable, Camerer and Weber arrived at the same irrational escalation findings that Staw and Hoang had previously discovered. Dilger (2002) estimated hazard rates in the NBA as well, yet methodologically he used a Cox semi-parametric proportional hazards model. He hypothesized that the league hazard, or that probability of leaving the NBA, depends mostly on the player s performance. Also, he hypothesized that team hazard, or the probability of a player quitting the team, depends on the player s team specific performance and salary (cost to team). Using longitudinal data from the 13

14 NBA seasons and including new variables not considered before like race and an all star status variable, Dilger found that a higher draft number resulted in a higher hazard rate for both league and team hazard. Higher salaries improved the probability of staying in the league as well. Positive performance variables had a significant impact on reducing the hazard rate. Thus, the results from this study are consistent with his original hypotheses and consistent with the previous survival analysis of both Staw and Hoang (1995) and Camerer and Weber (1999). Although extensive field research of the sunk cost fallacy has been conducted in the NBA, there is a lack of literature that focuses on both sunk costs and survival analysis in the context of our professional baseball league. Previous baseball related literature has looked at predicting winners (Barry & Hartigan, 1993), wage disparity and team productivity (Depken, 2000). There has also been comprehensive research on players salaries. Nevertheless, a number of baseball related studies relate to the research goals of this thesis. Spurr (2000) used a probit model and choice based sampling to determine whether certain factors other than a player s draft position, such as college experience or position, are useful in predicting whether a player will reach the Majors. After realizing it would not be feasible to obtain data on all drafted players for all years of the draft, they used data on all players drafted during the amateur drafts of 1966 through 1968 and The study used a binary dependent variable that was based on whether the player ever played for a Major league club as the measure of success. Although the main hypothesis of the study focused on factors other than draft order, the study found that the worse the player s draft position, or the higher it is numerically, the less likely it is that he will ever reach the Majors. Also, his results supported that after about the 34 th round of the draft the draft position loses its marginal value as an indicator of the athlete s prospects. This study did not 14

15 control for player performance, but rather included variables such as schooling level, position, and club to determine the factors significant in predicting whether a player reaches the Majors. Chapman and Southwick s (1991) study involved the use of hazard rates concerning the matching hypothesis in Major League Baseball. They looked at the probability of job separation given a particular number of years on the job for managers, since there are no significant data limitations about inputs in the sports leagues and managers are highly comparable. Their objective was to estimate the contribution of managers and of manager-team matches to team productivity while controlling for such factors as team fielding, pitching, and hitting capability. Minor league players were considered reserve inputs. The researchers hypothesized that job separation should first increase and then decrease as tenure rise. In other words, the probability of job separation given a particular number of years on the job (i.e., the hazard rate) should first increase and then decrease. The study found that hazard rate rises from the first three years on the job and declines for the next three. Job-matching theory predicts that wages and job tenure should be positively related in cross-sectional data because workers with good matches will tend to stay at their jobs for longer periods. Although it is not concerned with sunk costs, this study adds to background on the use of survival analysis and hazard rates and their application to Major League Baseball. Burger and Walter s (2009) study calculated an internal rate of return (IRR) to evaluate the rates of return on professional baseball players to quantify if draft picks pay off. They used historical data ( drafts, players drafted in rounds 1-10) to calculate the probability that a particular draft pick will pay off and the typical size of realized returns. The IRR was measured using a present value finding that included the time interval it took for a particular player to reach the Majors. Using this measurement, they found that first round draft picks have 15

16 a 44% IRR compared to 29% expected return for players drafted in the second round, as well as dropping one slot in the first round costs a player 5.5%. Overall, this study found that first round picks over the period have a much higher probability of becoming a regular, good, or star quality player in the Majors, demonstrating that draft position explains a great deal of the variance in the probability of reaching the Majors. This research supports that investments in Major league baseball are both risky and costly, and it similarly includes data on the time interval to reach the Majors incorporated into my thesis. Moreover, it highlights the importance of the draft number of the player, which is central to my sunk cost hypothesis. 16

17 III. Data and Methodology The data used in this study was obtained from Gary Cohen s baseball archive ( which contains a wide collection of statistical information on everyone who has ever played in Major League Baseball (Cohen, 2010). The longitudinal data used in this study includes players drafted from in the Rule Four first-year amateur player drafts, regardless of whether or not they ultimately made it to the Major Leagues. Statistics for players were collected for all seasons that the athlete played baseball, whether in the Minor or Major Leagues, or until the 2010 season, if the player is still active. Data collection for each player included their draft year, draft round, overall draft pick, education, position, organization, and level of play. Homeruns, runs batted in (RBIs), and on-base percentage (OBP) were used to reflect the player s hitting ability and performance, while the number of errors per season was included to demonstrate negative player performance. In order to reflect the productivity of a player while he is on the field, it was sensible to divide some of the performance statistics by the number of games played, such as homeruns, RBIs, stolen bases, and errors. The player s team winning percentage was included in the data collection, since it is hypothesized that successful teams might be less likely to trade or make significant changes to their roster, if they are doing well. Also, there are differences in potential for playing time between being drafted by a winning or losing team. Considering that the draft has 50 rounds per year with around 1500 players in total, there were thousands of players to include over the twenty year span. I limited my data to the first 34 rounds of the drafts because many of the players after that round had missing data, dropped out of the league after two years or less, and did not have robust performance statistics. I also considered including pitchers and their various performance statistics, yet due to time constraints 17

18 I dropped all pitchers from my study. As a result, my final data included 7,681 players with a total of 59,117 observations. I created several variables to embody information about the individual player. For example, a dummy variable mlb (0 for reaching the Majors that statistical year, 1 for reaching the Majors) was included to indicate whether a player had reached the MLB during that season, and it was useful in the survival analysis regressions. Similarly, another dummy variable made_it described if a player ever made it to the Majors during their tenure of playing baseball. As evidenced in the Shaw and Hoang (1995) study, I also found it necessary to include a dummy variable for being traded because the new organization might play a player more if his position or services are in demand. This control variable, traded, was equal to 1 if a player was traded during or before a particular season and 0 otherwise. A variable was also created to account for if a player had ever been traded (evertraded). Likewise, I created a dummy variable for college (college) experience to add to my regression as a control, since it could be the case that college players are drafted higher than high school players, or vice versa. All of these control variables were included in the linear regression analysis that focused on whether draft order was a significant predictor of games played regardless of performance, or whether performance was the primary predictor of playing time. The summary statistics shown in Table 1 (see Appendix) describe some of these variables. For many of these variables it was more enlightening to give descriptive statistics by i.d., or to show unique values for each player. For example, the mean of draft round (draft_round) is This is presumably because the players drafted in the earliest rounds would have more observations because they would play for more years. Thus, the average draft round of the entire sample would be biased towards earlier rounds. However, when this variable 18

19 is separated by each player i.d., each player only has one observation. Subsequently, the mean draft round was (player_draftround). Since variables like made_it are dummy variables, the mean of player_made_it, (which similarly has only one observation per player) is equal to the percent of people who made it to the Majors. Thus, of the 7,681 players observed only 17.6% (1,353) ever made it to the Major Leagues. Likewise, 70% of the sample went to college. Using the data collected for draft year and level, I was able to create a variable called years_to_mlb, which calculated the number of years it took a player to reach the Major Leagues from the year the player was drafted. The average number of years for players of the 20 year span that I observed to reach the MLB was approximately four, with a maximum of 15 years and a minimum of zero. For additional information about the sample, I created several graphs to visually observe the influence the draft had on the chances a player would reach the Majors. Figure 1 shows how draft round impacts the number of years on average it will take a player to reach the MLB. The graph suggests that the further a player is drafted in the draft, it will take him on average more years to reach the Majors, which is evident from the positive trend of the line. After about the third round, the average years to Majors is higher than the sample average of four. Figure 2, a bar graph, demonstrates that after the second round, with the exception of the sixth and eighteenth round, the number of years on average it will take a player to reach the Majors is greater than four. Figure 3 demonstrates the negative relationship between draft round and the average proportion of players reaching the Majors. There is a sharp decrease in the proportion of players making it as a player moves from round 1 (~70%) to round 3 (~35%). After around round 10, the player s chances are approximately less than 20%. 19

20 To test the sunk cost hypothesis prior to regression analysis, several of the graphs were broken down based on pre-mlb batting averages and on-base percentages into 5 quintiles. The first quintile represented the poorest performing players; correspondingly, the fifth quintile indicated the players with the highest averages. Support for the hypothesis would show that high draft pick players reached the Majors in fewer years, eventually made it to the Major Leagues even when they were playing the worst, played in more games, and received more at bats. For example, Figure 4 shows that players drafted in the lowest rounds and in the lowest quintile (1) played in more games. Also, there is a decreasing trend of average number of games played as a player is drafted further in the draft in that quintile. In all of the quintiles, a slightly negative trend can also be seen. It can also be observed that as a player has a higher batting average (in higher quintiles), he plays on average in more games (~75 in quintile 4 and 5). Similarly, Figure 5 shows that players drafted in the lowest rounds received more at bats. The negative relationship between draft round and at bats is most evident in the first and second quintile. Figure 6 is again divided into quintile by batting average. This graph shows that few players in the first quintile ever make it to the Majors, since these graphs demonstrate the average number of years it takes a player to reach the MLB based upon draft round and batting performance. However, for the three observed players in the first quintile it should be highlighted that the player drafted in the lower round reached the Majors slightly quicker than the other two players. In the third and fifth quintiles those players who were drafted earlier, made it to the Majors quicker, with a few exceptions. In Figure 7, the relationship of draft round on the proportion of players making it to the Major Leagues is observed. In the first and second quintile many of the observations are zero. Since, player_made_it is a dummy variable all of the observations are either zero or one. The 20

21 fourth and fifth quintile suggests that a player drafted in one of the earliest rounds would have on average a 100% chance of making it, yet it is most likely the case that there is one player who made it during these rounds (1/1=1). The third quintile suggests that those drafted in lower round have a better chance of making it in comparison to those in the later rounds. This seems true for both the fourth and fifth quintiles as well. The remaining descriptive graphs were separated into quintiles by on-base percentage. Figure 8 shows a greater number of observations in the first quintile of Figure 10 in comparison to the first quintile of Figure 6, which also measures how draft round impacts the number of years it will take a player to reach the Major Leagues. Again, in general those picked in the lower rounds reached the MLB quicker (evident in quintiles 1, 2, 3). The evidence that those who were drafted in the earlier rounds have a better chance of eventually making it to the Majors is clearer in Figure 9. In all quintiles, players drafted in the first ten rounds have higher proportion of players making it than later round, which further supports the sunk cost hypothesis. 21

22 IV. Analysis A. Linear Model In the first section of my analyses, I estimated several linear regression models to investigate the hypothesis that draft number had an influence on games played and number of at bats even after controlling for performance because of a sunk cost effect. The first and simplest models estimated were: (Regression A1) g it = β 0 + β 1 overall it + β 2 year_avg it + ε it (B1) ab it = β 0 + β 1 overall it + β 2 year_avg it + ε it where the dependent variables were g = games player and ab = total number of at bats, overall = player s draft number, year_avg = batting average during that season, and ε = the error term. Next, I re-ran this regression adding several control variables and additional performance variables (See Table 2). Included in these control variables were a dummy variable for being traded during a season (traded), a dummy variable for college experience (college), an interaction term between draft number and traded (draftxtrade), and draft year (draft_year). The interaction term was added to model Camerer and Weber (1999) mentioned in the literature review. The addition of this interaction variable was included to observe if the sunk cost effect was inherited by the new team after the player is traded. The player s on-base percentage (year_obp), number of steals per game (year_steals), the number of rbis per at bat (year_rbis), homeruns per at bat (hr_avg),and errors per game (errors) were incorporated as supplementary performance statistics. 22

23 B. Survival Analysis The second section of this thesis focused on the survival of players in both the Minor and Major Leagues of baseball, which also takes into account sunk costs. A highly drafted player (low draft pick numerically) may be pulled up to the Major Leagues faster than a lower draft pick because of a sunk cost effect. This type of examination requires more complicated regression techniques that the assumptions and characteristics of standard linear regression analysis do not incorporate. For example, ordinary regression analyses (e.g. OLS) cannot easily comprehend changes in the value of explanatory variables over time, nor can they adequately handle right-censored cases, i.e the players for which the events reaching of Majors or leaving the league altogether have not occurred during the time period of study (Staw & Hoang, 1995). Thus, survival analysis is utilized for this duration hypothesis because survival functions and hazard rates concern analyzing the time to the occurrence of an event and encompass methods for analyzing the probability and rate that these events will occur. The effect of duration is important in this thesis because I would expect that a player s risk of being cut will increase with the number of years the player remains in the league. Also, the longer a player remains in the Minors past a certain point might lower the probability that he will ever reach the Majors or remain in baseball. Also, it is important to discover the probability of a player s leaving the league (e.g. cut) because the remuneration is so high that it can be most likely assumed that no player leaves completely willingly; If the player is cut, it is because they are not worth the investment to management. My analysis is somewhat counterintuitive since I am looking at when a player successfully reaches the Major Leagues and how draft number influences this probability, while survival analysis typically observes when a failure occurs. Using a Cox proportional hazard model, which does not limit the 23

24 pattern of the hazard rate, problems of censoring can be solved and my hypothesis can be properly tested. The Cox regression assumes that the covariates multiplicatively shift the baseline hazard function. This model asserts (Cleves, Gutierrez, Marchenko, & Gould, 2008) that the hazard rate for the jth subject in the data is: exp or log log where is the baseline hazard and, the regression coefficients, are estimated from the data, and is a vector of individual characteristics. The baseline hazard is given no particular parameterization, and the shape of the hazard can be increasing, decreasing, or either. If the risk of the event occurring is rising with time, so is the hazard. The hazard rate is the probability that the event will occur. In this portion of the study, I continued to test the influence of draft number. After formatting my data into a duration format and declaring it to be survival data (stset command: stset date1, id(id) origin (date0) failure (mlb)), I was able to run the regressions that took the following forms: (C1) exp (C2) exp where again overall = the player s draft number, average = the players year average, and obp = the player s on-base percentage. 24

25 C. Logit Model Lastly, I included a model that used a binary dependent variable, the logit model, which simply allowed for the exploration of how each explanatory variable affects the probability of a certain event occurring. Binary dependent variables have two values, typically coded as 0 for a negative outcome (the event did not occur) and 1 as a positive outcome. In other words, this model uses a dummy variable as the dependent variable (Long & Freese, 2006). This model takes the following form: where i indicates the observation and is a random error. Cases with positive values of Y* are observed as y = 1, and cases with negative or zero values of Y* are observed as y=0 (Long & Freese, 2006). In order to discover the probability of y=1 given x, leads to the equation: Pr 1 (Long & Freese, 2006) This model was introduced in the present thesis because it complemented the other two models and only would augment support for the sunk cost hypothesis. If a low numerical draft pick had a higher probability of reaching the Majors even after controlling for performance, then a sunk cost effect must be present. In this model, I used player_made_it as the binary dependent variable. 25

26 V. Results A. Linear Model Table 2 presents the results from the regressions which used games played as the dependent variable. From this table, it can be seen that in all of the regressions the player s overall draft pick (overall) was statistically significant (A1-A6, Table 2). This was true even when controlling for performance, being traded, and college experience. Interpreting the coefficient for overall is counterintuitive. The regressions (A1-A6) showed that every increment in the draft number decreased the number of games played by approximately -.01, holding all else equal. The inclusion of the various control variables diminished the effect of the draft number but only slightly. Both a player s batting average (year_avg) and on-base percentage were also statistically significant in all the regressions. A one unit increase of a player s batting average had the greatest positive impact on the number of games played (A6, ). Thus, a player s batting performance was associated with more games played, and was therefore a significant predictor of the amount of playing time the player was given. College experience had a significantly positive impact on the number of games played except in the last regression, and being traded was also a predictor of games played. The draft and trade interaction term was also significant, which suggests that the sunk cost effect might be inherited by the new team. Draft year was statistically significant, even when broken into dummy variables for each year. Draft years 1987 (p-value of.092), 1988 (.083), and 1999 (.025) were the only statistically significant year dummies. The supplementary performance variables used as controls were all statistically significant and had a positive impact on the number of games played. As predicted, the number of errors has a negative impact on the number of games played. The number of RBIs per at bat (year_rbis) also 26

27 had a negative impact, which is unexpected considering it is a measurement of positive performance. Table 3 presents the impact of draft order and performance on the number of at bats. Again, a player s overall draft pick was statistically significant in all regressions even when controlling for performance. A one increment increase in a player s draft pick resulted in approximately.05 less at bats and, when adding controls, approximately.04 less at bats. Once more, a player s batting average was the primary performance variable associated with a greater number of at bats. In all four regressions (B1-B4), year batting average was stastically significant, and on-base percentage was statistically significant for all regressions except B2. College experience was only statistically significant in the B3 regression, and had a positive impact on the number of at bats. Traded and the interaction term were both statistically significant in predicting the number of at bats. 27

28 B. Survival Analysis The results from the Cox proportional hazard model regressions are presented in Table 4. In these two regressions, failure was considered to be reaching the Majors and the hazard ratios represent the probability that failure will occur in the next period. For example, if the hazard ratio of a coefficient is equal to.8, then a 1 unit increase in the covariate variable decreases the hazard by 20%. Column C1 displays results from a regression in which the variable overall was considered a constant covariate, while year_avg was a time-varying covariate. Although the player s overall draft pick was significant, the player s batting average was not. The hazard ratio of.9977 can be interpreted as a 1 unit increase in draft number decreases the hazard by.0023%. Or in other words, the later a player is drafted, the lower the probability that he will make the Majors in the next period, and in general. The draft number not only impacts the probability a player will ever reach the Majors, but also influences the speed at which he does or doesn t. The second regression tested year_obp as the time-varying covariate. In this regression, both the player s draft pick and the performance variable were significant. The hazard ratio for draft pick was again.9977, which can be interpreted in the same manner as above. The hazard ratio for the on-base percentage variable, 1.263, demonstrated that the better a player was performing, the higher the odds that he would reach the Majors in the next time period. The hazard ratio can be interpreted that a 1 percentage point increase in on-base percentage increases the probability by 26.3% that failure (reaching the MLB) will occur in the next period. However, since a 1 percentage increase in on-base percentage is a very large increase, it makes the most sense to change the units to ease interpretation. In order to do so, I had to generate a new variable which multiplied year_obp by 100. Now, the hazard ratio can be interpreted that for every.01 increase in batting average increases the hazard of reaching the Majors by.0023%. 28

29 In survival analysis, a number of graphs can be produced to visually demonstrate the survival and hazard functions. Figure 10, the Kaplan-Meier survival estimate, plots the portion of individuals surviving at a particular analysis time. In this sample, the maximum number of years to reach the Majors was 15 years, consequently the survival function tapers off at that point. It can be observed that as time passes, the proportion of people that survive to reach the endpoint of reaching the Majors decreases. Figure 11 demonstrates that given only overall draft pick, a player s chance of survival drops significantly after 4 years, which might suggest that the significance of draft pick in decision making lasts only the first few years after the player is drafted. In comparison, the baseline survivor function is less steep given only the player s batting average. This might suggest that a player s performance is typically considered in decisions throughout the player s entire tenure of playing. Lastly, Figure 13 shows the smoothed hazard function. From this graph, we can see that the hazard function increased from year 1 to year 8, after which it decreased. This suggests that a player s probability of reaching the Majors increased in earlier years, and then decreased as tenure continued. This model contained probable error as a result of 6,888 multiple records occurring at the same instant and 2,266 observations ending on or before the origin. The number of subjects that remained after taking into account this probable error was 2,090, and this issue was not resolved. 29

30 C. Logit Model The results from the Logit model regressions are presented in Table 5. In the first Logit regression (D1), a player s overall draft number, year average, and draft year were included to investigate these variables influence on the odds of a player making it (player_made_it was the binary dependent variable). In both regressions D1 and D3 a player s overall draft pick and year batting average were statistically significant. The logistic regression coefficients were the change in the log odds of the outcome given one unit increases in the predictor variables. Thus, for every one unit increase in overall, the log odds of making it to the Majors (versus not making it) decreased by.005. The odds ratio for overall listed in the D1-OR column is.9947, which is simply. From this odds ratio, we are able to see that for a one unit increase in draft number, the odds of making it to the Majors decrease by a factor of For every one unit increase in a player s batting average, the player s log odds of making it to the Majors (versus not making it) increased by Regression D3 used year_obp in place of batting average. Similarly, an increase in draft number decreased the log odds of making it (-.0052). For every one unit increase in on-base percentage, the log odds of making it to the Majors (versus not making it) increased by In all of the regressions (D1-D3), draft year was not significant even when separating it into different dummy variables for each draft year. 30

31 VI. Conclusions These results support my hypothesis that there is a sunk cost effect in the managerial decision making processes of the MLB. Descriptive graphs suggested this phenomenon prior to regression analysis. In every section of the analysis, overall draft pick was significant. After linear regression analysis, it was clear that draft number was a significant predictor of both games played and received at bats. Survival analysis results suggested that the further a player is drafted from, the lower his chances are making it to the MLB in the next period. Thus, the Cox model results supported the idea that a player will make it to the Majors quicker, if he is a low draft pick numerically. Lastly, results from the Logit model suggested that an increase in draft number decreased the odds that a player would make it to the Majors at all. Future research on this thesis topic should focus on the inclusion of a number of variables that would add to the depth of the analysis of the sunk cost effect in Major League Baseball. For example, the inclusion of a team s winning percentage (like in Staw & Hoang, 1995) could impact the playing time of a player. A player s performance could be a function of the overall performance of his team. Also, a player traded to a team with a high or low winning percentage could make it easier or more difficult for an incoming player to receive at bats. A variable that indicates if there are other players at the same position would be useful as well. These variables should be taken into account because they could change the significance of draft number on games played and at bats. It wasn t possible to add team winning percentage in the current study because some players played for multiple teams in a single season, typically in the Minors, so constructing a team record variable was not possible at this time. The winning percentage of the MLB organization team should ve been included (if collected) because it could impact players playing time in the organization s farm system (Minor League affiliates). With these extra 31