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Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

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Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy. Dayton, OH 45435 [email protected] For presentation at the meetings of the Western Economic Association June 30, 2010 Portland, Oregon - PowerPoint PPT Presentation

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Page 1: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy
Page 2: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy
Page 3: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

UpsetsEvan Osborne

Wright State UniversityDepartment of Economics

3640 Col. Glenn Hwy.Dayton, OH 45435

[email protected] presentation at the meetings of the Western Economic Association

June 30, 2010Portland, Oregon

Abstract: The paper models the upset – a low-probability outcome of a team competition. It is assumed that the upset is an independent component of consumer preferences, whose marginal willingness to pay grows with time. The decision rule for a league on upset timing is a competitive balance problem, but is unlike standard models of competitive balance. Upset timing is likened to the optimal harvest time of a growing asset, and implications for competitive balance in this environment are derived.

Page 4: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

We like…

• Our team to win;• Sustained irresolution;• To watch the best talent;• To be part of a collective experience;• To consume concessions and parking;• The other team to lose;• The wildly improbable?

Page 5: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

The basic approach

• Assume that a sports league manages a portfolio of competition series, each one an asset.

• The question is the timing of asset liquidation, given that during the interim it produces income.

Page 6: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

The Hirshleifer/Samuelson tree model

• In continuous time T, tree produces g(T) in lumber income if it is harvested at T.

• Cost of waiting until T to harvest is cT.• And so the optimization problem is

Page 7: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

• The FOC is

Page 8: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

Interpretation

• Extend harvest time until discounted, diminishing marginal return to extending it equals discounted marginal cost of tending to the tree.

• The farmer thus harvests all trees at same date, although he will have a farm full of trees of varying ages.

Page 9: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

Upsets as an extension of the tree model - differences• An asset – a “tree” – is a competition series

between two teams i, j out of n. • Revenue can be earned before the asset is

harvested, from fans of better team.

Page 10: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

Model 1 – certainty, with harvest time as the decision variable.• i denotes favored team, j team not favored.• Rij(T) is the combined net revenue at time t from

markets i and j if team i defeats team j. Revenue from market j if j wins is the opportunity cost of i winning, and vice versa. Thus, Rij(T) > 0 > Rji(T).

• wij(T) is revenue in T from outside markets i, j if j defeats i. It is instantaneous, convex, and wij(0) = 0. It is willingness to pay for the upset for its own sake, as distinct from the willingness of fans in market j to pay for a victory against i.

• Each Rij(T) and wij(T) is assumed to be independent of the others.

Page 11: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

Example of an asset portfolio: 4-team leagueR12(T) R13(T) R14(T)

R23(T) R24(T)

R34(T)

Page 12: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

• For each market pair the objective is to

Page 13: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

• The FOC is

Page 14: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

• Interpretation: extend harvest time until marginal revenue from extending continuity (Rij(T)) plus the marginal increase in the upset revenue when it is deferred (wij‘(T)) equals the marginal cost – discounted income from the upset (rwij(T)).

Page 15: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

• Implication: victories by small-market teams against big ones have independent value (contrary to conventional competitive-balance models), but only if they are aged properly.

Page 16: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy
Page 17: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

Model 2 - uncertainty• Instead of optimal harvest, model optimal

distribution of talent, which determines probability of upset.

• Sij = Si – Sj is the talent difference between i, j.• F(T; Sij) is a cdf indicating probability that upset

never occurs by time T.• Specifications: F’T > 0, F’’T = f’T < 0, F’S > 0.• w is now wij(T, Sij); w’T > 0, w’’T > 0, w’S > 0.• R is as before; fans in i,j care only about winning,

not talent per se.

Page 18: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

• Optimization problem is now

Page 19: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

Implications, model 2• If Rij(T) > Rkj(T), the talent differential, and hence expected

time to upset, should be greater for i against j than k against j.

• Standard competitive-balance models with only market based demand for success are special cases. If there is no demand for upsets, w = 0, and optimal talent distribution is driven by market WTP, as usual. If there is no difference among markets, Rij = o for all i, j, and then it is Quirk and Fort (1992) 50-percent model.

• But in this model competitive balance based purely on these considerations, which ignores w, equilibrium competitive balance is too high, once again because of gains to aging.

Page 20: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

Where does this model belong?• Existing models of demand: • (1) Demand as standard microeconomic good, with

quantity dependent on price, and demand on available complements and substitutes.

• (2) Demand for success• (3) Demand for suspense• (4) Demand for quality performance• But what fans like to see is an area that could be expanded

further – this is a model about quality, but of the game experience rather than the players; of uncertainty, but the utility of the improbable rather than suspense; of success, but of some other generally ignored team.

Page 21: Upsets Evan Osborne Wright State University Department of Economics 3640 Col. Glenn Hwy

Things still to be worked through

• Why do we like upsets so much? An adornment model of utility?

• Deriving an explicit equilibrium out of the talent-allocation model.