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

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9 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 poit-shavig scheme. The expected payoff fuctios for the two teams become π = g V e ηe, (8) π = g V σ e, (9) where ( > 0) Poit-Shavig i NCAA Basketball / 77 η represets the favored team s additioal uit cost of effort i the presece of poit-shavig corruptio. From each team s expected payoff fuctio, we calculate the first-order coditios as follows: (0) () π e = V ( + η) = 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) ** ; (3) g σ ** + η = g =. + σ + η + σ + η ** ; Thus, the presece of poit-shavig activity reduces effort ad, to some extet, likelihood of victory for Team. While icreasig likelihood of victory for Team, corruptio by Team has a ambiguous effect o Team s effort level. DOI: 0.0/

10 78 / REVIEW OF LAW AND ECONOMICS 5:, THE EFFECTS OF POINT-SHAVING CORRUPTION ON TEAM EFFECTS AND 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 (4a) (4b) * * * V E = e + e = ; + σ V E = e + e = + σ + η ** ** **. We thus have (4c) * ** E > E. 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 (5) e e ση d = = < 0. e + η ** * ** * e As d approaches zero from the left, the level of match distortio (itegrity) falls (rises). From equatio (5), we fid that (6) d < 0. 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 poit-shavig activity. This is true because poit-shavig Review of Law & Ecoomics, 009 by bepress

16 84 / REVIEW OF LAW AND ECONOMICS 5:, 009 () Similarly, () (3) c~ ( λ)( β) ( γ) m = a + bt β γ + c~ λ ( λ)( β) β γ. ( γ) m + 3 = a + bt c~ k λ ( λ)( β) ( γ) m + k+ k = a k + bt λ for k (,,3,..., ( ) ) β γ From equatios (9) to (3), we preset the followig propositio. Propositio : A player is more likely to violate NCAA poit-shavig rules, ceteris paribus, the more attractive are his professioal appreticeship opportuities ( a ), the more bettig iterest his team geerates ( b i 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 might be quite substatial. O the other had, if t 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. Review of Law & Ecoomics, 009 by bepress

21 ( λ)( β) ( γ) c% = a + bt β γ m for k = ; + λ ( λ)( β) ( γ) c% = a+ λ bt β γ m for k = ; + ( λ)( β) c ~ = a + bt β γ λ λ c% = a+ bt β( γ) m for k =. + λ ( γ) m + for k = ; Pluggig this stream of critical earigs { c%,..., c% } ito the preset value formula: PV = c% + βc% β c% + β c%, we have Poit-Shavig i NCAA Basketball / 89 ( 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+ bt β( γ) m+. λ t + Simplifyig the above expressio yields ( λ)( β) ( λ) ( ) PV = β a + β b + β b β γ γ m sice i i i i t t + i= i= λ λ i= ( λ) ( ) i β ai bt β γ m, + i= λ = + DOI: 0.0/

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