risk aversion in mlb

8/3/2019 Risk Aversion in MLB

1/23

Risk Aversion in Major League Baseball

and its Impact on Winning Percentage

Devin Ensing

ECON 385

Professor Treber

December 4, 2011


2/23

Ensing 2

I. Introduction

Payroll disparity in baseball is a widely discussed topic, and many attribute the

disparity to differences in revenue between small and large market teams. The underlying

cause for concern is competitive balance, as studies have shown that teams with higher

payrolls typically enjoy greater success on the field. Another payroll related topic that has

received little attention is how payrolls are actually spent. Teams differ not only in how

much they spend on players but also how they distribute their payroll. For example, the

wildly successful 2001 Seattle Mariners spent only 48.7% of their payroll on starting

players while the 1998 New York Yankees enjoyed even greater on field success while

spending almost 63% of their payroll on starting players. Moreover, the 2004 Detroit

Tigers won only 72 games while spending over 79% of their payroll on starting players,

and the 2003 Baltimore Orioles won only 71 games while spending just over 26% on

starting players. Anecdotal evidence is inconclusive regarding whether there is a

relationship between payroll allocation and winning. While these examples suggest

payroll distribution may not influence team success, I believe that payroll distribution

will in fact influence a teams winning percentage. If such a relationship does exist, then

it is another issue to consider when addressing competitive balance.

I am interested in determining whether risk aversion on the part of owners can

explain variation in payroll distribution for Major League Baseball (MLB) teams, and as

an extension, whether variation in payroll distribution contributes to differences in

winning percentages. Although general managers complete all team transactions

themselves, I contend that owners have the final say and thus teams are constructed to fit

their preferences. Personal preferences and risk aversion are very difficult to measure,


3/23

Ensing 3

especially for owners in professional sports. However, risk averse individuals generally

prefer to be insured rather than uninsured. I speculate that money spent on non-starters in

MLB serves as insurance against poor performance or injury to starters. Consequently, I

argue that the higher the percentage of payroll spent on non-starters, the more risk averse

the owner.

To test this conjecture I assume owners in small revenue markets would be more

risk averse than owners in large revenue markets. This assumption begets the question of

whether large market teams spend a greater proportion of their payroll on starting players.

To address this question I estimate a simple model of payroll distribution. I then turn to

address the question of whether spending a higher percent on starting players impacts

winning percentage.

The remainder of this paper is constructed as follows. Section II provides an

overview and discussion of the relevant literature pertaining to the economics of Major

League Baseball and past estimates of risk aversion and winning percentage. Section III

lays out an economic model, the Von Neumann-Morgenstern expected utility model, to

illustrate how risk aversion could impact the payroll distribution in MLB. Section IV

develops empirical models to address the primary questions of interest and discusses the

data used to estimate the regression equation. Section V interprets the results from the

two regressions, first estimating risk aversion and then determining whether or not

payroll distribution has an impact on winning percentage. Finally, Section VI concludes

the paper by discussing implications of the regression results and wraps up by discussing

possible improvements in the study and extensions for future research.


4/23

Ensing 4

II. Literature Review

While there have been studies that focused on aspects of risk aversion in sports,

this paper deviates from all previous studies by estimating risk aversion from the owners

perspective. However, other papers have components that are valuable to study and learn

from. Bishop et al (1990) examined risk aversion and free agency in the NFL. In the

context of a median voter model, they use risk aversion to investigate player support of

free agency. They find that a players attitude towards downside risk may be an important

determinant of his willingness to support free agency. In addition, the restricted form of

free agency may well be preferred by a majority of players to unconditional free agency

(Bishop et al, 115).

Bill and Linda Woodland (1991) focused on a different group in a study on the

effects of risk aversion on sports wagering, notably the differences between betting on

point spread versus odds. The authors use calculus to determine maximum likelihoods of

risk aversion for bettors, finding that the amount of money wagered on point spread bets

was greater than that generated by odds betting. They also found that the current market

structure is a consequence of risk averse attitudes of bettors (Woodland, 638).

The closest a paper has come to dealing with the topic of risk aversion in baseball

from an owners perspective is Maxcys (2004) paper examining risk management for

long-term contracts. The author found that firms have an incentive to reallocate risk with

long-term labor contracts (Maxcy, 109). Although this paper is not concerned with how

contracts are structured, they do play a part in payroll allocated to certain players. Owners


5/23

Ensing 5

usually have to pay a premium to keep their star players, either from a higher average

annual value (AAV) contract or a longer contract.

While there have not been many papers dealing with risk aversion, there have

been papers trying to estimate winning percentage in baseball, which is the second topic

this paper is concerned with. The most notable paper that attempts to estimate winning

percentage is Scullys (1974) paper wherein he estimates players marginal revenue

products (MRPs). Scully uses a two-equation model, first estimating a teams win-loss

record from different team inputs, then estimating the team revenue function that relates

team winning percentage among other statistics to revenues. He finds that a team raising

their win-loss record by one point increases team revenue by $10,330 (Scully, 922).

MacDonald and Reynolds (1994) build off of Scullys paperand argue that a

players value is based on his contribution to team winning percentage, as team winning

percentage is significantly correlated with team revenue. Owners want players that most

increase the teams revenue, but the authors do not estimate whether owners prefer high-

risk/high-reward players, or players who are more consistent. The regressions show that

mean runs scored is arguably the best indicator of an offensive players production

(MacDonald and Reynolds, 447), and thus is the statistic that should be used in

determining whether or not a player should be acquired.

Hakes and Sauer (2006) wrote their paper as an Economic Evaluation of the

MoneyballHypothesis, based on the bookMoneyball by Michael Lewis. Before the

book was published, there were certain offensive statistics that were overvalued, such as

batting average and runs batted in, and some were undervalued, such as on-base


6/23

Ensing 6

percentage and slugging percentage. Hakes and Sauer show that the ability to get on base

was undervalued and conclude that the Oakland Athletics strategy for winning games in

the early 2000s was a successful exploitation of a profit opportunity (Hakes and Sauer,

183). The authors also argue that the market corrected itself within a year of thebooks

publication, showing that owners adjusted their personal preferences for risk aversion

based on the new information.

III. Model

I am interested in whether owners exhibit risk aversion in putting together a team

each season. I argue that this would be observable in decisions regarding the proportion

of payroll dedicated to backup players. A risk averse owner would sign more players with

less overall talent. A risk preferring owner would focus their resources on securing high

quality starters and dedicate a much smaller fraction of their payroll to backup players.

This concept can be illustrated using the Von Neumann-Morgenstern expected

utility model. Expected utility is defined as the expected value of utility over all possible

outcomes (Frank, 180). I want to determine the risk aversion of owners that leads to

their highest expected utility. Instead of using wealth to measure utility, I will be using

the number of wins for a team in a season to measure the total utility generated by the

team for the owner.

In the expected utility model, a risk averse owner will have a concave expected

utility function, as he experiences diminishing marginal utility of wins, as seen in Figure

1. This means that as the number of wins by the team increases, the owners marginal

benefit from each additional win decreases. We cannot conclusively determine the risk


7/23

Ensing 7

aversion of an owner simply based on wealth or revenue, but I believe wins are a better

measure to determine utility. I want to determine how risk averse they are, in the sense of

how much they are willing to gamble in order to increase their odds of winning more

games. Investing more into your starting players and less into your backup players can be

seen as more of a gamble, as injuries and subpar performances can derail a season easier

for teams with more invested in star players. Thus, a team with more invested in starting

players is much less risk averse than a team with payroll distributed more evenly.

While in most cases the expected utility function is concave, in some instances the

function can be convex or linear. If the owner is risk preferring, then the expected utility

function will be convex, as seen in Figure 2, where the owner will have increasing

marginal utility of wins. If the owner is risk neutral, then he has a constant marginal

utility of winning, which results in a linear expected utility function, as seen in Figure 3.

I hypothesize that owners of teams in small revenue markets will be much more

likely to be risk averse and thus have concave utility functions. As they have a lower

payroll, an injury to a player taking up a large chunk of the payroll would diminish the

number of wins, and thus the revenue that the team would generate. By the same

reasoning, I believe that large market teams will have convex utility functions, as they are

able to overcome injuries much easier by simply spending more money on replacement

players.

We can use this theoretical framework to show why a small market owner may

choose to field a team with a balanced payroll, while a large market owner may choose to

field a team with a less balanced payroll, with more money going to star players.


8/23

Ensing 8

Suppose an average team, with 81 wins per season, was considering signing two

star free agents. The owner estimated that if these players produced as expected the team

would win 90 games. However, if the stars underperformed or were injured, the team

would win only 70 games. The owner assumes there is a 50% chance either could

happen. If the owner did not sign the free agents and continued to have a more balanced

payroll the team is virtually guaranteed to again win 81 games.

Based on my assumption that an owner of a small market team would be risk

averse, I use an expected utility model of E(U) = Wins. If the owner were to continue to

have a more balanced payroll and get 81 wins, their expected utility would be exactly 9.

Would it be worth it to spend the extra money and sign the two free agents? The owners

expected utility from this gamble would be 8.93 ((0.5)*70 + (0.5)*90 = 8.93). Since

the owners expected utility from the gamble would be less than the expected utility

without signing the free agents, they would choose not to sign the star players and instead

continue to employ a more balanced payroll, which can be seen in Figure 4.

My assumption for large market teams is that they would be risk loving, so their

expected utility model would be E(U) = Wins2. Signing the two free agents would give

the team a 50% chance of winning 75 games and a 50% chance of winning 87 games.

Keeping a balanced payroll and winning 81 games would result in an expected utility of

6,561 (this number is only important to view in the context of other risk loving utilities).

The expected utility of the gamble of signing the two free agents would be 6,597

((0.5)*752 + (0.5)*872= 6,597). Since the owners expected utility from the gamble is

higher than keeping a balanced payroll, they would choose to sign the star players, which

can be seen in Figure 5. Their preference is for a top-heavy payroll, with stars making a


9/23

Ensing 9

lot of money. They can more easily afford to make mistakes or deal with injuries because

their revenue is greater, so they can simply sign a free agent or trade for a good player on

another team.

These examples show that there is a higher probability of a large market team

having higher risk preferences than a small market team. In the next section, I will run

regressions that attempt to quantify whether or not small market teams really are likely to

be more risk averse.

IV. Empirical Model and Data

This paper uses a panel data set covering each Major League Baseball team from

1998 through 2010. I chose this period because it captures all of the years after MLB

expanded to 30 teams with the inclusion of the Arizona Diamondbacks and the Tampa

Bay Devil Rays in 1998. For each team year, I collected payroll data for both teams and

individual players, offensive statistics for teams, and the market size each team belonged

to. The information was collected from several different baseball websites.1 Table 1

presents summary statistics on all of the variables used in my regressions.

To answer my questions about risk aversion and whether it matters, I ran two

different regressions involving risk aversion. The first regression is intended to test for

the presence of risk aversion in payroll decisions. This regression should show why

1Team salary data was collected fromhttp://content.usatoday.com/sportsdata/baseball/mlb/salaries/team/,www.cbssports.com/mlb/salaries,www.baseball-reference.com, andwww.mlbcontracts.blogspot.com/. Individual player salaries, used to calculate the percentage oftotal team payroll utilized for starting and backup payroll, was collected fromwww.baseball-reference.comandwww.baseball1.com. Market sizes were found using Forbes estimates forvalues of MLB teams atwww.forbes.com/lists/2011/33/baseball-valuations-11_land.html.
http://content.usatoday.com/sportsdata/baseball/mlb/salaries/team/http://content.usatoday.com/sportsdata/baseball/mlb/salaries/team/http://www.cbssports.com/mlb/salarieshttp://www.cbssports.com/mlb/salarieshttp://www.baseball-reference.com/http://www.baseball-reference.com/http://www.baseball-reference.com/http://www.mlbcontracts.blogspot.com/http://www.mlbcontracts.blogspot.com/http://www.baseball-reference.com/http://www.baseball-reference.com/http://www.baseball-reference.com/http://www.baseball-reference.com/http://www.baseball1.com/http://www.baseball1.com/http://www.baseball1.com/http://www.forbes.com/lists/2011/33/baseball-valuations-11_land.htmlhttp://www.forbes.com/lists/2011/33/baseball-valuations-11_land.htmlhttp://www.forbes.com/lists/2011/33/baseball-valuations-11_land.htmlhttp://www.forbes.com/lists/2011/33/baseball-valuations-11_land.htmlhttp://www.baseball1.com/http://www.baseball-reference.com/http://www.baseball-reference.com/http://www.mlbcontracts.blogspot.com/http://www.baseball-reference.com/http://www.cbssports.com/mlb/salarieshttp://content.usatoday.com/sportsdata/baseball/mlb/salaries/team/


10/23

Ensing 10

certain teams have a preference for spending a smaller proportion of their payroll on

starters. The equation for the first regression model is as follows:

PctStartingPayroll = 0 + 1*League + 2*LgMarket + 3*SmMarket + 4*Lag1WinPct

In this regression, I am including an indicator variable for the league that the team

is in, as well as the market indicators. The league indicator variable is used to control for

the difference in offensive environments due to the designated hitter rule. The DH is used

in the American League, but not the National League, which leads to more runs scored in

the AL. This could lead to different preferences on spending money, as owners in the AL

need to spend more money on an extra starting hitter. This means the league indicator

variable, using a 1 for AL teams and a 0 for NL teams, should be positively correlated

with risk aversion. The market indicator variables will control for the difference in total

payrolls caused by the difference in revenue potentials from market size. There will be

two different market indicator variables, one for large market teams (such as the New

York Yankees and Boston Red Sox), and one for small market teams (such as the Tampa

Bay Rays and San Diego Padres).

For both the first and second regressions, I collected total team payroll for the

year, and manually calculated starting and backup payroll using individual player salaries

for the eight or nine starting position players (depending on the league) and the starting

pitcher on Opening Day. There is a wide range of starting payroll percentages, and I

would like to discuss why some teams have certain values. The minimum percent of

starting payroll was only 24.85% by the San Diego Padres in 2002. They had a payroll of

just over $41 million and spent only $10,295,000 on starting players. Two players


11/23

Ensing 11

accounted for about half of the bench payroll: Trevor Hoffman, one of the greatest

closers of all time ($6,600,000), and outfielder Ray Lankford, who was being paid over

$8 million but only started half of the teams games. The Padres only won 66 games, and

finished last in their division. The maximum percent of starting payroll was 82.14% by

the 1998 Chicago White Sox. Their total payroll was $38,335,000, of which $31,490,000

was spent on starting players. They were incredibly risk loving, as a large majority of

their payroll was spent on their nine starting hitters. Still, the White Sox won only 80

games in 1998, showing that such a strategy does not guarantee success.

The worst team over the period was the 2003 Detroit Tigers who won only 26.5

percent of their games. Interestingly, they dedicated a nearly identical percentage of total

payroll to starters (62.4 percent versus 62.9 percent) as the 1998 New York Yankees, the

team with the second best record in the data set. This seems to indicate that the risk

aversion factor might not be a good predictor of current winning percentage.

Unfortunately, while the team statistics are entirely accurate, salary information is

not. Some player salaries include earned bonuses while others do not, and some salaries

depend on the team that the player is on. Many times, a player is not being paid what he

is worth because he is either very young and in his first contract, or very old and getting

paid for past production. So team payroll is not a direct representation of team skill. The

only issue with payrolls is the few cases where team payroll did not match up to the sum

of player salaries that played for the team. There are explanations for this, such as player

bonuses being included or excluded, player trades, or teams paying a portion of salaries

of players on different teams (usually from the dumping of mediocre players on to

other teams, where the trading team agrees to cover a portion of the players salary in


12/23

Ensing 12

exchange for not having to play the player anymore). This affects the percentage of

starting payroll variable slightly, but I found in most cases team payroll matched up and

the difference is statistically negligible.

While I am interested in determining whether or not I can measure risk aversion, I

am also interested in whether this decision impacts team success. The second regression

uses risk aversion as a predictor variable, along with other team statistics, to try and

predict team-winning percentage. The coefficient on the risk aversion variable will tell us

whether spending more on your starting players should help you win or lose more games.

The equation for the second regression model is as follows:

WinPct = 0 + 1* PctStartingPayroll + 2*BattingAge + 3*RpG + 4*OPS+

The individual level statistics I collected for each team are used in this second

regression. They were the average age of their hitters, the number of players that had an

at-bat in a year, and team offensive statistics, such as runs per game, hits, home runs, and

on-base percentage. Like Scully, I collected these statistics to estimate winning

percentage. The average age of a hitter should be positively correlated with team winning

percentage as the older a hitter is, the more experience he should have. However, both the

1999 Florida Marlins, which had the youngest team in the sample, and the 2006 San

Francisco Giants, who fielded the oldest team, had losing records. The number of players

that batted for a team in a year should theoretically be negatively correlated with winning

percentage, as it usually means there are injuries or players from the minor leagues that

are getting at bats, signifying that the teams best players are not hitting as much or as


13/23

Ensing 13

well as they should. The team offensive statistics should all be positively correlated with

winning percentage, as the better a team hits, the more games they should win.

The one offensive statistic that I ended up using in my regression, on-base

percentage plus (OPS+), needs explanation. On-base plus slugging percentage (OPS) is

simply the sum of on-base percentage (OBP) and slugging percentage (SLG). OBP is

calculated as the number of times a player reaches base divided by the total number of

chances a player has of reaching base. SLG is calculated as the total number of bases

divided by at-bats. OPS+ normalizes OPS by adjusting for park effects and league effects

to get a better estimate of how each hitter (or team) performed. It is placed on an easy to

understand scale, where 100 OPS+ is exactly league average, and every point above or

below is one percentage point above or below league average hitting. OPS+ can be

compared across teams and years because it is adjusted, unlike normal batting statistics

such as average or OPS. The mean OPS+ for the sample was 96.6, meaning that the past

thirteen years were worse offensively when compared to the rest of baseball history. The

mean OPS+ for all time is 100, but since there has been an inflated hitting environment in

the past decade, a hitter in 2011 will be considered worse than a hitter in 1971 with the

same statistics.

Many of the offensive measures for teams that I collected could not be used.

Some cannot be used to compare across teams and years as the offensive environment has

changed, but the bigger problem is confounding variables. There are some variables that

cannot be included in regressions because it is impossible to increase one variable while

holding another constant. Home runs provide a good example of this. Unfortunately, it is

impossible to have an increase in home runs without an increase in OPS+, so I am not


14/23

Ensing 14

able to include both home runs and OPS+ in my regressions, as the coefficient on OPS+

would not accurately reflect the contribution of OPS+ to winning percentage. As a result,

OPS+ is the only team offensive statistic that is included in either regression.

The biggest issue I faced in attempting to measure risk aversion was determining

what constituted a starting lineup. Was it only position players? Or position players,

starting pitchers, and the closer? For simplicitys sake, as well as the belief that the

starting lineup of a baseball team will be the players that take the field during the first

inning of the first game of the season, I defined the starting roster to be the starting

position players in game one of the season and the starting pitcher. For American League

teams, this is the eight position players and the designated hitter, plus the starting pitcher,

for a total of ten players. For National League teams, this is only the eight position

players and the pitcher, for a total of nine players (there is no DH in the NL). The starting

lineup qualification was used to determine percent of payroll spent on starting and

reserve players. Baseball teams have a total of 25 players on the roster, so the other 15 or

16 players make up the payroll spent on reserve players.

V. Results and Analysis

The results from linear estimation of the first equation are provided in Table 2.

The only coefficient that is statistically significant is the league indicator variable, with a

p-value of 0.001. This shows that the only consistent variable that influences an owners

choice of risk aversion is the league in which the team plays in.

The league indicator coefficient suggests that if a team were to switch from the

National League to the American League, the percentage of payroll dedicated to starters


15/23

Ensing 15

would increase by 3.67 percentage points. This shows the differences in payroll related to

the number of starting players. The variable used to measure risk aversion depends

mostly on hitter salaries, so having an extra hitter in the lineup (as the DH) means that a

team will have to spend more money on hitters and will thus be less risk averse.

Although the coefficients on the market size variables were statistically

insignificant, they could still be economically significant. The coefficient on the large

market variable shows that an increase of one in the market size from medium to large

market size will lead to a 1.94 percentage point increase in percentage of payroll devoted

to starting players. The coefficient on the small market variable shows that an increase of

one in the market size from small to medium size will lead to 0.19 percentage point

decrease in percentage of payroll devoted to starting players. Small market teams are

expected to spend less on their starting players and more on their backups than large

market teams, which is reflected in the magnitude of the coefficients.

The last variable in the first regression was one-year lagged winning percentage.

My hypothesis is that the higher a teams winning percentage in the previous year, the

less risk averse the owner will be this year as they are more likely to go for broke, and

try to win it all the next year. The statistic is not significant in the regression, but the

coefficient suggests that a one percentage point increase in winning percentage last year

actually leads to a 5.79 percentage point decrease in percentage of payroll devoted to

starting players, suggesting a team that won more games the year before will be more risk

averse. This is in direct opposition to the hypothesis that I claimed before running the

regression. One potential reason for this is that teams spent above their normal capped


16/23

Ensing 16

payroll the year before and the owner wants to cut back on spending this season so they

do not lose money.

The results from running a linear estimation on the second equation can be found

in Table 3. All statistics in this regression were found to be very significant with p-values

of 0.000. An increase of one year in the average age of batters on a team leads to a 0.0117

percentage point increase in winning percentage. The older a team is, the more

experience it has, and the better it performs. Obviously, this is not true by the time

players are in their late 30s, but younger hitters will then replace them, so the cycle

continues. Also, a one percentage point increase in OPS+ leads to a 0.0033 percentage

point increase in winning percentage.

An increase of one run per game leads to a 0.0399 percentage point increase in

winning percentage. This is very significant. For example, a team with a .500 winning

percentage would then have a winning percentage of .540 if they scored one more run per

game, which is about 6.5 more games won per season, a large increase equivalent to an

average team becoming a contender for the playoffs. This backs up MacDonald and

Reynolds claim that runsscored is arguably the best indicator of a player or teams

offensive production.

Finally, a one percentage point increase in the percentage of player salaries

devoted to starting players leads to a 0.102 percentage point decreasein the teams

winning percentage. This regression shows that the more risk averse a team is (only to a

certain extent as they have to have some percentage of payroll devoted to starting

players), the more they will win.A team should spend more money on backup players


17/23

Ensing 17

and less on starting players. If a team were to decrease their spending on starting players

by one standard deviation, they would spend 10.20% more of their payroll on backup

players. This means a team would increase their winning percentage by 1.04 percentage

points, or a .500 team would now have a winning percentage of .5104. Over an entire

season, that is the equivalent of 1.68 more wins, which could easily be the difference

between making the playoffs and staying home. Had the 2011 Atlanta Braves increased

their win total by just 1.68, they would have made the playoffs and the St. Louis

Cardinals would not have even made the playoffs, let alone won the World Series.

VI. Conclusions

One difficulty that I ran into while completing this paper was differentiating risk

aversion of owners with different spending habits. As the definition of my starting lineup

consists of almost all position players, a team that wants to spend more money on

position players will be seen as less risk averse. Although, it is risk aversion in itself to

spend more money on hitting as pitchers have a higher probability of getting injured than

hitters. The real intention of the paper was to see how owners allocate their money,

whether to a few star players or spreading it out more to role players. While the definition

could be changed based on the researchers own beliefs, I believe that my definition of

risk aversion was appropriate for the task at hand.

Future research on this topic should use larger sample sizes to more accurately

measure how teams have been spending money. Perhaps spending habits have fluctuated

over time, and we are just now at the point where teams are valuing starting players

higher than before. I also did not attempt to evaluate the impact of outliers (such as the


18/23

Ensing 18

Yankees) on the data set, so a further study should determine whether some team payrolls

should be excluded. A final improvement would be to look at more team statistics,

including pitching statistics, to determine whether that would impact the risk aversion

coefficient and ultimately the impact on winning percentage.

While the conclusions stemming from my regression may not be groundbreaking

results, the idea behind this paper could be.Moneyball was a best-selling novel because it

showed how one small-market team could exploit inefficiencies to become one of the

best teams in baseball, regardless of payroll. The idea behind risk aversion could

theoretically do the same thing. As Fangraphs notes, you can make a case that teams are

currently being too risk-averse and that there is a possible inefficiency that could be

exploited.2 If an MLB team could tweak this model and use it to determine the optimal

amount and percentage of money they should spend constructing their roster, they could

be gaining an advantage over other teams. My regressions showed that a team would

benefit from spending a lesser percentage of their payroll on starting players and a greater

percentage on backups. While this does not mean they should have starting players with

lesser talent so that they do not have to pay them as much, it does mean that backups are

more important than their current valuation.

2Dave Cameron, Linear Dollars Per Win, Again.http://www.fangraphs.com/blogs/index.php/linear-dollars-per-win-again/


19/23

Ensing 19

Figures and Tables

Figure 1: risk averse owner

Figure 2: risk loving owner

Wins

Utility

W1 W2

U(W1)

U(W2)

U = U(W)

Wins

Utility

W1 W2

U(W1)

U(W2)

U = U(W)


20/23

Ensing 20

Figure 3: risk neutral owner

Figure 4: risk averse owner example

Wins

Utility

70 80 81 90

U = U(W)9.49

8.37

9.008.92

Wins

Utility

W2W1

U(W2)

U(W1)

U = U(W)


21/23

Ensing 21

Figure 5: risk loving owner example

Table 1: Descriptive Statistics

Variable Mean Std. Deviation Minimum Maximum

Total Payroll $70,699,056 $33,070,793 $9,202,000 $209,081,577

Starting Payroll $39,833,950 $21,264,617 $5,595,000 $142,574,714

Backup Payroll $30,865,107 $14,929,546 $3,607,000 $85,421,103

Pct of Starting Payroll 55.89% 10.20% 24.85% 82.14%

Winning Percentage 50.00% 7.28% 26.50% 71.60%

League Indicator 0.467 0.500 0 1

Large Market Indicator 0.333 0.472 0 1

Small Market Indicator 0.333 0.472 0 1

Batting Age 29.05 1.425 25.2 33.5Runs per Game 4.757 0.503 3.17 6.23

OPS+ 96.60 8.12 77 118

Wins

Utility

75 87

5,625

7,569

U = U(W)

81

6,597

6,561


22/23

Ensing 22

Table 2: Risk Aversion of Owners

N = 390, R2 = 0.0415

Variable Coefficient p-valueLeague Indicator .0367353

(.0109108)0.001

Large Market Indicator .0193987(.0132494)

0.144

Small Market Indicator -.0018552(.013552)

0.891

Lagged Win % -.0578703(.07701)

0.453

Standard Errors in parentheses

Table 3: Impact on Winning Percentage

N = 390, R2 = 0.4874

Variable Coefficient p-value

Pct of Starting Payroll -.1020363(.0264865)

0.000

Batting Age .0116631(.0019613)

0.000

Runs per Game .0399073

(.0083906)

0.000

OPS+ .0032768(.0005238)

0.000

Standard Errors in parentheses


23/23

Ensing 23

References

Bishop, J.A., Finch, J.H., and Formby, J.P. 1990. "Risk Aversion and Rent-SeekingRedistributions: Free Agency in the National Football League." Southern Economic

Journal 57(July): 114-124.

Cameron, Dave. "Linear Dollars Per Win, Again." Fangraphs. 4 Nov. 2011. Web. 5 Nov.2011. .

Frank, Robert H.Microeconomics and Behavior(7th ed). New York: McGraw-Hill,2008.

Hakes, Jahn K., and Sauer, Raymond D. "An Economic Evaluation of theMoneyballHypothesis."Journal of Economic Perspectives, Vol. 20 No. 3 (Summer 2006), pp. 173186.

MacDonald, Don N., and Reynolds, Morgan O. Are Baseball Players Paid theirMarginal Products?Managerial and Decision Economics, Vol. 15, No. 5 (SeptemberOctober 1994), pp. 443-457.

Maxcy, J. 2004. "Motivating Long-term Employment Contracts: Risk Management inMajor League Baseball."Managerial and Decision Economics 25(March): 109-120.

Scully, Gerald W. Pay and Performance in Major League Baseball. The AmericanEconomic Review, Vol. 64, No. 6 (December 1974), pp. 915-930.

Slowinski, Steve. "OPS and OPS+." Fangraphs. 16 Feb. 2010. Web. 7 Nov. 2011..

Woodland, B.M., and Woodland, L.M. 1991. "The Effects of Risk Aversion onWagering: Point Spread versus Odds."Journal of Political Economy 99(No. 3): 638-653.

risk aversion in mlb

Documents