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BASEBALL PLAYERS LABOR MARKETCoase Theorem.In the absence of significant transactions cost (few parties), any asset (talent) will be usedin its most efficient manner (highest marginal revenue product), regardless of ownership(reserve/transfer system or free agency.)Invariance proposition.“A market in which freedom is limited by a reserve rule distributes players about as a freemarket would.”“No matter who owns the right to sell the contract for the services of a baseball player, thedistribution of players among teams will remain the same.”Yankee Paradox.Self-defeating dominance of the league would be internalized by the large market club.Exploitation.If competitive balance is unaffected by ownership then the only purpose of the reserve ruleand other limitations of the labor market is to transfer rent from players to owners.Player development expense PDX.If teams cannot recover player development costs, then the player development system inthe minor leagues would cease to exist and the quality of play will be reduced. Players areexploited to the extent that they are paid less than their marginal revenue product afterplayer development expenses.Marginal revenue product.In a competitive market a player will be paid the value of his marginal revenue product.The marginal revenue product of talent is equal to the marginal product of talent multipliedby a team’s marginal revenue of winning. In a monopsony market a players salary willapproach his opportunity cost (reservation wage) at the limit.Strong form invariance.The distribution of playing talent will not be affected by any rules limiting labor marketmobility. These rules (player draft, roster limits, salary caps, revenue sharing) serve onlyto exploit playing talent by depressing wages.How to break up the Yankees.The only solution is to increase competition (reduce monopoly power) in the product marketwhere the large market club enjoys its revenue advantage. This solution uses the power ofcompetition in the product market rather than further limiting competition in the labormarket (by increasing monopsony power).

Competitive Balance before and after Free Agency in 1976MLB Player Salaries before and after Free Agency in 1976

Analysis of Titans‐Rams Trade 2016TITANS GETYearRound Overall l Value of Trade 162016L.A. RAMS GETRound Overall pick1141136177 Value1.0000.0940.0751.169Source: John Vrooman; subsequent picks discounted @ 10%The RGIII Trade 2012ST. LOUIS RAMS GETYearRound Overall 35160201412Total Value of TradeWASHINGTON REDSKINS GETYearRound Overall pick Value2012120.707 0.707Source: John Vrooman; subsequent picks discounted @ 10%CC

How to determine the marginal revenue product of talent MRP.S1 R1 - C1 S1 R1 [ m1 , w1( t1 , t2 )] - ct1MRP1 ( R1/ t1) ( R1/ w1)( w1/ t1) MR1 MP1 cS1 profit for team 1R1 team revenue which is a function of market size m1 and win percent w1w1 w ( t1) win percent which is a function of relative talent w1 t1 /(t1 t2)C1 ct1 payroll where c cost per unit of talentMRP1 MR1 MP1MRP is the product of the marginal revenue of a win MR and the marginal productof talent MP where both are assumed to have diminishing marginal returns.


MAJOR LEAGUE BASEBALL SELECTED PLAYER CONTRACTSJOSH HAMILTON: 5 years/ 125M (2013-17)Year Age TeamGSalary WAR M/WAR2007 26 Cincinnati Reds90 380,0002.5 0.152008 27 Texas Rangers156 396,8305.4 0.07 555,0000.6 0.932009 28 Texas Rangers892010 29 Texas Rangers133 3,250,0008.7 0.372011 30 Texas Rangers121 8,750,0003.7 2.363.9 3.532012 31 Texas Rangers148 13,750,0002013 32 Los Angeles Angels151 17,000,0001.5 11.332014 33 Los Angeles Angels89 17,000,0001.4 12.14 20,710,0002015 34 Los Angeles Angels39 25,400,0002016 35 Texas Rangers 26,410,000 28,410,000 28,410,000 26,410,0002017 36 Texas RangersMIKE TROUT: 6 years/ 144.5MYear Age Team201119 Los Angeles Angels201220 Los Angeles Angels201321 Los Angeles Angels201422 Los Angeles Angels201523 Los Angeles Angels201624 Los Angeles Angels201725 Los Angeles Angels201826 Los Angeles Angels201927 Los Angeles Angels202028 Los Angeles AngelsCARLOS BELTRAN: 3 years/ 45M (2014-16)Year Age TeamGSalary WAR M/WAR1998 21 Kansas City Royals14 170,0000.3 0.571999 22 Kansas City Royals156 200,0004.7 0.042000 23 Kansas City Royals98 350,0000.8 0.442001 24 Kansas City Royals155 425,0006.4 0.072002 25 Kansas City Royals162 3,500,0004.3 0.812003 26 Kansas City Royals141 6,000,0005.8 1.032004 27 Kansas City Royals69 9,000,0002.3 1.322004HOU:Trade904.5 1.322005 28 New York Mets151 11,571,4292.9 3.992006 29 New York Mets140 13,571,4288.2 1.662007 30 New York Mets144 13,571,4295.4 2.512008 31 New York Mets161 18,622,8096.9 2.702009 32 New York Mets81 19,243,6823.6 5.352010 33 New York Mets64 19,401,5690.7 27.722011 34 New York Mets98 19,325,4363.6 4.202011SFG:Trade441.0 4.202012 35 St. Louis C ardinals151 13,000,0003.9 3.332013 36 St. Louis C ardinals145 13,000,0002.4 5.422014 37 New York Yankees109 15,000,000 -0.2- 75.002015 38 New York Yankees 15,000,0000.8 18.752016 39 New York Yankees 15,000,000CC SABATHIA: 5 years/ 122M (2012-16), plus 2017 optionYear Age TeamGSalary WAR M/WAR200120 Cleveland Indians33 200,0002.9 0.07200221 C leveland Indians33 700,0003.2 0.22200322 C leveland Indians30 1,100,0003.7 0.30200423 C leveland Indians30 2,700,0003 0.90200524 C leveland Indians31 5,250,0001.8 2.92200625 C leveland Indians28 7,000,0004.6 1.52200726 C leveland Indians34 8,750,0006.3 1.39200827 C leveland Indians18 11,000,0001.9 1.622008MIL:Trade174.9 1.62200928 New York Yankees34 15,285,7146.2 2.47201029 New York Yankees34 24,285,7144.6 5.28201130 New York Yankees33 24,285,7147.5 3.24201231 New York Yankees28 23,000,0003.5 6.57201332 New York Yankees32 23,000,0000.3 76.67201433 New York Yankees8 23,000,000 -0.6- 38.33201534 New York Yankees 23,000,0000.3 76.67201635 New York Yankees 25,000,000201736 New York Yankees 25,000,000CLAYTON KERSHAW: 7 years/ 215M (2014-20)Year Age TeamGSalary WAR M/WAR2008 20 Los Angeles Dodgers22 390,0001.4 0.282009 21 Los Angeles Dodgers31 404,0004.7 0.092010 22 Los Angeles Dodgers32 440,0005.5 0.082011 23 Los Angeles Dodgers33 500,0006.5 0.082012 24 Los Angeles Dodgers33 8,000,0006.2 1.292013 25 Los Angeles Dodgers33 11,000,0007.8 1.412014 26 Los Angeles Dodgers27 22,000,0007.5 2.932015 27 Los Angeles Dodgers 30,000,0006.3 3.492016 28 Los Angeles Dodgers 32,000,0002017 29 Los Angeles Dodgers 33,000,0002018 30 Los Angeles Dodgers 33,000,000 Player option2019 31 Los Angeles Dodgers 32,000,0002020 32 Los Angeles Dodgers 33,000,000(2015-20)GSalary WAR40 414,0000.7139 480,000 10.8157 510,0008.9157 1,000,0007.9 5,250,0007.5 15,250,000 19,250,000 33,250,000 33,250,000 33,250,000BUSTER POSEY: 9 years/ 167MYear Age Team200922 San Francisco Giants201023 San Francisco Giants201124 San Francisco Giants201225 San Francisco Giants201326 San Francisco Giants201427 San Francisco Giants201528 San Francisco Giants201629 San Francisco Giants201730 San Francisco Giants201831 San Francisco Giants201932 San Francisco Giants202033 San Francisco Giants202134 San Francisco Giants202235 San Francisco Giants M/WAR 0.59 0.04 0.06 0.13 0.70(2013-21), plus 2022 team optionGSalary WAR M/WAR7 400,000 -0.1- 4.00108 400,0003.9 0.1045 575,0001.4 0.41148 615,0007.3 0.08148 8,000,0004.9 1.63147 12,500,0005.3 2.36 16,500,0005.4 3.06 20,000,000 21,400,000 21,400,000 21,400,000 21,400,000 21,400,000 22,000,000 Team option ( 3M)

Vrooman Salary Analysis: C.C. Sabathia 2008Base salaryCy Young RaiseTotal Salary 2008 9 million 2 million 11 million2008 SeasonCleveland ALMilwaukee NL2008 TotalW-L6-811-217-10ERA3.831.652.70Brewers Win %With SabathiaWithout SabathiaExtra Win %W-L90-7279-7020080.5560.5300.026IP122130253Split %48.6%51.4%100.0%Traded July 7 2008GamesSplit %8954.9%7345.1%162100.0%Milwaukee Estimated Attendance Multiple since 1998 (NL) 5 million * win%Brewers extra attendance from Sabathia: ATT 129,220 5 million * .026Brewers 2008 total revenue multiple per fan 60 (guesstimate): VTS 34%Brewers 2008 local revenue multiple per fan 40 (total revenue - VTS)Brewers 2008 Attendance 3,068,458Brewers Total Revenue Estimate 184.1 millionBrewers Local Revenue Estimate 122.7 millionDid the Brewers get their money's worth from CC Sabathia in 2008? YES and thensome2008 Extra local revenue for Brewers from Sabathia 5.17 million ( 40 * 129,220)2008 Salary split paid by Brewers: 5.0 million (45.1% * 11 million)2008 MRP Salary for Sabathia in Milwaukee 11.5 million ( 5.17/.451)Should the Brewers compete with the Yankees for CC? NO the game is too rich.Estimated total revenue multiple in New York is 120 per fan or 80 per fan net HTS.The 2009 MRP salary for Sabathia in New York City is 2X Milwaukee 23 million.Would revenue sharing make the Brewers more competitive with the Bombers? NOrevenue sharing would not change the relative revenue advantage of NYC.If the VTS was doubled to 68% then Sabathia's salary would be proportionately cut inhalf in both Milwaukee and NYC but his relative MRP of 2:1 would not change.In this case CC would still move to the Yankees except his salary would also be cut inhalf to 11.5 million in NYC compared to 5.75 million for the Brewers. All theYankees needed to offer was a salary just above the next highest offer.What would happen without revenue sharing? CC would then be paid his full MRP buthe would still go to the Bombers.If revenue sharing was eliminated then CC's MRP in NYC would jump to 31.2 millioncompared to 15.6 million in Milwaukee, but the MRP ratio would remain 2:1 in favorof NYC.In the land of the bottom line, CC Sabathia is a "gone pecan" regardless of revenuesharing and the only effect of more revenue sharing is to lower CC's relative salary forall clubs by the VTS (visiting-team share).Milwaukee Journal-Sentinel interview with John Vrooman, Vanderbilt University

Figure 1. Unconstrained Yankee Dominance


2008 31 New York Mets 161 18,622,809 6.9 2.70 2011 30 New York Yankees 33 24,285,714 7.5 3.24 2009 32 New York Mets 81 19,243,682 3.6 5.35 2012 31 New York Yankees 28 23,000,000 3.5 6.57 2010 33 New York Mets 64 19,401,569 0.7 27.72 2013 32 New York Yankees 32 23,000,000 0.3 76.67 2011 34 New York Mets 98 19,325,436 3.6 4.20 2014 .

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