1. MARGINAL REVENUE
PRODUCTS IN MAJOR LEAGUE
BASEBALL
An Analysisof the 2015 Season
Patrick Jennings
Pat.jennings77@gmail.com
Abstract
This paper sets out to discover the most overvalued and undervalued players in MLB over the
2015 season based on their Marginal Revenue Product. I did this by creatinga model for a
team’s winningpercentage as well as a model for how teams drive revenue. I derived my
variablesfromother models and altered some variables atmy discretion. In previous research,it
was discovered that players who played above average defense were consistently undervalued.
My main goal of this research was to determine if defensive metrics have become better valued
by front office personnel sincethat study. Other findings would come to fruition.
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Table of Contents
Introduction......................................................................................................................................................................................2
Past Models......................................................................................................................................................................................2
Scully..................................................................................................................................................................................2
Macdonald and Reynolds............................................................................................................................................3-4
Maurice...........................................................................................................................................................................4-5
Winning Percentage Model .......................................................................................................................................................5-6
Revenue Model…………………………………………………………………………………………………………………………………………………… 6-7
Marginal Revenue Product…………………………………………………………………………………………………………………………………. 7
Results……………………………………………………………………………………………………………………………………………………………… 8-13
Undervalued Position Players……………………………………………………………………………………………………………… 8-10
Undervalued Pitchers………………………………………………………………………………………………………………………….10-11
Overvalued Pitchers……………………………………………………………………………………………………………………………. 11
Overvalued Position Players………………………………………………………………………………………………………………. 12
Best Contracts……………………………………………………………………………………………………………………………………. 13
Conclusion………………………………………………………………………………………………………………………………………………………. 14
Regressions……………………………………………………………………………………………………………………………………………………. 15
Data………………………………………………………………………………………………………………………………………………………………. 16-28
Revenue Data………………………………………………………………………………………………………………………………….. 16-21
Catchers………………………………………………………………………………………………………………………………………….. 22
FirstBasemen………………………………………………………………………………………………………………………………….. 22
Second Basemen……………………………………………………………………………………………………………………………… 23
Third Basemen………………………………………………………………………………………………………………………………… 23
Shortstops………………………………………………………………………………………………………………………………………. 24
Outfielders………………………………………………………………………………………………………………………………………. 25-26
Pitchers……………………………………………………………………………………………………………………………………………. 27-28
Citations………………………………………………………………………………………………………………………………………………………… 29
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Introduction
Over recent times, advanced metrics in the game of baseball have been universally
accepted more and more frequently. While there are definitely still flaws in some statistical
measures, knowing the value of each measure and how to look at the big picture when
evaluating a player is important. 15 years ago there was no defensive metrics at all and
determining a players’ defensive ability was done with the eye test. Scouts’ opinions
determined if a player was a good defensive player or not. Since defensive metrics have been
introduced, they have slowly but surely become accepted by front offices, media, and fans.
This study sets out to investigate not only whether players are paid their marginal
revenue product (MRP), but if players with superb defensive metrics are starting to earn
paychecks closer to their MRP than 6 years ago. I have scoured different models that have
been published in the past on this same topic – the baseball marketplace. Through trial and
error regression analysis I checked multiple variables for their significance on Winning
Percentage and generating Revenue for MLB teams. I will go through some of the past models
and explain my process.
Baseball is a unique industry that has a multitude of specific success measures at
everyone’s disposal. When you couple that with the fact that all contracts are public, this
makes for interesting economic studies about the labor market. At the end of this study I hope
to find an answer to how much value teams are putting into defensive metrics as the years
have gone on, as well as discover any other trends the data might produce.
Past Models
Pay and Performance in Major League Baseball
Gerald Scully, 1974.
Back in the 1970’s, Gerald Scully presented his research which estimated players’ MRP
in MLB. This is considered to be the first account of attempting to determine such measures in
the sports industry. Scully’s method includes the following: estimate the relationship between
team performance and revenue, estimate the impact of individual performance on team
performance, and then use the estimates from the first two steps to produce marginal revenue
product estimates for individual players. This same core concept is consistent throughout the
rest of the models I studied, as well as my own.
Scully used the best measures of performance that were available to him at the time in
the mid 1970’s. He used statistics like slugging percentage for hitters and strike-out to walk
ratio for pitchers. These statistics at the time were more than acceptable and specifically,
strike-out to walk ratio is a much better measure than simple ERA (earned run average).
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Scully wrote that by his calculations many superstars in the game were getting paid far
less than their MRP (Scully). He determined that Hank Aaron was worth $520,800 to the Braves
in 1968 and Aaron never earned more than $250,000 in any single season in his entire career.
Scully’s results show that players were paid only 10-20% of their marginal revenue product in
data for the 1968-69 seasons (Scully). This notion that superstars are extremely underpaid has
not held true over time, and further studies would determine stars are being severely overpaid.
Are Baseball Players PaidTheir Marginal Revenue Products?
Don N. MacDonaldand Morgan O. Reynolds, 1994
This research examined if the new contractual systemof free agency and final-offer
arbitration brought salaries into line with marginal revenue products. Using public data for the
1986-87 seasons, Macdonald and Reynolds include all players who were on a major league
roster as of August 31, 1986 and August 31, 1987. First, they analyzed whether any economic
evidence of owner collusion existed during the 1986-87 seasons. Secondly, they use a
systematic analysis of final-offer arbitration in baseball – established three years before free
agency – and find it has a stronger independent effect on salaries than the much publicized free
agency (MacDonald and Reynolds).
They determined that players were paid close to 100% of their MRP as recent as the
1994 season. Macdonald and Reynolds present a model for winning percentage that accounts
for the following variables:
RUNS = total number of runs scored per team for the season
ERA = team’s earned run average per 9 inning game
CONT = dummy variable, 1 = team finished within five games of first place in the division, 0 =
otherwise
OUT = dummy variable 1 = team finished 20 or more games out of first place in the division, 0 =
otherwise
Their reasoning behind the dummy variables is that they believed teams would pull out
all the stops to win games down the stretch if in a playoff race. On the reverse, they believed
teams would rest superstars and bring up young minor leaguers to play late in the season when
they were completely out of the race (Macdonald and Reynolds).
Macdonald and Reynolds then present their model for team revenue. They present five
independent variables for determining a team’s revenue. These variables are:
WP = winning percentage
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POP = population
Y = personal income
LOSER = dummy variable for whether a team is above or below .500
TT = dummy variable for whether there is another team in the same metropolitan area
(ex. Mets and Yankees)
Below are both models from Macdonald and Reynolds written in regression form.
WP = 461.42 + .53RUNS – 86.37ERA + 22.42CONT – 20.02OUT
R2 = .86
REV = 7.56 + .027WP – 9.63POP + .75Y – 8.53LOSER -4.69TT
R2 = .75
The conclusions drawn from this research was that young players are generally paid
below their MRP and experienced players are paid in line with their MRP. Clearly younger
players are breaking in and receiving “entry level” pay while some may be better than many
experienced players in the league. The free agency market is the main reason for this as players
aren’t able to hit free agency and test their value on the open market until after six years of
MLB experience.
The Value of Major League Baseball Players
Chris Maurice, 2010
In an analysis done by Chris Maurice of Haverford College, he examines the previous
models and adjusts the variables. Completed in 2010, defensive statistics are relatively new to
this era and that is where the author of this model implements something new to the
Macdonald and Reynolds’ model.
In this model, ERA is changed to Fielding Independent Pitching (FIP). FIP is a statistic
that estimates a pitcher’s run prevention independent of the performance of their defense. FIP
is based on outcomes that do not involve defense: strikeouts, walks, hit by pitches, and home
runs allowed. FIP uses those statistics and approximates an ERA assuming average outcomes
on balls in play. FIP is generally a better representation of a pitcher’s performance than ERA
(fangraphs). FIP is calculated as follows. (The constant changes with the run environment)
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FIP = ((13XHR + 3(BB+HBP) – 2K)/IP) + FIP constant
Added to the Macdonald and Reynolds’ model is a defensive metric, Ultimate Zone
Rating (UZR). UZR is one of the most widely used, publicly available defensive statistics. UZR
puts a run value to defense, attempting to quantify how many runs a player saved or gave up
through their fielding ability (or lack thereof). There are a couple different components to UZR,
including:
● Outfield Arm Runs (ARM) – The amount of runs above average an outfielder saves with their
arm by preventing runners from advancing.
● Double-Play Runs (DPR) – The amount of runs above average an infielder is by turning
double-plays.
● Range Runs (RngR) –Do they get to more balls than average or not?
● Error Runs (ErrR) – Does the player commit more or fewer errors compared with a league-
average player at their position?
The other three variables, RUNS, CONT, and OUT, were all kept in his winning
percentage model. The main conclusion in his model was that above average defensive players
were consistently paid less than their MRP (Maurice).
Winning Percentage Model
For my winning percentage model I took pieces from Macdonald and Reynolds but left
out the dummy variables. Even though when implementing the CONT and OUT dummy
variables I found they were significant, I still amnot completely sold on the actual effects of
those variables. I think in today’s game there are so many young talented minor leaguers that
even if a team that is ‘OUT’ of the playoff race brings up young talent in order to evaluate them,
they might be better than the older talent they are replacing; therefore, giving the team a
better chance to win. I simply believe teams are out there to win every game when they take
the field, compete for future jobs and future personal contracts.
I decided to keep the defensive metric UZR in my model after deliberation over
changing it to DEF (defensive efficiency). DEF measures a player’s defensive value relative to
league average. League average is set to zero. The main difference between DEF and UZR is
that DEF includes a positional adjustment so that you can compare players over different
positions in one defensive statistic (Fangraphs). At first I wanted to use DEF, but UZR fits better
because you simply can’t put just anybody at first base, you can only put a first baseman. You
can’t fill a team with 9 third baseman and expect to be defensively efficient. Teams need
players who can play specific positions. UZR is able to isolate each position and compare them
separately so I decided that is the best defensive metric to use for this model.
I then decided to change the FIP variable to xFIP. xFIP is a statistic that measures
expected run prevention independent of the performance of their defense. xFIP differs from
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FIP in that it normalizes a pitcher’s homeruns allowed based on their fly ball rate rather than
simply using the raw number of home runs allowed (Fangraphs). This statistic basically adds
the measure of how many home runs a pitcher should have given up over the course of the
season. This attempts to take lucky (and unlucky) factors such as wind and fence distance out
of play. xFIP is a terrific way to get a sense of how well a pitcher has been performing. xFIP tells
us about a pitcher’s strikeout and walk rates, which are very important, and also inherently
provides us with information about their batted ball profiles because fly ball rate is built into
the model (Fangraphs).
Finally, I changed the classic ‘RUNS’ variable that was kept in Maurice’s model to
Weighted Runs Created (wRC). wRC is regarded as the ultimate measure of offensive
production. To understand wRC one must first understand the linear weights theory which
begins with Weighted On-Base Average (wOBA). wOBA is a rate statistic that attempts to credit
a hitter for the value of each offensive event rather than treating all hits or times on base
equally (Fangraphs). wOBA is on the same scale as On Base Percentage and is definitely a
better representation of offensive value than ordinary batting average, RBI’s or even OPS (On-
Base Plus Slugging). The weights of the events change slightly according to the run
environment but the general formula is as follows.
wOBA = .69BB + .72HBP + .89(1B) + 1.27(2B) + 1.62(3B) + 2.1(HR)/AB + (BB-iBB) + SF + HBP
wRC is then derived from a player’s wOBA and is calculated as follows.
wRC = (((wOBA-League wOBA)/wOBA Scale)+(League R/PA))*PA
League wOBA, wOBA Scale, and League Runs per Plate Appearance (R/PA) change each
year based on the run environment.
My winning percentage model consists of the 2010 through 2015 seasons and all three
variables are statistically significant. The model in regression form is as follows.
WP = 552.86 + .458*wRC + .498*UZR + (-93.144)*xFIP
R2 = .48
Revenue Model
The model I developed to predict a team’s revenue lacked a major factor that previous
models have implemented in some capacity. That factor is popularity of the team based on
media rights, television viewers, or teams that own their own station. This information would
have been ideal to implement but information was simply not available for all seasons from
2010 through 2015. Media is definitely a major revenue driver for teams but that factor was
not included in my model.
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I took many variables from the Macdonald and Reynolds revenue model. The variables
that I used from their model obviously included winning percentage (WP), but also population
of the metropolitan area as well as income per capita. They also had included a dummy
variable of whether a team was above .500 or not and whether there were two teams in the
same market. I attempted regressions with both of those variables and they were not
significant for the time period between 2010 and 2015. My population and income per capita
data came from the Bureau of Economic Analysis (BEA). The BEA only had data through 2013
so in order to calculate 2014 and 2015 I estimated population growth (or decline) and income
per capita change by the average growth or decline since 2010. This gave me a solid estimation
for the past two years.
Through trial and error regressions, the best model I came up with included taking
population (POP) and income per capita (IPC) from Macdonald and Reynolds and adding
average ticket price (TIX) as a final variable. I have read from other models that gate receipts
have been used as a variable for team revenue, which makes sense because it is a portion of
total revenue. I decided to take average ticket price seeing that it is a function of gate receipts
but is not as directly related to total revenue. My average ticket price data came from Team
Marketing Report who is the leading publisher of sports marketing information. They release
data each year on average prices of tickets, merchandise, parking, etc. for all four major sports
in the United States. All variables were statistically significant and my revenue model had an R2
of .66. My revenue model written is regression form is as follows.
REV = -10,377,133.13 + 125,806.56*WP + 4.65*POP + 3,502,298.96*TIX + 927.22*IPC
R2 = .66
Marginal Revenue Products
Based on the models I developed for winning percentage and team revenue I can then
derive the marginal revenue product of a position player and a pitcher based on their wRC,
UZR, and xFIP. We can now see how much a player affects their team’s winning percentage and
therefore how they affect the team’s revenue. The coefficients in the following formulas are
derived from the previous models.
MRPPosition Player = (.458 * 125,806.56 * wRCplayer) + (.498 * 125,806.56 * UZRplayer)
To find the MRP for pitchers, we must multiply the formula by the percentage of total
innings that particular player pitched for his team.
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MRPPitcher = (125,806.56 * (552.86 + -93.144*xFIPplayer)) *(IPplayer/IPteam)
Catchers
UZR is not calculated for catchers and Fangraphs evaluates catchers with the following
factors.
Stolen base prevention
Regular fielding
Blocking
Pitch framing
Game management
All of these measures are calculated in different ways and are aggregated into a DEF
(defensive efficiency metric). In order to evaluate the MRP of catchers in the league I had
to alter my winning percentage model for DEF instead of UZR. I used this model only for the
catchers. The model (similar to my other WP model) reads as follows.
WP = 535.34 + .472*wRC + .49*DEF + (-91.16)*xFIP
Results
UndervaluedPositionPlayers
The first thing we will examine are the overall most undervalued position players of
2015 to see if there are any trends. All players examined had to have played at least 900 innings
at that position.
At first glance we see two things. First off the notion that players do not get paid their
MRP prior to entering free agency seems to hold true. The only exception here is Paul
Goldschmidt, who has signed a 5-year deal worth $32M through 2018 with a club option for
Name Pos wRC UZR MRP $/2015 Difference
Manny Machado 3B 113 8.4 7,030,792$ 548,000$ 6,482,792$
A.J. Pollock OF 107 6.5 6,566,409$ 519,500$ 6,046,909$
Bryce Harper OF 151 -2.4 8,541,770$ 2,500,000$ 6,041,770$
Nolan Arenado 3B 106 5.3 6,433,686$ 512,500$ 5,921,186$
Kris Bryant 3B 103 4.8 6,229,679$ 471,448$ 5,758,231$
Paul Goldschmidt 1B 136 5.1 8,148,064$ 3,000,000$ 5,148,064$
Mookie Betts OF 94 0 5,410,969$ 514,500$ 4,896,469$
Kole Calhoun OF 79 13.8 5,411,851$ 537,500$ 4,874,351$
Kevin Kiermaier OF 59 30 5,275,234$ 513,800$ 4,761,434$
Matt Duffy 3B 78 10.6 5,153,862$ 509,000$ 4,644,862$
10. 9 | P a g e
2019 (Spotrac). Goldschmidt is an absolute superstar in the game today and this clearly shows
how great of a deal this was for the Arizona Diamondbacks. Next year, in his age 29 season,
Goldschmidt is set to make a modest $5.85M (Spotrac). The strategy of locking up young stars
prior to free agency to multi-year deals is seldom used by franchises because of the fact they
would need to pay slightly more for the arbitration years. But if teams know they have a
potential superstar on their hands, this strategy could have huge benefits in the future as the
Diamondbacks will be paying a very cheap price for a top talent in the game during his prime.
All other players on this list are still arbitration eligible.
Another finding from this top 10 list is the prevalence of superior defense. 8 out of the
10 most undervalued position players in the game are above average defensive players; with
some being superstar level defenders. The only exceptions are Bryce Harper, who is had the
best offensive season in baseball in 2015, and Mookie Betts who is an average defender
(probably because he is a natural second baseman playing centerfield). Other than those two
players, the average UZR for the remaining top 10 is 10.6! To put this into perspective here is a
chart from Fangraphs providing a general rule of thumb for interpreting UZR numbers.
Defensive Ability UZR
Gold Glove Caliber +15
Great +10
Above Average +5
Average 0
Below Average -5
Poor -10
Awful -15
Clearly at first look, it seems defense is still being underpaid. To test this further, let’s
look at the top 10 UZR leaders of 2015.
Again, we see the underpaid defensive trend. 9 of the top 10 UZR leaders of 2015 were not
paid their MRP, and the only one that was overpaid was barely overpaid.
Name Pos wRC UZR MRP $/2015 Difference
Kevin Kiermaier OF 59 30 5,275,234$ 513,800$ 4,761,434$
Jason Heyward OF 84 22.6 6,250,838$ 7,800,000$ (1,549,162)$
Andrelton Simmons SS 55 17.3 4,249,542$ 3,000,000$ 1,249,542$
Adeiny Hechavarria SS 50 15.8 3,867,775$ 1,925,000$ 1,942,775$
Kevin Pillar OF 69 15.2 4,923,902$ 512,000$ 4,411,902$
Ender Inciarte OF 68 14.5 4,822,495$ 513,000$ 4,309,495$
Billy Hamilton OF 29 14.5 2,577,519$ 545,000$ 2,032,519$
Lorenzo Cain OF 91 14.1 6,121,403$ 2,825,000$ 3,296,403$
Kole Calhoun OF 79 13.8 5,411,851$ 537,500$ 4,874,351$
Michael Taylor OF 42 12.4 3,194,315$ 478,122$ 2,716,193$
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To test this further I compiled the average MRP and 2015 salary for all above average
defensive players (UZR>5) and the average MRP and 2015 salary for all below average
defensive players (UZR<-5). The results are as follows.
Clearly there is a glaring difference. Defenders with UZR greater or equal to 5 were paid
an average of $780,311 below their MRP and below average defenders were overpaid by
almost $4.2M on average. In 2015, the below average defender was overpaid by an average of
$3,392,511 more than the above average defender. In 2009 Chris Maurice determined good
defensive players were consistently underpaid relative to their MRP. In 2015 it seems to be
similar to those results and the pay gap is pretty significant.
UndervaluedPitchers
The following table consists of the top 10 most underpaid starting pitchers according to
their MRP. All pitchers evaluated had pitched at least 160 innings in 2015.
Examining this chart, the main thing that stands out is the consistency with the position
players on the fact that players prior to free agency are always paid under their MRP. The
exceptions here are Corey Kluber, Chris Archer, and John Lackey. Kluber and Archer’s stories
are similar in the way that their teams’ took the strategy the Diamondbacks took on Paul
Goldschmidt. They locked up their stars prior to free agency at what seems like very ‘team-
friendly’ deals. Both players were in the first year of that deal in 2015 and both made a little
over $1M. Both players see incremental increases year after year. Kluber is set to make $4.7M
in 2016 and Archer is set to make a modest $2.9M (Spotrac). By locking up these two to long
Avg MRP Avg $/2015 Difference
Above Avg UZR 4,948,388$ 4,168,076$ 780,311$
Below Avg UZR 3,394,535$ 7,567,357$ (4,172,823)$
Name xFIP MRP $/2015 Difference
Dallas Keuchel 2.75 6,009,793$ 524,500$ 5,485,293$
Jacob deGrom 2.92 4,615,773$ 556,875$ 4,058,898$
Corey Kluber 3.05 5,241,184$ 1,200,000$ 4,041,184$
Gerrit Cole 3.16 4,542,669$ 531,000$ 4,011,669$
Chris Archer 3.01 5,001,489$ 1,166,666$ 3,834,823$
Matt Harvey 3.24 4,084,924$ 614,125$ 3,470,799$
Kyle Hendricks 3.25 3,876,838$ 510,000$ 3,366,838$
Carlos Martinez 3.28 3,808,413$ 520,000$ 3,288,413$
Sonny Gray 3.69 3,789,760$ 512,500$ 3,277,260$
John Lackey 3.77 3,778,135$ 507,500$ 3,270,635$
12. 11 | P a g e
term deals prior to entering the open market they are able to maximize the amount of years
the player can perform below, just at, or just above their respective MRPs.
The most interesting top 10 pitcher on the list is John Lackey. John Lackey was a 37-
year-old, proven veteran in 2015. He made over $15M in 2014 and pitched in 2015 for about
the league minimum! This was due to a clause in his previous contract that read he would
make only league minimum if he missed an ‘extended period of time’ due to injury. In 2012
Lackey had Tommy John Surgery and missed the entire year. In 2015, that clause kicked in and
he honored it by pitching for league minimum (Perry). As a result, the Cardinals received a top
10 undervalued starting pitcher at age 37.
OvervaluedPitchers
The following table consists of the top 10 overpaid pitchers relative to their MRP in
2015.
These results were quite interesting considering Clayton Kershaw led the league in xFIP
and was the most overpaid pitcher relative to his MRP. This goes to show the exorbitant
amount of money top pitchers in the game are offered and how even when at the top of the
league, they don’t produce as much revenue to the ball club as their paycheck might suggest.
However, in my opinion, I would rather be paying Kershaw $25M above his MRP than have the
contracts of CC Sabathia, Mark Buehrle, John Danks, or R.A. Dickey on my payroll. To me, these
four were the worst pitching contracts of 2015. In terms of production at least their respective
teams got something out the rest of the pitchers on this list. The average xFIP for the starting
pitchers analyzed was 3.76. The below average results of those four, coupled with their
declining age seems to be a nightmare for front offices assessing their payroll.
Name xFIP MRP $/2015 Difference
Clayton Kershaw 2.09 7,240,074$ 32,571,428$ (25,331,354)$
CC Sabathia 3.99 2,614,289$ 23,000,000$ (20,385,711)$
Felix Hernandez 3.33 4,198,896$ 24,050,000$ (19,851,104)$
Zack Greinke 3.22 4,892,443$ 23,000,000$ (18,107,557)$
Mark Buehrle 4.46 2,378,208$ 19,000,000$ (16,621,792)$
Jon Lester 3.06 4,727,662$ 20,000,000$ (15,272,338)$
John Danks 4.65 1,838,163$ 15,750,000$ (13,911,837)$
Jordan Zimmermann 3.82 3,477,722$ 16,500,000$ (13,022,278)$
Max Scherzer 2.88 5,697,004$ 17,317,857$ (11,620,853)$
R.A. Dickey 4.72 2,116,333$ 12,000,000$ (9,883,667)$
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OvervaluedPositionPlayers
Below is a chart of the top 10 overvalued position players in 2015.
There are really no surprises on this list. Every player on this list has signed enormous
free agent contracts and their teams should be noticing that these huge free agent deals rarely
work out – especially at the back end. The one player that stands out to me is Pablo Sandoval
since he just signed a fresh 5-year, $95M contract before the 2015 season to play third base for
the Boston Red Sox (Spotrac). Sandoval really cashed in on his clutch 2014 postseason and his
teams’ World Series win. Sandoval posted a career best 13.2 UZR in 2011 but since then, he has
been up and down in terms of his defense, right around average. He posted a -4.7 UZR in 2013
and a 3.5 UZR in 2014 (Fangraphs). The San Francisco Giants (Sandoval’s previous team) was
very adamant about him staying in shape. He is a larger guy for a third baseman and keeping
his weight down kept him agile at the hot corner. Reportedly one of the reasons he wanted to
leave the Giants and head to Bean town was because the Giants wanted Sandoval on a strict
diet and weigh-in plan and they included incentives in his contract for keeping up with their
goals. The Red Sox on the other hand had the exact opposite philosophy and told Sandoval he
could do what he wants as long as he’s ready to perform on the field (Berman). Sandoval
jumped ship to the Sox and clearly did not continue his San Francisco work-out program.
Reports at spring training had Sandoval in horrible shape and it clearly showed in 2015 as he
posted the worst UZR of his career, by far, of -16.9 (Fangraphs). He also posted the worst wRC
of his career at 47 which was a 37% decrease from his mark with the Giants in 2014. This may
be a long and burden filled contract for the Red Sox for the next four years.
Name Pos wRC UZR MRP $/2015 Difference
Ryan Howard 1B 54 -5 2,795,264$ 25,000,000$ (22,204,736)$
Robinson Cano 2B 88 -7.9 4,570,788$ 24,000,000$ (19,429,212)$
Joe Mauer 1B 74 0.7 4,303,542$ 23,000,000$ (18,696,458)$
Jacoby Ellsbury OF 49 -3.2 2,620,186$ 21,142,857$ (18,522,671)$
Pablo Sandoval 3B 47 -16.9 1,646,988$ 20,000,000$ (18,353,012)$
Mark Teixeira 1B 77 0.4 4,457,443$ 22,500,000$ (18,042,557)$
Matt Kemp OF 79 -17.2 3,470,230$ 21,000,000$ (17,529,770)$
Miguel Cabrera 1B 98 -0.1 5,634,960$ 22,000,000$ (16,365,040)$
Adrian Gonzalez 1B 93 3.6 5,578,884$ 21,000,000$ (15,421,116)$
Andre Ethier OF 69 1.3 4,053,304$ 18,000,000$ (13,946,696)$
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Best Contracts
We have seen a trend through this analysis that it benefits a team greatly when they are
able to lock up their young players before they blossom into superstars. This gives the team
years of the player playing around their MRP before they enter the free agent market and
inevitably get overpaid. The following chart consists of 3 position players and 3 pitchers whose
teams were able to lock up early and therefore will reap the benefits.
Corey Kluber, Chris Archer, and Paul Goldschmidt were mentioned before. The Houston
Astros were able to lock up Jose Altuve to a 4-year, $12.5M contract when he was only 23 in
2013. This contract also includes club options in 2018 and 2019 at a reasonable $6M and
$6.5M respectively (Spotrac). This is an extreme team-friendly deal that allows the Astros to
have a star on their payroll in the prime of his career at around his MRP.
The Royals had a similar strategy with shortstop Alcides Escobar. They locked him up to
a 4-year $10.5M contract in 2012 that will see him making a little over $5M in 2016 with a club
option of $6.5M in 2017 when Escobar will be 30 (Spotrac). Escobar’s defense has been
consistent throughout his career and if he can boost his offense minimally, he will be close to
his dollar value for the rest of this contract.
The Royals had the same strategy for young star Yordano Ventura and signed him to a 5-
year $24M deal in 2014. This puts him on pace to make $1M in 2016 and only $3.25M in 2017
(Spotrac). They might be overpaying him a little in 2018 and 2019 but not by much and by
getting the performance value of the first three years under Ventura’s MRP is worth the
contract.
The main conclusion of this strategy is that it seems to be performed by smaller market
teams. All of those six players listed above come from small market teams – The
Diamondbacks, The Astros, The Royals, The Indians, and The Rays. These teams are
incentivized more to make these ‘bets’ on their young talent since if they don’t, they most likely
won’t be able to afford them when they do blossominto superstars.
Name Pos wRC UZR MRP $/2015 Difference
Paul Goldschmidt 1B 136 5.1 8,148,064$ 3,000,000$ 5,148,064$
Jose Altuve 2B 96 3.2 5,726,521$ 2,525,000$ 3,201,521$
Alcides Escobar SS 52 7.1 3,437,996$ 3,100,000$ 337,996$
Name IP IP/Team xFIP MRP $/2015 Difference
Corey Kluber 222 1432.2 3.05 5,241,184$ 1,200,000$ 4,041,184$
Chris Archer 212 1453.1 3.01 5,001,489$ 1,166,666$ 3,834,823$
Yordano Ventura 163.1 1452 3.6 3,074,179$ 1,750,000$ 1,324,179$
15. 14 | P a g e
Conclusion
The labor market in Major League Baseball doesn’t support paying players their MRP ad
this has been clear for a long time. However, my study has shown that the value placed in
defense is still not as high as it should be. Players that are above average defenders are still
consistently underpaid, which was the same results as the study done by Chris Maurice in 2009.
On top of them being underpaid, there is also a significant pay gap between the good defenders
and the bad defenders. The progress in defensive statistics in the game today is apparent, but
the value teams are putting on these statistics doesn’t seem to be showing up in players’
contracts.
My study also concludes a similar result to past studies in that players are generally
underpaid prior to having six years of experience and entering free agency. The MLB system
takes advantage of younger players and they are not paid their MRP across the board. This is
the conclusion of every model I have gone through and sure enough, it holds up in my study as
well.
The strategy of locking up younger players is seen as a positive throughout my research.
The small market teams have shown their ability to identify star talent in the making, bypass
their arbitration years, and lock these players up long term to team-friendly contracts. By doing
so, these teams are able to reap these players’ prime years at or around their MRPs. After their
team-friendly deal expires, the player will usually enter the market and get overpaid by one of
the big market franchises. Referring back to the table of the top 10 overvalued position players,
the teams that employed those players consist of the Yankees, the Red Sox, the Dodgers, the
Phillies, the Tigers, the Twins, and the Mariners. While Minnesota and Seattle aren’t normally
considered “Big Markets” they aren’t necessarily small. Clearly all of the other teams are in the
largest markets in all of baseball which makes this strategy apparent.
All in all, no professional sports market is perfect in terms of paying players exactly how
much they produce on the field/court/ice. Yet, teams that can accurately predict and receive
more value on the field than what they actually pay for will always be at an advantage as they
will be able to allocate resources to other team needs.
16. 15 | P a g e
Regressions
Winning Percentage Model
Revenue Model
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.69209135
R Square 0.478990437
Adjusted R Square 0.470109593
Standard Error 49.3797804
Observations 180
ANOVA
df SS MS F Significance F
Regression 3 394540.9855 131513.6618 53.93523332 8.94859E-25
Residual 176 429151.8374 2438.362713
Total 179 823692.8229
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 552.8622965 64.06570843 8.629613409 3.55584E-15 426.4264179 679.2981752 426.4264179 679.2981752
UZR 0.497862811 0.124512878 3.9984845 9.36897E-05 0.252132365 0.743593257 0.252132365 0.743593257
wRC 0.457566541 0.050453499 9.069074496 2.33235E-16 0.357994826 0.557138256 0.357994826 0.557138256
xFIP -93.14371723 14.07899299 -6.615793989 4.28319E-10 -120.929094 -65.35834041 -120.929094 -65.35834041
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.813472146
R Square 0.661736932
Adjusted R Square 0.654005205
Standard Error 37209220.7
Observations 180
ANOVA
df SS MS F Significance F
Regression 4 4.73991E+17 1.18498E+17 85.58720561 3.80107E-40
Residual 175 2.42292E+17 1.38453E+15
Total 179 7.16283E+17
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept (10,377,131.13) 27783718.49 -0.373496842 0.709230761 -65211424.17 44457161.92 -65211424.17 44457161.92
WPS 125,803.56 41127.80256 3.058844722 0.002571397 44633.21814 206973.9055 44633.21814 206973.9055
POP 4.65 0.650883498 7.148732244 2.2829E-11 3.368400067 5.937583634 3.368400067 5.937583634
TIX 3,502,298.96 344372.4032 10.17009181 2.20724E-19 2822641.292 4181956.624 2822641.292 4181956.624
IPC 927.22 400.106494 2.317433091 0.021637715 137.5648665 1716.875192 137.5648665 1716.875192
25. 24 | P a g e
Shortstops
Name Pos wRC UZR MRP $/2015 Difference
Xander Bogaerts SS 87 1 5,070,657$ 543,000$ 4,527,657$
Didi Gregorius SS 60 7.4 3,917,294$ 553,900$ 3,363,394$
Marcus Semien SS 67 -10 3,230,425$ 510,000$ 2,720,425$
Freddy Galvis SS 54 0.6 3,146,009$ 513,500$ 2,632,509$
Nick Ahmed SS 38 11.3 2,895,165$ 508,500$ 2,386,665$
Jean Segura SS 45 0.4 2,615,411$ 534,000$ 2,081,411$
Adeiny Hechavarria SS 50 15.8 3,867,775$ 1,925,000$ 1,942,775$
Jose Iglesias SS 52 2.3 3,137,358$ 1,443,750$ 1,693,608$
Brandon Crawford SS 71 10.9 4,769,707$ 3,175,000$ 1,594,707$
Jordy Mercer SS 32 1.5 1,935,981$ 538,000$ 1,397,981$
Andrelton Simmons SS 55 17.3 4,249,542$ 3,000,000$ 1,249,542$
Alcides Escobar SS 52 7.1 3,437,996$ 3,100,000$ 337,996$
Starlin Castro SS 54 1 3,171,062$ 6,000,000$ (2,828,938)$
Asdrubal Cabrera SS 64 -6 3,308,267$ 7,500,000$ (4,191,733)$
Erick Aybar SS 55 -7.1 2,721,299$ 8,500,000$ (5,778,701)$
Alexei Ramirez SS 53 -6.4 2,650,015$ 10,000,000$ (7,349,985)$
Ian Desmond SS 62 -3.7 3,337,195$ 11,000,000$ (7,662,805)$
Jimmy Rollins SS 50 -6.2 2,489,851$ 11,000,000$ (8,510,149)$
J.J. Hardy SS 26 7.1 1,941,345$ 11,500,000$ (9,558,655)$
Troy Tulowitzki SS 69 3.9 4,216,150$ 14,459,016$ (10,242,866)$
Jhonny Peralta SS 77 -7.2 3,981,433$ 15,000,000$ (11,018,567)$
Elvis Andrus SS 63 -0.1 3,620,237$ 17,000,000$ (13,379,763)$
26. 25 | P a g e
Outfielders
Name Pos wRC UZR MRP $/2015 Difference
A.J. Pollock OF 107 6.5 6,566,409$ 519,500$ 6,046,909$
Bryce Harper OF 151 -2.4 8,541,770$ 2,500,000$ 6,041,770$
Mookie Betts OF 94 0 5,410,969$ 514,500$ 4,896,469$
Kole Calhoun OF 79 13.8 5,411,851$ 537,500$ 4,874,351$
Kevin Kiermaier OF 59 30 5,275,234$ 513,800$ 4,761,434$
Charlie Blackmon OF 94 -7.3 4,953,749$ 517,500$ 4,436,249$
Kevin Pillar OF 69 15.2 4,923,902$ 512,000$ 4,411,902$
Starling Marte OF 83 8.8 5,328,940$ 1,000,000$ 4,328,940$
Ender Inciarte OF 68 14.5 4,822,495$ 513,000$ 4,309,495$
David Peralta OF 86 -2.4 4,800,142$ 512,000$ 4,288,142$
Odubel Herrera OF 69 9.9 4,591,947$ 507,500$ 4,084,447$
Adam Eaton OF 96 -10.2 4,887,240$ 850,000$ 4,037,240$
Gregory Polanco OF 69 6.8 4,397,785$ 525,000$ 3,872,785$
Joc Pederson OF 76 -3.9 4,130,558$ 510,000$ 3,620,558$
J.D. Martinez OF 105 7.7 6,526,441$ 3,000,000$ 3,526,441$
Lorenzo Cain OF 91 14.1 6,121,403$ 2,825,000$ 3,296,403$
Christian Yelich OF 71 -3.7 3,855,267$ 570,000$ 3,285,267$
Eddie Rosario OF 54 7.4 3,571,913$ 424,303$ 3,147,610$
Billy Burns OF 64 -5.2 3,358,373$ 432,622$ 2,925,751$
Michael Taylor OF 42 12.4 3,194,315$ 478,122$ 2,716,193$
Avisail Garcia OF 59 -6.2 3,007,922$ 523,000$ 2,484,922$
Marcell Ozuna OF 51 -1.5 2,841,789$ 422,896$ 2,418,893$
Mike Trout OF 132 0.2 7,610,909$ 5,250,000$ 2,360,909$
Delino Deshields OF 57 -7.5 2,811,373$ 507,500$ 2,303,873$
Anthony Gose OF 56 -10.4 2,572,174$ 515,000$ 2,057,174$
Billy Hamilton OF 29 14.5 2,577,519$ 545,000$ 2,032,519$
Jake Marisnick OF 34 9.3 2,539,645$ 511,200$ 2,028,445$
27. 26 | P a g e
Outfielderscont.
Juan Legares OF 40 3.5 2,521,755$ 553,696$ 1,968,059$
Josh Reddick OF 77 -1.7 4,325,914$ 4,100,000$ 225,914$
Michael Brantley OF 93 -3.3 5,146,717$ 5,000,000$ 146,717$
Jason Heyward OF 84 22.6 6,250,838$ 7,800,000$ (1,549,162)$
Andrew McCutchen OF 114 -4.5 6,280,391$ 10,050,000$ (3,769,609)$
Cameron Maybin OF 60 -7.2 3,002,853$ 7,000,000$ (3,997,147)$
Austin Jackson OF 56 7.2 3,674,513$ 7,699,999$ (4,025,486)$
Colby Rasmus OF 65 0.5 3,772,944$ 8,000,000$ (4,227,056)$
Dexter Fowler OF 88 -1.7 4,959,112$ 9,500,000$ (4,540,888)$
Torii Hunter OF 60 0.3 3,472,600$ 10,500,000$ (7,027,400)$
Angel Pagan OF 47 -14.3 1,809,834$ 9,000,000$ (7,190,166)$
Alex Rios OF 35 4.5 2,296,571$ 9,500,000$ (7,203,429)$
Ryan Braun OF 88 -6 4,689,791$ 12,000,000$ (7,310,209)$
Nick Markakis OF 85 -3.7 4,661,156$ 12,500,000$ (7,838,844)$
Jose Bautista OF 115 -9.9 5,999,737$ 14,000,000$ (8,000,263)$
Jay Bruce OF 71 -4.2 3,823,950$ 12,000,000$ (8,176,050)$
Adam Jones OF 75 7.1 4,761,956$ 13,075,000$ (8,313,044)$
Shin-Soo Choo OF 101 -3.9 5,569,645$ 14,000,000$ (8,430,355)$
Melky Cabrera OF 73 -7.4 3,738,652$ 13,000,000$ (9,261,348)$
Brett Gardner OF 81 -2.7 4,493,535$ 14,000,000$ (9,506,465)$
Justin Upton OF 83 2 4,903,036$ 14,500,000$ (9,596,964)$
Curtis Granderson OF 100 5.9 6,125,884$ 16,000,000$ (9,874,116)$
Carlos Gonzalez OF 93 -1.7 5,246,930$ 16,050,000$ (10,803,070)$
Carlos Beltran OF 74 -4.5 3,977,851$ 15,000,000$ (11,022,149)$
Andre Ethier OF 69 1.3 4,053,304$ 18,000,000$ (13,946,696)$
Matt Kemp OF 79 -17.2 3,470,230$ 21,000,000$ (17,529,770)$
Jacoby Ellsbury OF 49 -3.2 2,620,186$ 21,142,857$ (18,522,671)$
28. 27 | P a g e
Pitchers
Name xFIP MRP $/2015 Difference
Dallas Keuchel 2.75 6,009,793$ 524,500$ 5,485,293$
Jacob deGrom 2.92 4,615,773$ 556,875$ 4,058,898$
Corey Kluber 3.05 5,241,184$ 1,200,000$ 4,041,184$
Gerrit Cole 3.16 4,542,669$ 531,000$ 4,011,669$
Chris Archer 3.01 5,001,489$ 1,166,666$ 3,834,823$
Matt Harvey 3.24 4,084,924$ 614,125$ 3,470,799$
Kyle Hendricks 3.25 3,876,838$ 510,000$ 3,366,838$
Carlos Martinez 3.28 3,808,413$ 520,000$ 3,288,413$
Sonny Gray 3.69 3,789,760$ 512,500$ 3,277,260$
John Lackey 3.77 3,778,135$ 507,500$ 3,270,635$
Danny Salazar 3.48 3,716,800$ 468,674$ 3,248,126$
Collin McHugh 3.91 3,347,005$ 516,300$ 2,830,705$
Shelby Miller 4.07 3,146,165$ 535,500$ 2,610,665$
Kyle Gibson 3.95 3,131,248$ 537,500$ 2,593,748$
Carlos Carrasco 2.66 4,909,723$ 2,337,500$ 2,572,223$
Jake Arrieta 2.61 6,107,590$ 3,630,000$ 2,477,590$
Michael Wacha 3.88 2,979,200$ 520,000$ 2,459,200$
Anthony DeSclafani 3.97 2,919,659$ 507,500$ 2,412,159$
Taijuan Walker 3.82 2,867,033$ 513,100$ 2,353,933$
Chris Heston 3.98 2,811,831$ 485,314$ 2,326,517$
Rubby de la Rosa 4.10 2,760,877$ 516,000$ 2,244,877$
Jimmy Nelson 4.06 2,712,374$ 511,500$ 2,200,874$
Erasmo Ramirez 3.88 2,703,585$ 522,800$ 2,180,785$
Jake Odorizzi 3.96 2,693,953$ 522,000$ 2,171,953$
Jeff Locke 3.94 2,639,557$ 531,000$ 2,108,557$
Julio Teheran 4.19 2,873,464$ 1,000,000$ 1,873,464$
Tom Koehler 4.58 2,082,680$ 555,000$ 1,527,680$
Yordano Ventura 3.60 3,074,179$ 1,750,000$ 1,324,179$
Jose Quintana 3.51 4,033,799$ 3,400,000$ 633,799$
Trevor Bauer 4.28 2,384,002$ 1,940,000$ 444,002$
Garrett Richards 3.80 3,598,490$ 3,200,000$ 398,490$
Chris Sale 2.60 5,603,671$ 6,015,000$ (411,329)$
Tyson Ross 3.15 4,442,486$ 5,250,000$ (807,514)$
Andrew Cashner 3.84 3,140,859$ 4,050,000$ (909,141)$
29. 28 | P a g e
Pitchers cont.
Hector Santiago 5.00 1,371,706$ 2,290,000$ (918,294)$
Wade Miley 4.08 2,900,919$ 4,000,000$ (1,099,081)$
Wei-Yin Chen 4.01 3,006,490$ 4,750,000$ (1,743,510)$
Colby Lewis 4.62 2,182,705$ 4,000,000$ (1,817,295)$
Madison Bumgarner 3.02 5,159,770$ 7,000,000$ (1,840,230)$
Chris Tillman 4.58 1,916,060$ 4,315,000$ (2,398,940)$
Marco Estrada 4.93 1,480,059$ 3,900,000$ (2,419,941)$
Mike Pelfrey 4.45 1,980,844$ 5,500,000$ (3,519,156)$
Aaron Harang 4.99 1,312,296$ 5,000,000$ (3,687,704)$
Alfredo Simon 4.78 1,742,585$ 5,500,000$ (3,757,415)$
Lance Lynn 3.90 2,852,470$ 7,000,000$ (4,147,530)$
Jon Niese 4.11 2,577,789$ 7,000,000$ (4,422,211)$
Edinson Volquez 4.26 2,705,783$ 7,500,000$ (4,794,217)$
A.J. Burnett 3.55 3,078,449$ 8,500,000$ (5,421,551)$
Jason Hammel 3.47 3,365,471$ 9,000,000$ (5,634,529)$
James Shields 3.70 3,676,301$ 10,000,000$ (6,323,699)$
Ian Kennedy 3.70 3,057,824$ 9,850,000$ (6,792,176)$
Jeff Samardzija 4.31 2,807,004$ 9,800,000$ (6,992,996)$
Yovani Gallardo 4.31 2,431,555$ 10,000,000$ (7,568,445)$
Francisco Liriano 3.16 4,066,562$ 11,666,666$ (7,600,104)$
Gio Gonzalez 3.59 3,357,544$ 11,100,000$ (7,742,456)$
Bartolo Colon 3.94 3,105,695$ 11,000,000$ (7,894,305)$
Brett Anderson 3.51 3,541,999$ 12,400,000$ (8,858,001)$
Rick Porcello 3.72 3,083,646$ 12,500,000$ (9,416,354)$
Ubaldo Jimenez 3.83 3,165,389$ 12,650,000$ (9,484,611)$
R.A. Dickey 4.72 2,116,333$ 12,000,000$ (9,883,667)$
Max Scherzer 2.88 5,697,004$ 17,317,857$ (11,620,853)$
Jordan Zimmermann 3.82 3,477,722$ 16,500,000$ (13,022,278)$
John Danks 4.65 1,838,163$ 15,750,000$ (13,911,837)$
Jon Lester 3.06 4,727,662$ 20,000,000$ (15,272,338)$
Mark Buehrle 4.46 2,378,208$ 19,000,000$ (16,621,792)$
Zack Greinke 3.22 4,892,443$ 23,000,000$ (18,107,557)$
Felix Hernandez 3.33 4,198,896$ 24,050,000$ (19,851,104)$
CC Sabathia 3.99 2,614,289$ 23,000,000$ (20,385,711)$
Clayton Kershaw 2.09 7,240,074$ 32,571,428$ (25,331,354)$
30. 29 | P a g e
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