Chapter 25 Exercises

Section 25.1: The Economics of Soccer

Exercise 25.1 (Conceptual) Explain the dual objective problem faced by professional soccer clubs. How does this differ from the profit-maximization assumption in standard microeconomics? Provide two examples of decisions where sporting and financial objectives might conflict.

Exercise 25.2 (Data Analysis) Using publicly available revenue data from Deloitte's Football Money League or equivalent sources, calculate the Herfindahl-Hirschman Index (HHI) for revenue concentration in the English Premier League, La Liga, and the Bundesliga. Compare the competitive balance implications of each league's revenue distribution model.

$$HHI = \sum_{i=1}^{N} s_i^2$$

where $s_i$ is the revenue share of club $i$.

Exercise 25.3 (Short Answer) Describe three ways in which the Bosman ruling (1995) altered the economic dynamics of the player labor market. For each, explain whether the change primarily benefited players, clubs, or had mixed effects.

Exercise 25.4 (Critical Thinking) In what sense is the soccer transfer market "efficient"? Identify three systematic biases documented in the literature that suggest market inefficiency. For each bias, propose a data-driven strategy that a club might use to exploit it.

Section 25.2: Market Value Estimation

Exercise 25.5 (Mathematical) Given the hedonic pricing model:

$$\ln(V_i) = 2.5 + 0.45 \cdot \text{Age}_i - 0.009 \cdot \text{Age}_i^2 + 1.2 \cdot \text{Goals}_{90} + 0.8 \cdot \text{Assists}_{90} + 0.3 \cdot \text{Contract}$$

(a) Calculate the peak value age. (b) Estimate the market value of a 24-year-old player with 0.5 goals/90, 0.3 assists/90, and 3 years remaining on contract. (c) How does the value change if the player is 30 years old with identical performance statistics?

Exercise 25.6 (Programming) Using the dataset provided in code/example-01-market-value.py, implement a Random Forest model for market value estimation. Compare its performance (RMSE, MAE, R-squared) against the hedonic pricing model. Discuss the trade-off between interpretability and accuracy.

Exercise 25.7 (Programming) Extend the market value model to include interaction effects between age and performance. Specifically, test whether the marginal value of goals scored varies with player age. Use a gradient boosted tree model with SHAP values to visualize the interaction.

Exercise 25.8 (Data Analysis) Collect market value data for 50 players from Transfermarkt at two time points (e.g., start and end of a season). Build a model to predict value changes ($\Delta V$) based on performance metrics during the intervening period. Which performance metrics are most predictive of value appreciation?

Exercise 25.9 (Mathematical) Prove that the optimal age in the quadratic age-value model $\ln(V) = \beta_0 + \beta_1 \text{Age} + \beta_2 \text{Age}^2$ yields a maximum (not minimum) when $\beta_2 < 0$. Under what conditions would the model predict no peak (monotonically increasing or decreasing value)?

Section 25.3: Transfer Fee Modeling

Exercise 25.10 (Mathematical) For the contract depreciation function $g(c) = 1 - e^{-\lambda c}$, compute: (a) The fee as a proportion of market value when the contract has 1, 2, 3, and 5 years remaining, assuming $\lambda = 0.8$. (b) The marginal value of an additional year of contract at each of these points. (c) At what contract length does extending by one year add less than 5% of market value?

Exercise 25.11 (Programming) Using historical transfer data, fit a model that predicts transfer fees from market values and contract lengths. Test whether the exponential depreciation function $g(c) = 1 - e^{-\lambda c}$ fits better than a linear alternative $g(c) = \min(c/c_{\max}, 1)$.

Exercise 25.12 (Data Analysis) Analyze transfer fee inflation across the top five European leagues from 2010 to the present. Construct a transfer price index (analogous to the Consumer Price Index) using a basket of "representative" player profiles. Has inflation been uniform across leagues, or do some leagues show faster price growth?

Exercise 25.13 (Programming) Build a logistic regression model to predict transfer success, defined as the player maintaining or improving their performance metrics in the season following the transfer. Include features for: - League similarity (same league, same tier, different tier) - Age at transfer - Transfer fee relative to the selling league's average - International caps at time of transfer

Report the model's accuracy, precision, recall, and AUC-ROC.

Exercise 25.14 (Short Answer) Explain the concept of "anchoring" in transfer negotiations. How might a record-breaking transfer (such as Neymar's move to PSG in 2017) create an anchor effect that distorts subsequent transfer fees? Provide a numerical example.

Section 25.4: Wage Structure Analysis

Exercise 25.15 (Mathematical) Calculate the Gini coefficient for the following hypothetical squad wage distribution (weekly wages in thousands):

Interpret the result in the context of the inverted-U hypothesis discussed in Section 25.4.

Exercise 25.16 (Programming) Using the wage optimization framework from code/example-03-wage-optimization.py, determine the optimal wage allocation across positions (goalkeeper, defenders, midfielders, forwards) for a club with a total wage budget of EUR 80M per year. Assume the following position importance weights and diminishing returns parameters:

Exercise 25.17 (Data Analysis) Collect wage data for two squads competing in the same league (use estimates from credible sources if exact figures are unavailable). Compare their wage distributions using: (a) The Gini coefficient (b) The coefficient of variation (c) The ratio of the highest to median wage Discuss which measure best captures "unhealthy" wage dispersion.

Exercise 25.18 (Critical Thinking) A club's highest-paid player earns 4x the squad median wage. The player's agent is requesting a 30% raise. Using the concepts from Section 25.4, analyze the potential consequences for squad cohesion and wage structure. What alternative approaches could the club consider?

Section 25.5: ROI and Value Assessment

Exercise 25.19 (Mathematical) A club signs a player for EUR 40M on a 4-year contract at EUR 5M/year wages. The player generates estimated revenue of EUR 15M/year. After 3 years, the club sells the player for EUR 20M.

(a) Calculate the financial ROI. (b) Calculate the accounting profit/loss at the time of sale. (c) Compute the NPV of the contract using a 10% discount rate.

Exercise 25.20 (Programming) Implement a Monte Carlo simulation to estimate the distribution of ROI for a hypothetical player signing. Use the following parameter distributions: - Transfer fee: EUR 30M (fixed) - Annual wages: EUR 6M (fixed) - Annual revenue contribution: Normal(EUR 12M, EUR 3M) - Resale value after 3 years: Lognormal(mean=EUR 25M, std=EUR 10M) - Contract length: 4 years - Discount rate: 10%

Report the mean ROI, 5th percentile (downside risk), and 95th percentile (upside case).

Exercise 25.21 (Data Analysis) Select 10 high-profile transfers from the past 5 years. For each, estimate: (a) The total cost (fee + estimated wages over tenure) (b) The sporting contribution (using available performance data) (c) Whether the transfer was "value for money" relative to comparable deals

Present your findings in a structured table with clear methodology.

Exercise 25.22 (Mathematical) Derive the formula for the "break-even season" --- the number of seasons required for a player's cumulative revenue contribution to exceed their cumulative cost (transfer fee amortization plus wages). Express this as a function of the transfer fee $F$, annual wages $w$, annual revenue contribution $R$, and contract length $T$.

Section 25.6: Financial Fair Play Implications

Exercise 25.23 (Mathematical) A club has the following financial projections for the next three seasons:

(a) Calculate the break-even result for each year and the three-year aggregate. (b) Is the club compliant with the EUR 60M acceptable deviation? (c) The club wants to sign a player for EUR 50M on a 5-year contract at EUR 8M/year. Recalculate the FFP position including this signing.

Exercise 25.24 (Programming) Build a Financial Fair Play simulator that takes as inputs: current revenue, wage bill, amortization schedule, and planned transfers. The simulator should project the club's FFP position over a 3-year rolling window and flag any potential breaches. Test it with the scenario from Exercise 25.23.

Exercise 25.25 (Critical Thinking) Evaluate the following claim: "Financial Fair Play protects the established elite and prevents new entrants from competing." Present arguments for and against, supported by examples from European football. Consider both the original FFP regulations and the 2022 reforms.

Exercise 25.26 (Short Answer) Explain how player swap deals can be used to create artificial accounting profits under FFP. Illustrate with a numerical example involving two clubs exchanging players of similar ability at inflated valuations.

Section 25.7: Contract Optimization

Exercise 25.27 (Mathematical) A club is negotiating with a 23-year-old midfielder. Two contract options are on the table:

Option A: 4-year contract, EUR 4M/year base, EUR 1M appearance bonus, no release clause. Option B: 5-year contract, EUR 4.5M/year base, EUR 0.5M appearance bonus, EUR 80M release clause.

Assuming the player's market value will be approximately EUR 50M at the end of option A and EUR 45M at the end of option B, and using a 10% discount rate, calculate the NPV of each option from the club's perspective. Which option is preferable?

Exercise 25.28 (Programming) Implement a contract renewal timing model. Given a player's current market value trajectory (modeled as a function of age) and their contract expiry date, compute the optimal time to offer a renewal. The model should account for: - Declining bargaining leverage as the contract shortens - Uncertainty about future performance - The cost of the new contract (wage inflation from negotiation)

Exercise 25.29 (Data Analysis) Analyze the distribution of contract lengths across a league (use available data from a public source). Test whether contract length varies systematically by: (a) Player age (b) Player position (c) Transfer fee paid (d) Club revenue level

Report your findings with appropriate statistical tests.

Exercise 25.30 (Critical Thinking) Design an optimal bonus structure for a striker signed by a mid-table Premier League club. Specify: (a) Base salary and target total compensation (b) Individual performance bonuses (with specific targets) (c) Team achievement bonuses (d) Explain how your structure avoids moral hazard problems

Integrated Exercises

Exercise 25.31 (Comprehensive Project) Select a real club and conduct a complete economic analysis: (a) Estimate the market value of 5 first-team players using the hedonic pricing model (b) Calculate the squad's Gini coefficient for wages (c) Assess the club's FFP position based on available financial data (d) Identify one potential signing and evaluate the ROI using the NPV framework (e) Propose a contract structure for the potential signing

Exercise 25.32 (Programming) Build an integrated Transfer Decision Support System that: 1. Estimates a target player's market value 2. Predicts a likely transfer fee based on contract and market conditions 3. Projects the impact on the club's wage structure 4. Simulates the FFP implications over a 3-year window 5. Calculates the expected ROI with confidence intervals 6. Produces a single-page summary recommendation

Use the code examples from this chapter as building blocks.

Exercise 25.33 (Research Question) Using publicly available data, test the hypothesis that clubs with lower wage dispersion (Gini coefficients) achieve better league positions after controlling for total wage expenditure. Discuss the challenges of establishing causality in this analysis.

Exercise 25.34 (Ethical Analysis) Discuss the ethical implications of using advanced analytics to optimize player contracts. Consider: (a) The asymmetry of information between clubs with analytics departments and players/agents without comparable resources (b) The potential for analytics to reduce players to financial instruments (c) How transparency requirements might address these concerns (d) Whether regulatory bodies should mandate disclosure of valuation models used in negotiations