Corruption on the Court: The Causes and Social Consequences of Point-Shaving in NCAA Basketball

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1 Corruptio o the Court: The Causes ad Social Cosequeces of Poit-Shavig i NCAA Basketball by Yag-Mig Chag * ad Shae Saders ** October 8, 007 * Departmet of Ecoomics, Kasas State Uiversity, 39 Waters Hall, Mahatta, KS , Tel: (785) , Fax: (785) , ** Ecoomics Departmet, Aubur Uiversity Motgomery, 34C Clemet Hall, Motgomery, AL , Tel: (334) , Fax: (334) , correspodig author. We would like to thak Bhaveet Walia for commets ad suggestios. All errors are our ow.

2 Corruptio o the Court: The Causes ad Social Cosequeces of Poit-Shavig i NCAA Basketball Abstract This paper is cocered with the ecoomic icetives of crime amog agets withi a private orgaizatio. Specifically, we preset a cotest model of a college basketball game to idetify the wiers, losers, ad social welfare cosequeces of poit-shavig corruptio i me s NCAA basketball as a example of participatio i illicit activities. It is show that, uder reasoable coditios, such activities lower the level of social welfare derived from college basketball play by reducig aggregate efforts i a game ad distortig relative efforts across teams. We the examie the ecoomic icetives of a player to poit-shave ad discuss player-types that are at a relatively high risk of egagig i poit-shavig corruptio. Private ad public mechaisms to miimize corruptio are compared i terms of efficiecy, ad differetial hoesty premiums are discussed as a efficiet way for the NCAA to decrease or elimiate player corruptio. Key Words: Corruptio; Poit-shavig; Match-fixig; NCAA basketball; Team effort JEL Classificatios: K4, D0, D60

3 . Itroductio This paper is cocered with the ecoomic icetives of crime amog agets withi a private orgaizatio. With high-profile cases such as Ero ad WorldCom i recet years, corruptio amog private sector employees has gaied much media attetio as a potetially high-stakes crime whose victim is ofte the outside ivestor. I the preset study, we address the causes ad social welfare effects of poit-shavig corruptio i NCAA basketball as a example of corruptio amog agets withi a private orgaizatio. Further, we compare the efficiecy of private ad public mechaisms to miimize such corruptio. Poit-shavig is a subtle form of match-fixig that occurs regularly i major me s NCAA sportig evets. A poit-shavig scheme typically ivolves a sports gambler ad oe or more players of the favored team for a give corrupted match. I exchage for a bribe, a corrupted player agrees to adjust his match effort such that his team is ulikely to cover the poit spread or wi by at least the publicly expected margi. The gambler the wagers agaist such a evetuality with the advatage of (orchestrated) iside iformatio. Poit-shavig is a subtle form of corruptio i the sese that it does ot typically alter the outcome of a match but merely shaves a small umber of poits from the favored team s (true) expected margi of victory. I a poit-shavig scheme, a gambler geerally iduces a player s cooperatio by offerig him a outcome cotiget bribe (Wolfers, 006). Should the player s team wi by less tha the spread, he will receive a agreed upo amout of moey. However, the player will Wolfers (006) states that poit-shavig usually occurs betwee gamblers ad members of the favored team because players geerally compete with a great deal of itesity. Thus, it is much easier to adjust efforts dowward. Gamblers ca cotract with coaches to poit-shave as well. However, gambler-player poit-shavig is by far the most documeted form. As the preset value of a coach s expected lifetime basketball salary is much higher tha that of the typical college player, it may ot ofte be optimal for a coach to risk job dismissal by poit-shavig.

4 3 receive o moey i the evet that his team covers the spread. There have bee may cases of poit-shavig i NCAA Divisio I Me s Basketball. City College of New York (95), Bosto College (978, 979), Tulae (985), Arizoa State (994), ad Northwester (995) are all otable examples i which players were implicated, if ot covicted, o charges such as sports bribery ad racketeerig. However, illegality does ot ecessarily imply ecoomic iefficiecy. Leff (964) ad Hutigto (968) suggest that corruptio might improve ecoomic welfare by (i) allowig etrepreeurs to avoid excessive bureaucratic red tape ad (ii) causig govermet officials to work harder i order to maitai their job. However, subsequet studies o the subject, such as Shleifer ad Vishy (993), geerally fid that corruptio is costly to ecoomic welfare. Mauro (995) cocludes that corruptio lowers ecoomic growth by lowerig the level of ivestmet i a coutry. I this study, we first costruct a cotest model of a college basketball game to idetify the wiers, losers, ad overall social welfare cosequeces of poit-shavig activities i me s college basketball. The model shows that poit-shavig activities by members of the favored team both decrease aggregate effort ad distort relative effort across teams. As i Amegashie ad Kutsoati s (005) aalysis of boxig matches, a decrease i aggregate effort i a curret college basketball game is expected to shift iward the demad curve for subsequet NCAA Me s Basketball matches. Further, we argue that distortios of relative effort across teams away from the expectatio of fas will have a similar effect. Thus, it is show that, uder reasoable coditios, poit-shavig lowers the level of social welfare geerated by college basketball. This is a otable result, as there are o prior exploratios cocerig the welfare cosequeces of corruptio i sport. I a ovel study, Wolfers (006) provides empirical evidece for the presece ad extet

5 4 of poit-shavig i NCAA Divisio I Me s Basketball. The author estimates that six percet of matches featurig a strogly favored team (i.e., oe favored to wi by at least twelve poits) are corrupted by the presece of poit-shavig activities. Further, Wolfers provides a geeral explaatio for the presece of poit-shavig i college basketball: The key icetive drivig poit-shavig is that bet pay-offs are discotiuous at a poit- the spread- that is (or should be) essetially irrelevat to the players. That is to say, a player is essetially idifferet betwee his team wiig by seve poits or by eight poits. A spread bettor, o the other had, might care immesely about such a distictio. Thus, it is asymmetric icetives betwee gamblers ad players that create mutually gaiful opportuities for corruptio i college basketball. However, if all matches featurig a strogly favored team preset a opportuity for mutually gaiful cotractig betwee players ad gamblers, why is corruptio of such matches ot foud to be more pervasive? To aswer this questio, oe must ote that the player s decisio to accept a bribe is far from costless i expectatio. I our aalysis, we cosider a riskeutral, expected payoff maximizig collegiate basketball player (see Sectio 3). Much like Becker ad Stigler s (974) potetially malfeasat cop, each (amoral) player compares the preset value of hoest work to that of corruptio at the begiig of each decisio period i his collegiate playig career. Thus, we are able to adapt Becker ad Stigler s aalysis to the uique expected payoff structure of a appreticig workforce that is highly heterogeeous ad fid coditios uder which a idividual from this workforce will egage i corruptio. Wolfers explais that a shortfall of the ecoomic approach to studyig corruptio is its iability to idetify specific violators. While certaily true, our theoretical aalysis is able to idetify player types withi me s NCAA basketball that are more corruptible (i.e., more likely to egage i poit-shavig activities). Further, give that poit-shavig creates cosiderable

6 5 social costs ad little i the way of social beefit, we cosider a restructurig of NCAA player paymets to provide greater poit-shavig disicetives. The resultig policy suggestio adapts Becker ad Stigler s fidigs to the uique case of the appreticig basketball player ad leds support to a private mechaism by which to miimize poit-shavig corruptio. The remaider of the paper is orgaized as follows. I Sectio, we preset a cotest model of a sports game to idetify the wiers, losers, ad overall social welfare cosequeces of poit-shavig activities i me s college basketball. I Sectio 3, we aalyze the coditios uder which a player chooses to poit-shave ad discuss possible player-types that are more likely to violate the NCAA rules. We further preset policy implicatios of our aalysis for the NCAA to reduce or elimiate the icidece of poit-shavig corruptio. Sectio 4 cocludes.. Poit-Shavig: Wiers, Losers, ad Net Effect o Social Welfare. A Meritorious Cotest The Bechmark Case To uderstad the welfare cosequeces of poit-shavig, we cosider a meritorious (i.e., ucorrupted) basketball game. As i Szymaski (003, 004) ad Szymaski ad Késee (004), we use a cotest approach ad the Nash equilibrium solutio cocept to characterize the expected outcome of sports competitio. The likelihoods of victory ( g i ) for two teams ( i=,) i a match are give by the followig cotest success fuctios (CSFs): 3 3 Szymaski ad Késee (004) ad Szymaski (004) are amog the first to icorporate CSFs ito the ecoomic aalysis of sport. Skaperdas (996) presets axiomatic characterizatios of various forms of CSFs. The additive form CSF has bee widely employed to examie various issues, such as ret-seekig ad lobbyig, touramets ad labor cotracts, political coflict, war ad peace, ad siblig rivalry. See, e.g., Tullock (980), Lazear ad Rose (98), Hillma ad Riley (989), Hirshleifer (989), Grossma (004), Chag ad Weisma (005), Garfikel ad

7 6 g e = e + e e ad g = e + e, () where e i is effort by Team i. We assume that Team is strogly favored over Team i the match. Withi the model, this hierarchy is represeted i the suppositio that Team ejoys a lower uit cost of productive efforts o the basketball court, where a team s uit cost of effort is primarily a fuctio of player talet, coachig talet, recet travel demads, ad recet schedule demads. Let players o Team collectively maximize the followig expected payoff fuctio: π = g V e, () ad players o Team collectively maximize the followig expected payoff fuctio: π = g V σ e, (3) where σ ( > ) represets the uit cost of armig for Team ad V is the value of wiig the game (to a team of players). We assume that a regularly-playig, Divisio I college basketball player, who is ot directly remuerated based o fa iterest, cares primarily about exposure to talet evaluators (i.e., professioal scouts) ad competitive experiece whe participatig i a game. Thus, players o a team exert uits of effort to accumulate a sufficiet umber of wis to (i) eter the post-seaso ad (ii) be cosidered successful by professioal scouts. It is assumed, therefore, that each team values a wi i a cotest by the amout V for these reasos ad associates o ecoomic value with a loss. As stated above, V is ot a fuctio of fa iterest i subsequet college basketball games but is more a parameter based o the (exogeous) value of Skaperdas (000, 006), ad Chag, Potter, ad Saders (007a, 007b). Korad (007) presets a systematic review of applicatios i ecoomics ad other fields that use CSFs similar to those i equatio ().

8 7 opportuities i post-collegiate professioal basketball. To determie the optimal effort expediture by each team, we use () ad (3) to derive first-order coditios for the two teams: π e = V = 0 ; (4) e e + e ( ) π e = V σ = 0. e e + e ( ) (5) Solvig (4) ad (5) for the Nash equilibrium efforts by the two teams yields e = Vσ * ( + σ) ad e V * =. ( + σ) (6) I equilibrium, the expected probabilities of victory are: g * = σ + σ ad g * =. + σ (7) It follows from (6) ad (7) that Team, the favored team, exerts more effort tha its oppoet ad is thus more likely to wi the game. I what follows, we will use this meritorious (ucorrupted) game as a bechmark by which to evaluate the outcome of a corrupted cotest.. The Same Two Teams i a Corrupted Cotest I a corrupted cotest, or oe i which members of Team egage i poit-shavig activities, Team s uit cost of effort will rise. Assume each regular player o Team agrees to egage i poit-shavig. The uit cost of effort will rise because each additioal uit of effort icreases the likelihood that these players will ot receive the outcome cotiget poit-shavig bribe. Assume oly oe or two players o Team agree to egage i poit-shavig. The uit cost of effort for the team will still rise, as there are productivity spillovers i basketball productio (Kedall, 003). By puttig forth less effort (i.e., failig to set a scree for a drivig teammate, overlookig a pass to a teammate who has worked hard to become ope,

9 8 failig to double team a oppoet o defese oce a teammate has trapped him, or elicitig more playig time for a less taleted replacemet player), a corrupted player makes it more costly for his teammates to put forth productive efforts. This is true eve if his teammates are ot complicit i poit-shavig. I a corrupted game, the cotest success fuctio for each team is the same as equatio () i a meritorious game. However, Team s uit cost of effort rises i the presece of a poitshavig scheme. The expected payoff fuctios for the two teams become π = g V e ηe, (8) π = g V σ e, (9) where η ( > 0) represets the favored team s additioal uit cost of effort i the presece of poitshavig corruptio. follows: From each team s expected payoff fuctio, we calculate the first-order coditios as π e = V ( + η) = 0 ; (0) e e + e ( ) π e = V σ = 0. () e e + e ( ) Usig (0) ad (), we solve for the Nash equilibrium efforts ad expected probabilities of victory: e Vσ ** = ; ( + σ + η) e = V( + η) ( + σ + η) ** ; () g σ ** + η = g =. (3) + σ + η + σ + η ** ; Thus, the presece of poit-shavig activity reduces effort ad, to some extet, likelihood

10 9 of victory for Team. While icreasig likelihood of victory for Team, corruptio by Team has a ambiguous effect o Team s effort level..3 The Effects of Poit-Shavig Corruptio o Team Efforts ad Social Welfare Next, we calculate the effect of poit-shavig corruptio o the cotest s aggregate effort level. It is easy to verify from (6) ad () that * * * V E = e + e = ; (4a) + σ ** ** ** V E = e + e =. (4b) + σ + η We thus have * ** E > E. (4c) As i Amegashie ad Kutsoati (005), we take aggregate match effort as a partial determiat of match excitemet ad therefore of the demad fuctio. From iequality (4c), it is clear that poit-shavig corruptio reduces match excitemet ad, correspodigly, causes a leftward shift i the demad curve for subsequet NCAA basketball games. Further, before each match, we assume that some fas form a expectatio regardig relative efforts across competig teams. These educated fas value match itegrity, as it is ecessary i accurately assessig teams relative to oe aother. Thus, we take such fas as passively evaluatig the itegrity of a match as the differece betwee realized ad expected relative team efforts. For a corrupted match, the level of itegrity is measured accordig to e e ση d = = < 0. (5) e + η ** * ** * e As d approaches zero from the left, the level of match distortio (itegrity) falls (rises). From equatio (5), we fid that

11 0 d < 0. (6) η That is, match itegrity is decreasig i the level of poit-shavig activity that occurs. Thus, the demad fuctio for subsequet NCAA basketball games is decreasig i the level of poitshavig activity. This is true because poit-shavig causes aggregate efforts to declie ad relative team efforts to become distorted. With o offsettig effects o the demad side, it is clear that poit-shavig activity causes a iward shift i the demad curve for NCAA basketball. Throughout the welfare aalysis of this sectio, we assume that the supply curve for NCAA basketball is uchaged by the presece of poit-shavig. I A- of the Appedix Sectio, it is explaied that, uder reasoable coditios, ay welfare gais from a supply curve shift are offset by losses to outside bettors (i.e., bettors who are uaware as to the presece of poit-shavig). Thus, we cosider oly demad effects of poit-shavig i assessig welfare chages, while assumig that the supply curve is uaffected by the presece of corruptio. The followig propositio summarizes the welfare effect of poit-shavig corruptio give reasoable assumptios o the supply curve. Propositio : Poit-shavig corruptio creates a decrease i the overall ecoomic welfare geerated by NCAA basketball. Such activity reduces aggregate efforts ad distorts relative team efforts for a give corrupted match, ad these effects, i tur, lower demad for subsequet matches. Figure presets a graphical illustratio of this welfare declie. Defie p as the market price of tickets to a basketball game ad S as the market supply curve of the game. Let Q * = D( p, E ) deote market demad for a meritorious game i which the aggregate effort of the match is * E as show i (4). I this match, producer surplus ca be measured by the area of

12 (A+B+C) ad cosumer surplus by the area of (E+F). I the presece of poit-shavig corruptio, other thigs beig equal, the aggregate effort of the match decreases to ** E as show i (5). As a result, market demad shifts leftward to Q ** = D( p, E ). Producer surplus is give by the area of A ad cosumer surplus by the area of (E+B). The resultig chage i producer surplus is (B+C), ad the resultig chage i cosumer surplus is (B F). Cosequetly, the et chage i social welfare is equal to (C+F), which is uambiguously egative. This idicates that poit-shavig corruptio has a perverse effect o social welfare ad is therefore iefficiet. Figure about here 3. The Player s Corruptio Decisio This sectio examies the coditios uder which a player has a icetive to egage i corruptio ad also provides a brief discussio o corruptible player-types i NCAA basketball. Further, we adapt the Becker ad Stigler otio of a hoesty premium to a heterogeeous set of appreticig workers (i.e., college basketball players). I so doig, we preset a relatively lowcost route toward the elimiatio or miimizatio of poit-shavig corruptio i NCAA basketball. It is plausible to assume that each (amoral) player will choose hoest play or corrupt play, depedig o which course maximizes the preset value of his lifetime expected earigs. That is, if acceptig a bribe reaps more beefit to the player tha expected cost, the the player will choose corruptio. This maximizatio decisio icorporates a stream of potetial paymets ad pealties durig the player s college ad professioal basketball careers, which are itercoected. Usig backward iductio, we ca characterize the player s corruptio decisio

13 i as may as periods of college basketball play. 4 Note that costitutes the umber of appreticeship or developmetal periods a player edures, where a player ca appretice i college basketball, i a professioal developmetal league, or i a developmetal role withi a premier professioal league. Further, is chose by each player based o his professioal prospects. I the th period of his college basketball career, a represetative player will poitshave if the preset value of hoest play falls short of the preset expected value of corrupt play. That is, the player will choose to poit-shave i this period if c + βm < λ( a + βγ m ) + ( λ)( c + b + β m ), (7) + + t + where c represets the direct value to the player of a period of college basketball participatio, β is the discoutig rate, m + is the potetial value of the player s professioal career should he derive the full skill ad reputatioal beefits that college basketball ca offer him, λ represets the likelihood that player corruptio is appreheded at the begiig of the period, a is the direct value to the player of a period of professioal basketball i a developmetal league or i a professioal developmetal role, γ represets the rate at which a player s (post-developmetal) professioal career is discouted should he be dismissed for corruptio ad ot receive the full skill ad reputatioal beefits that college basketball ca offer him, ad b t represets the value of a player s bribe opportuity give the level of (bettig) iterest i his team. O the other had, a player behaves hoestly i period if ( ) ( )( ) c + βm λ a + βγ m + λ c + b + βm. (8) + + t + Iequalities (7) ad (8) above tell us that the (risk-eutral) player will choose corruptio if its expected payoff, as represeted by either iequality s right had side, eclipses that of hoest play. 4 A player might be dismissed for corrupt play before the th period.

14 3 The model takes a player s time as a basketball appretice as set at periods. I the evet of beig caught for poit-shavig, a player will be dismissed from NCAA competitio. This implies that a dismissed player who had plaed to cotiue improvig his skills i college (i.e., oe who has ot deemed himself ready ) must do so i a developmetal league or i a developmetal role with a premier league. As NCAA Me s Basketball provides a uique opportuity for players to expose their talet ad improve their skills, dismissal from NCAA competitio ca costitute a sigificat cost. For the college player, who has already revealed a preferece for a college basketball appreticeship, there are two mai potetial costs associated with dismissal from NCAA basketball. The first potetial cost is the differece betwee c ad a, where c icorporates the value of tuitio paymets ad other stipeds the player might receive, as well as factors such as team camaraderie, fa base, ad the team s mode of travel. Divisio I college teams ted to travel better tha mior league basketball teams, for istace. Whereas chartered plae is the orm for Divisio I college teams, leagues such as the ABA ad NBDL ofte rely upo logdistace bus rides. 5 The secod potetial cost is associated with the discout rate of a dismissed player s (post-developmetal) professioal career ( γ (0,)). Due to ecoomies of scale i scoutig, NCAA Me s Basketball is more scouted by the NBA, for istace, tha are mior professioal basketball leagues such as the Natioal Basketball Developmetal League (NBDL) ad America Basketball Associatio (ABA). 6 That is, a give player receives more exteral 5 For a partial descriptio of player travel i the ABA, see Shirley (007, pp ). 6 I the first roud of the 007 NBA Draft, every U.S. player came directly from a NCAA Divisio I team. Overall 5 of the 30 first roud picks etered the NBA from a Divisio I team.

15 4 exposure i college basketball due to the fact that it is such a major talet pipelie. Scouts are more likely to atted a college game to see Player X i additio to five other prospects tha to atted a mior league game to see oly Player X. The margial cost of scoutig Player X is much lower i the former case. Further, teams i the NCAA provide kowledgeable coachig staffs with a vested iterest i player progress. Player progress is largely importat i the NCAA due to heavy restrictios upo player mobility. For istace, a team caot simply trade away a uderachievig player i the NCAA. I order to ejoy his potetial post-appreticeship earigs, the, a player must receive adequate exposure ad basketball traiig. These factors combie to make college basketball attractive to a represetative player as a ivestmet i his (postdevelopmetal) professioal career. The player weighs these expected costs agaist the magitude of his bribe opportuities ( b t ), the latter of which is iflueced by the stregth of the player s team. A atioal power will geerate more iterest, ad thus more bettig iterest, tha will a mediocre Divisio I team. Thus, we expect a player from a atioal power to have more lucrative bribe opportuities. This stads to reaso, as isider bettig becomes more lucrative the less ifluece iside bets have upo the bettig odds (or upo the poit spread i this case). We take all regular players withi a particular team or team type as havig idetically valued bribe opportuities. As stated by Wolfers (006), it is relatively easy for ay player to reduce his level of effort. Further, give spillovers i team basketball productio (Kedall, 003), such a willful adjustmet is difficult to detect (i.e., teammates also play worse). That is to say, ay regular player ca reder the etire team less effective without the act beig completely obvious. Eve the fifth starter ca ifluece a star teammate s effectiveess by turig over the ball, foulig, failig to double team a trapped oppoet o defese, failig to make a key pass, or fumblig the receptio of a key pass. To a

16 5 far greater degree tha i baseball, a basketball team must be ruig o all cyliders to be effective. Thus, we take each regular player o a basketball team as havig the same basic techology for team sabotage ad thus the same bribe opportuities. From the previous iequalities, the critical level of pay for a college player (i.e., the miimum amout to iduce hoest play) i the th period is equal to λ c% = a+ bt β( γ) m+ (9) λ Followig a backward iductive solutio path, we fid the critical level of compesatio for a player i period ( ) as follows c~ ~ ( a + βa + β γ m ) + ( λ)( c~ + b + βc~ β m ) + βc + β m+ = λ + t + +. (0) Should the player cheat i period ( ) ad ot be caught, his expected payoff i period is c ~ regardless of his actios i the latter period. This is due to the fact that his th period earigs are set such that he fids o advatage (i.e., o expected payoff greater tha c ~ ) by egagig i corruptio. Thus, the critical pay level of compesatio i period ( ) is Similarly, c~ ( λ)( β) ( γ) m + = a + bt β γ λ. () c~ ( λ)( β) ( γ) m + 3 = a + bt β γ c~ k λ ( λ)( β) ( γ) m + k+ k = a k + bt β γ λ for (,,3,..., ( ) ) () k (3) From equatios (9) to (3), we preset the followig propositio.

17 6 Propositio : A player is more likely to violate NCAA poit-shavig rules, ceteris paribus, the more attractive are his professioal appreticeship opportuities ( a i ), the more bettig iterest his team geerates ( b t ), the lower is the probability of apprehesio (λ ), ad the lower is the value of his post-appreticeship professioal basketball opportuities ( m + ). The critical level of pay is icreasig i the player s opportuity cost while appreticig (i.e. appreticig istead i a developmetal league or i a developmetal role withi a premier league). For istace, if the NBDL bega to pay more to players, the represetative college player would become more likely to egage i poit-shavig. This is true because the pealty of beig deied NCAA participatio would become less severe. Further, the critical level of pay to iduce hoest play is icreasig i the value of the college player s bribe opportuities ( b t ). As discussed previously, this value is determied by the team type o which a regular player competes. As a player s team geerates more bettig iterest, he is expected to receive more lucrative bribe opportuities. Thus, if the team is strog ad excitig eough to geerate a great deal of (bettig) iterest, b t might be quite substatial. O the other had, if the team is so bad as ever to be a strog favorite, the value could be equal to zero. Hece, as a give player s team geerates more iterest, ceteris paribus, he becomes more likely to egage i corruptio. The last term i equatio (3) represets the preset value of foregoe salary from the player s (post-developmetal) professioal career i the evet that he is caught poit-shavig. It is this term that separates the appreticig basketball player from Becker ad Stigler s law eforcer. Whereas law eforcemet was a ed professio i itself, college basketball is both a ed (i the sese that oe is directly compesated) ad a meas (i the sese that the player is ivestig i a skill that commads potetially large professioal earigs after the

18 7 appreticeship). Thus, a college basketball player is less likely to egage i corruptio so as ot to jeopardize his professioal prospects. This disicetive effect becomes stroger as a college player approaches his th period. It is importat to ote that the value m + varies greatly amog regular collegiate players. This is true eve amog regular players o a give college team or team type. Lookig across professioal leagues, salary compesatio for professioal basketball players is quite o-liear with respect to skill level, meaig that small drop-offs i skill ca mea a disproportioately smaller paycheck. I a 007 article etitled Almost-NBA Players Take Home Paltry Salaries, Tom Goldma writes, With a average aual salary of more tha $5 millio, NBA players are the highest-paid athletes i professioal sports. But for the may skilled professioals who have't quite made it ito the NBA, the fiacial gulf is huge Salaries i the developmet league (NBDL) rage from $,000 to $4,000 a seaso, paid i part by moey from the NBA. Based o the heterogeeity of a player s expected post-developmetal payoff, the, we expect cosiderable heterogeeity i the ature of corruptio decisios across the set of NCAA players. 3. Corruptible Player Types We ca ow determie which player-types are at a relatively high risk of egagig i corruptio accordig to the model. Give that compesatio, c, is similar across NCAA players, the model would describe a corruptible player as oe o a atioally strog team who, while playig regularly, does ot expect to ear a large professioal payday after his appreticeship. We might thik of a player who, while a key cotributor o a quality team, expects to fall somewhat short of the NBA level after his appreticeship. For istace, some effective college players do ot fall withi ay of the arrowly specified roles of a NBA team. A premier college player might be too short ad weak to play power forward i the NBA ad, at

19 8 the same time, ot sufficietly quick to play small forward i the NBA. 3. Applyig Becker ad Stigler s Notio of Hoesty Premium to a Heterogeeous Workforce We complete the aalysis by calculatig the preset value of salaries (at the oset of a college career) ecessary to keep the college player hoest throughout his college career. Usig equatios (9) to (3), the critical preset value of future salaries i decisio period oe is 7 PV c~ c~ c~... c~ = + β + β β ( λ) ( ) i β ai bt β γ m+. (4) i= λ = + Equatio (4) above states that the preset value of salaries ecessary to keep the collegiate basketball player hoest is equal to (i) the preset value of payoffs i a professioal appreticeship plus (ii) the preset value of payoffs from poit-shavig opportuities mius (iii) the preset value of post-developmetal professioal earigs lost i the evet that the player is caught for corruptio. This preset value formula ca be used to cosider a ati-corruptio policy for college basketball. Such a policy would require each eterig NCAA player to bod ito the orgaizatio by the amout of the secod ad third terms. Durig each period of hoest play, the player would receive a premium equal to the iterest icome geerated by the bod. Fially, the player would be retured the pricipal of the bod i the evet that he leaves college basketball with o evidece of poit-shavig ivolvemet. Give the NCAA s cocers, such a pay structure has the advatage of itroducig player icetives toward hoest play while simultaeously maitaiig a level of player pay cosistet with amateur status - whatever this term or ideal is iteded to mea. 7 See Appedix A- for a detailed derivatio of the preset value formula.

20 9 This paymet structure mirrors that proposed by Becker ad Stigler to elimiate malfeasace amog law eforcers. However, oe should agai ote that college basketball players are a heterogeeous set of appreticig workers ad therefore differ from the set of career police officers. The presece of the fial term i equatio (4) sigifies the appreticig ature of the college basketball player workforce. Further, the observed level of variability (across player) i this term causes the poit-shavig decisio to be potetially quite distict across NCAA player-types. For such a pay structure to successfully elimiate or miimize poitshavig activities, there must be accurate predictio of each eterig college player s future prospects. Such iformatio could be gathered through the establishmet of a futures market for basketball players. For example, the compay Itrade creates predictio markets that ca be used to determie the market-projected likelihood or value of future evets, sportig ad otherwise. Aother legitimate cocer surroudig such a policy is the fiacial ability of may youg players to bod ito college basketball. However, if serious about a etrace fee policy, the NCAA could sactio a player loa program. There are may ways for the NCAA to reduce the icidece of poit-shavig corruptio. Oe obvious, albeit costly, policy is to beef up eforcemet by moitorig players ad largescale bettors more closely. O the other had, Wolfers (006) poits out that the illegalizatio of spread bettig would decrease the icidece of poit-shavig corruptio. However, gamblig regulatio is costly to eforce. Further, gamblers value the ability to bet o matches i a variety of ways, each featurig a distict level of risk. To some degree, the, gamblig regulatio would trasfer social losses more directly upo those who egage i spread-bettig. However, a policy that requires players to differetially bod ito college basketball would provide a low-cost route toward the elimiatio or miimizatio of poit-shavig i college basketball.

21 0 4. Cocludig Remarks I this paper, we have preseted a cotest model of a sports game to show that poitshavig corruptio results i a et social loss give reasoable assumptios about the supply of NCAA basketball games. This is a otable result, as there are o prior exploratios cocerig the welfare cosequeces of corruptio i sport. Further, we idetify coditios uder which a amoral player will choose to egage i poit-shavig ad also desigate player types that are relatively likely to egage i poit-shavig corruptio. Lastly, we adapt Becker ad Stigler s aalysis to the case of (highly-differetiated) appreticig basketball players. If the NCAA truly wishes to miimize or elimiate poit-shavig corruptio without ivestig i additioal eforcemet resources, it might implemet a pay structure that provides premiums to ostesibly hoest players. Iterestigly, such a pay structure would ot compromise the NCAA s amateur pay scale provided that players bod ito NCAA basketball. As the problems faced by the NCAA are ot uique to a sports orgaizatio, the aalysis sheds light o how private sector corruptio might be viewed ad addressed i geeral. A limitatio ad hece possible extesio of the paper should be metioed. We assume that a player is risk-eutral i the sese that he maximizes expected payoff whe makig a corruptio decisio. A potetially iterestig extesio is to aalyze the case i which the player behaves risk aversely. 8 Next, we do ot examie issues related to the optimal eforcemet of laws such as sports bribery ad racketeerig. The efficiet allocatio of socially costly resources toward moitorig players ad bettors is a potetial issue for future research. 9 8 See the semial work of Ehrlich (973) that uses a state-preferece framework to aalyze a idividual s expectedutility-maximizig decisio o participatig i illegal activities. 9 For geeral studies o optimal eforcemet of laws, see Stigler (970) ad Polisky ad Shavell (00).

22 5. Appedices A-. Poit-shavig affects the supply of NCAA basketball games i three primary ways. First, paymets from bettors to players will allow NCAA teams to pay a lower wage to players. I this sese, poit-shavig shifts right the supply curve for NCAA basketball games. However, ay market surplus geerated by this shifted supply curve is merely a trasfer from outside bettors (i.e., those who do ot aticipate poit-shavig activity) to iside bettors, players, fas, ad the NCAA. As this shift creates o overall welfare gai, we abstract from it i our graphical welfare aalysis. Further, the presece of poit-shavig causes players to exert less aggregate effort toward what is take as the same aggregate prize (i.e., game experiece ad game exposure to professioal scouts). I this sese, players gai from poit-shavig. However, these gais are take as either egligible o a market scale or at least offset by expected costs, i the form of NCAA dismissal ad discouted professioal basketball earigs, bore by the corrupted player. 0 Give the origi of the first supply curve shift ad the offsettig ature of the latter two, we focus solely o the two demad curve effects i our welfare aalysis of Sectio. A-. To calculate the period- preset value of icome streams that discourages a player from participatig i poit-shavig corruptio, it is ecessary to make use of c% i derived i equatio (3). The term c% i measures the critical level of period-i compesatio such that the player fids o advatage by egagig i corruptio. It follows from (3) that 0 While we take these expected costs as sufficiet to overcome player gais from a reductio i aggregate effort, the cost of puishmet is obviously ot always sufficiet to overcome the value of the poit-shavig bribe itself.

23 ( λ)( β) ( γ) c% = a+ bt β γ m+ for k = ; λ ( λ)( β) ( γ) c% = a+ bt β γ m+ for k = ; λ c~ ( λ)( β) ( γ) m + = a + bt β γ λ for k = ; λ c% = a+ bt β( γ) m+ for k =. λ Pluggig this stream of critical earigs { c%,..., c% } ito the preset value formula: PV = c% + βc% β c% + β c%, we have ( λ)( β) PV = a + b β γ ( γ) m λ t + ( λ)( β) + β a + b β γ ( γ) m λ +... t + ( λ)( β) + β a + b β γ( γ) m λ λ β a b β( γ) m. λ t t + Simplifyig the above expressio yields ( λ)( β) ( λ) i i i = β i+ β t + β t β γ ( γ) + i= i= λ λ i= PV a b b m ( λ) ( ) i β ai bt β γ m+, i= λ = + i i sice β ( β) + β = ( β) + β = ad ( ) = ( ) i= β β i= γ γ γ γ = γ. γ

24 3 6. Refereces Becker, G. S., ad Stigler, G. J. (974). Law Eforcemet, Malfeasace ad Compesatio of Eforcers. Joural of Legal Studies 3, -8. Chag, Y.-M., Potter, J., ad Saders, S. (007a). The Fate of Disputed Territories: A Ecoomic Aalysis. Defece ad Peace Ecoomics 8(), Chag, Y.-M., Potter, J., ad Saders, S. (007b). War ad Peace: Third-Party Itervetio i Coflict. Europea Joural of Political Ecoomy, forthcomig. Chag, Y.-M., ad Weisma, D. L. (005). Siblig Rivalry ad Strategic Paretal Trasfers. Souther Ecoomic Joural 7, Ehrlich, I., (973). Participatio i Illegitimate Activities: A Theoretical ad Empirical Ivestigatio. Joural of Political Ecoomy 8(3), Garfikel, M. R., ad Skaperdas, S. (000). Coflict Without Misperceptios or Icomplete Iformatio: How the Future Matters. Joural of Coflict Resolutio 44(6), Garfikel, M. R., ad Skaperdas, S. (006). Ecoomics of Coflict: A Overview. Mauscript, Departmet of Ecoomics, Uiversity of Califoria, Irvie. Goldma, T. (007). Almost-NBA Players Take Home Paltry Salaries. Retrieved from World Wide Web, September 9, 007, Grossma, H. I. (004). Peace ad War i Territorial Disputes. Departmet of Ecoomics, Brow Uiversity. Hillma, A. L., ad Riley, J. G. (989). Politically Cotestable Rets ad Trasfers. Ecoomics ad Politics, Hirshleifer, J. (989). Coflict ad Ret-Seekig Success Fuctios: Ratio vs. Differece Models of Relative Success. Public Choice 63, 0-. Hutigto, S. (968). Political Order i Chagig Societies. New Have, CT. Yale Uiversity Press. Kedall, T. (003). Spillovers, Complemetarities, ad Sortig i Labor Markets with a Applicatio to Professioal Sports. Souther Ecoomic Joural 70(), Korad, K. A. (007). Strategy i Cotests A Itroductio. Discussio Paper SP II 007-0, Wisseschaftszetrum, Berli.

25 4 Lazear, E. P., ad Rose, S. (98). Rak-order Touramets as Optimum Labor Cotracts. Joural of Political Ecoomy 89, Leff, N. (964). Ecoomic Developmet through Bureaucratic Corruptio. America Behavioral Scietist 8(3), 8-4. Mauro, P. (995). Corruptio ad Growth. Quarterly Joural of Ecoomics 0(3), Polisky, A. M., ad Shavell, S. (00). Corruptio ad Optimal Law Eforcemet. Joural of Public Ecoomics 8(), -4. Shirley, P. (007). Ca I Keep My Jersey? New York, NY. Radom House, Ic. Shleifer, A., ad Vishy, R. W. (993). Corruptio. Quarterly Joural of Ecoomics 08(3), Skaperdas, S. (996). Cotest Success Fuctios. Ecoomic Theory 7, Stigler, G. (970). The Optimum Eforcemet of Laws, Joural of Political Ecoomy, 78, Szymaski, S. (003). The Ecoomic Desig of Sportig Cotests. Joural of Ecoomic Literature 4, Szymaski, S. (004). Professioal Team Sports Are Oly a Game: The Walrasia Fixed- Supply Cojecture Model, Cotest-Nash Equilibrium, ad the Ivariace Priciple. Joural of Sports Ecoomics 5(), -6. Szymaski, S., ad Késee, S. (004). Competitive Balace, ad Gate Reveue i Team Sports. Joural of Idustrial Ecoomics 5(), Tullock, G. (980). Efficiet Ret Seekig i: Toward a Theory of Ret-seekig Society, edited by J. M. Buchaa, R. D. Tolliso ad G. Tullock. College Statio: Texas A&M Uiversity Press, 97-. Wolfers, J. (006). Poit Shavig: Corruptio i NCAA Basketball. America Ecoomic Associatio Papers ad Proceedigs 96(),

26 5 Figure. Welfare cosequece of poit-shavig corruptio p S F E p 0 p B C A Q=D (p, E * ) Q=D (p, E ** ) 0 Q Q 0 Q

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