Chapter 39 Exercises: The Sports Betting Industry

Instructions: Complete all exercises in the parts assigned by your instructor. Show all work for calculation problems. For programming challenges, include comments explaining your logic and provide sample output. For analysis and research problems, cite your sources where applicable.

Part A: Conceptual Understanding

Each problem is worth 5 points. Answer in complete sentences unless otherwise directed.

Exercise A.1 --- The Vigorish and Market Percentage

Explain the concept of vigorish (vig) from the sportsbook's perspective. Address (a) how the vig is embedded in the odds offered to bettors, (b) why the implied probabilities from a two-outcome market typically sum to more than 100%, (c) how the overround varies by bet type (straight bets vs. parlays vs. same-game parlays), and (d) why a sportsbook can be profitable even when its odds do not perfectly reflect true probabilities.

Exercise A.2 --- B2C, B2B, and White-Label Models

Compare and contrast the three primary business models in the sports betting industry: Business-to-Consumer (B2C), Business-to-Business (B2B), and White-Label. For each model, describe (a) the primary revenue mechanism, (b) the cost structure and key risks, (c) the relationship to the end customer, and (d) a real-world company that operates under this model.

Exercise A.3 --- Customer Acquisition Cost and Lifetime Value

Define Customer Acquisition Cost (CAC) and Lifetime Value (LTV) in the context of sportsbook operations. Explain (a) what components are included in CAC, (b) why LTV must incorporate retention curves and discounting, (c) why the LTV/CAC ratio is the key profitability metric, and (d) why operators willingly operated at LTV/CAC ratios below 1 during the initial US market expansion phase (2019--2023).

Exercise A.4 --- Balanced Book vs. Position-Taking

Explain the difference between a balanced-book approach and a position-taking approach to sportsbook risk management. Address (a) how a balanced book guarantees profit equal to the overround, (b) why perfectly balanced books are rare in practice, (c) under what conditions a sportsbook would deliberately take a position (hold unbalanced liability), and (d) how the choice between these approaches relates to the sportsbook's confidence in its own pricing models.

Exercise A.5 --- The Odds Compilation Process

Describe the six-step odds compilation workflow outlined in Section 39.2. For each step, explain (a) the input data and tools used, (b) how the step contributes to the final published line, and (c) how the increasing automation of this process has changed the role of human traders.

Exercise A.6 --- The Technology Stack

Describe the major components of a modern sportsbook's technology stack. For each of the following, explain its function and why it is critical: (a) the trading platform, (b) real-time data feeds, (c) geolocation compliance systems, (d) KYC/AML systems, and (e) the event-driven processing architecture. Explain why the performance requirements rival those of financial trading firms.

Exercise A.7 --- Responsible Gambling Frameworks

Explain the purpose and components of responsible gambling regulation. Address (a) the player protection tools that operators must provide, (b) the operator obligations for identifying and responding to problem gambling behavior, (c) how regulatory enforcement works (including examples of fines and license actions), and (d) why the UK has been at the forefront of responsible gambling regulation. Discuss the tension between maximizing revenue and fulfilling responsible gambling obligations.

Exercise A.8 --- Tax Structures and Bettor Impact

Explain how tax rates on Gross Gaming Revenue (GGR) affect both sportsbook operators and bettors. Address (a) the formula relating minimum required margin to tax rate, (b) why bettors in high-tax jurisdictions (e.g., New York at 51% GGR tax) typically face worse odds than bettors in low-tax jurisdictions (e.g., Nevada at 6.75%), (c) how tax rates influence the number of operators willing to enter a market, and (d) the strategic implications for bettors who can shop lines across multiple states.

Part B: Calculations

Each problem is worth 5 points. Show all work and round final answers to the indicated precision.

Exercise B.1 --- Hold Percentage Calculation

A sportsbook takes the following action on a football game:

(a) Calculate the sportsbook's profit if Team A covers the spread.

(b) Calculate the sportsbook's profit if Team B covers the spread.

(c) Calculate the hold percentage for this market (GGR / Handle) under each outcome and the expected hold if each outcome is equally likely.

(d) Is this book balanced? If not, which direction should the line move to attract more action on the underbet side?

Exercise B.2 --- Customer Lifetime Value Computation

A sportsbook customer generates the following monthly Gross Gaming Revenue (GGR):

• Average monthly GGR: $45
• Monthly retention rate: 88%
• Monthly discount rate: 1.5%
• Evaluation horizon: 48 months

(a) Using the LTV formula $\text{LTV} = \sum_{t=1}^{T} \frac{\text{GGR}_t \times r_t}{(1 + d)^t}$, where $r_t = 0.88^t$, compute the LTV for the first 6 months. Show each term.

(b) Compute the full 48-month LTV. (You may use the geometric series approximation or compute directly.)

(c) If the Customer Acquisition Cost is $500, what is the LTV/CAC ratio? Is this customer segment profitable?

(d) How does the LTV change if the retention rate improves from 88% to 92%? Compute the new 48-month LTV and the percentage increase.

Exercise B.3 --- Market Overround Calculation

A sportsbook offers the following odds on a three-outcome soccer match:

(a) Calculate the implied probability for each outcome.

(b) Calculate the total market percentage (sum of implied probabilities).

(c) Calculate the overround (market percentage minus 100%).

(d) Calculate the "fair" probability for each outcome by removing the vig proportionally.

(e) If you believe the true probability of a Home Win is 52%, calculate your expected value per dollar wagered on Home Win at the offered odds.

Exercise B.4 --- Parlay Hold Calculation

A bettor places a four-leg parlay where each leg is priced at -110 (standard vig).

(a) Calculate the implied probability for a single -110 bet.

(b) If the true probability of each leg winning is 50%, calculate the true probability of all four legs winning.

(c) Calculate the parlay payout using the standard multiplication of decimal odds: $(1.909)^4$.

(d) Calculate the implied probability of the parlay payout and compare it to the true probability from (b). What is the effective hold percentage on this parlay?

(e) How does this compare to the hold on a single straight bet at -110?

Exercise B.5 --- Liability Management Scenario

A sportsbook has the following exposure on an NBA game:

(a) Calculate the sportsbook's net payout if the home team wins by exactly 7 points.

(b) Calculate the sportsbook's net payout if the away team wins outright.

(c) Calculate the sportsbook's net payout if the home team wins by exactly 3 points.

(d) Which outcome creates the worst-case scenario for the book? What is the maximum potential loss?

(e) Suggest one risk management action the book could take to reduce exposure.

Exercise B.6 --- Market Share and Revenue Analysis

Using the following US market data for 2024:

Assume the industry-average hold percentage is 8.5%.

(a) Calculate the estimated GGR for each operator.

(b) If FanDuel's operating costs are 85% of GGR, what is their estimated operating profit?

(c) If the average CAC is $400 and FanDuel acquired 1.2 million new depositing customers, what was their total acquisition spend?

(d) If FanDuel's average customer LTV is $650, what is their LTV/CAC ratio? Interpret the result.

Exercise B.7 --- Tax Impact on Required Margin

Consider two sportsbooks operating in different states:

• Book A: Nevada (GGR tax rate = 6.75%, operating costs = 3% of handle)
• Book B: New York Mobile (GGR tax rate = 51%, operating costs = 3% of handle)

(a) Using the approximation $\text{Minimum Required Margin} \approx \frac{\text{Tax Rate}}{1 + \text{Tax Rate}} + \text{Operating Costs as \% of Handle}$, compute the minimum required margin for each book.

(b) Convert each margin to equivalent moneyline odds for a 50/50 proposition (i.e., what odds would each book need to offer on each side?).

(c) Calculate the difference in expected cost to the bettor per $100 wagered between Book A and Book B.

(d) Explain why this calculation has strategic implications for line shopping.

Part C: Programming Challenges

Each problem is worth 10 points. Write clean, well-documented Python code. Include docstrings, type hints, and at least three test cases per function.

Exercise C.1 --- Odds Compilation Simulator

Build a complete odds compilation simulator that models how a sportsbook sets and adjusts lines in response to incoming bets.

Requirements: - Implement a Market class representing a two-outcome betting market with initial true probabilities, an applied margin, and current odds. - Implement a BetFlow generator that simulates incoming bets from a mix of sharp bettors (who bet toward the true probability) and recreational bettors (who exhibit public bias). - The simulator should adjust odds after each batch of bets based on the volume and source (sharp vs. recreational) of action. - Track and display the book's liability on each side, hold percentage, and line movement over time. - Generate a visualization showing line movement, cumulative handle on each side, and the final hold percentage.

Exercise C.2 --- Business Model Analyzer

Build a financial model for a sportsbook that compares the economics of B2C, B2B, and white-label operations.

Requirements: - Implement a SportsBookFinancials class that takes inputs: handle, hold percentage, tax rate, operating cost percentage, marketing spend, and (for B2B/white-label) platform revenue share. - For each business model, compute GGR, net revenue after tax, operating profit, and profit margin. - Implement a customer cohort model with configurable retention curves, average monthly GGR per customer, and CAC. - Produce a 36-month projection showing revenue, costs, and cumulative profit/loss for a new-market launch. - Generate comparative visualizations (bar charts, line plots) showing the profitability trajectory of each model.

Exercise C.3 --- Hold Percentage Calculator and Analyzer

Build a comprehensive tool that calculates and analyzes hold percentages across different bet types and market structures.

Requirements: - Implement functions to calculate hold percentage from American odds, decimal odds, and fractional odds for 2-outcome and 3-outcome markets. - Implement a parlay hold calculator that computes the effective hold for parlays of 2 through 10 legs at various per-leg vig levels. - Implement a Monte Carlo simulation that estimates the actual hold percentage achieved by a book given bet volume, true probabilities, and offered odds. - Produce a comparison table showing theoretical vs. simulated hold across bet types. - Generate a visualization showing how parlay hold percentage grows with the number of legs.

Exercise C.4 --- Liability Dashboard

Build a real-time liability monitoring dashboard simulator.

Requirements: - Implement a LiabilityMonitor class that tracks bets across multiple markets for a single event. - Support correlated markets (moneyline, spread, total) and track aggregate exposure. - Implement a worst-case scenario calculator that identifies the outcome combination that maximizes the book's loss. - Implement a risk alert system that triggers warnings when exposure exceeds configurable thresholds. - Generate a formatted text-based dashboard showing current liability by market, worst-case loss, and risk alerts.

Exercise C.5 --- Career Path and Salary Analyzer

Build an analysis tool that models career trajectories and compensation in the sports betting industry.

Requirements: - Create a data model representing career paths (Trader, Quant Analyst, Risk Manager, Compliance, Marketing, Engineering) with salary ranges at each level. - Implement a career progression simulator that models promotions with configurable probabilities and timing. - Calculate expected lifetime earnings for each career path over a 20-year horizon. - Implement a skills gap analyzer that takes a user's current skills and recommends development areas for each career path. - Generate a visualization comparing expected earnings across career paths and a skills radar chart.

Part D: Analysis & Interpretation

Each problem is worth 5 points. Provide structured, well-reasoned responses.

Exercise D.1 --- Analyzing Sportsbook Behavior

You observe the following behaviors at a major US sportsbook:

1. Your betting limits on NFL sides were reduced from $5,000 to $250 after a 62% ATS win rate over 200 bets.
2. The same sportsbook emails you daily offers for "Parlay Power Hours" with boosted parlay odds.
3. Your friend, a recreational bettor with a 46% win rate, receives a $500 free bet bonus offer but you do not.
4. The sportsbook's NFL opening lines consistently match Pinnacle's but diverge by closing time.

For each observation, explain (a) what sportsbook strategy or business logic drives the behavior, (b) how it relates to the concepts from Chapter 39 (LTV, player segmentation, hold percentage, odds compilation), and (c) what strategic response, if any, a bettor should consider.

Exercise D.2 --- Market Structure Analysis

Compare the US sports betting market structure to a mature European market (e.g., the United Kingdom). Address:

(a) How does the state-by-state licensing model in the US differ from the UK's single-regulator model, and what are the consequences for operators and bettors?

(b) Why has market consolidation been faster in the US than in Europe?

(c) How do the different tax structures (US state taxes ranging from 6.75% to 51% vs. the UK's 21% point of consumption tax) affect odds offered to bettors?

(d) What lessons from the mature UK market might predict the future trajectory of the US market?

Exercise D.3 --- Evaluating Promotional Offers

A sportsbook offers the following sign-up promotion: "Bet $1,000, Get $200 in Bonus Bets if your first bet loses." The bonus bets have a 1x playthrough requirement and cannot be withdrawn directly.

(a) Calculate the expected value of this promotion assuming you place the initial $1,000 bet at -110 on a 50/50 proposition.

(b) What is the effective cost to the sportsbook, assuming bonus bets have a 70% conversion rate (i.e., 70% of bonus bet face value is eventually wagered and generates GGR)?

(c) If the sportsbook's average CAC for this promotion (including marketing costs) is $350 per new depositing customer, and the average customer generates $25/month in GGR, how many months until the promotion breaks even?

(d) From the bettor's perspective, what is the optimal strategy for maximizing the value of this promotion?

Exercise D.4 --- Technology Build vs. Buy Decision

You are advising a mid-size casino company that wants to launch online sports betting in three US states. They are deciding between building a proprietary technology stack and using a B2B platform provider.

(a) List the major components they would need to build in-house and estimate the approximate cost range for a full build.

(b) What are the advantages and disadvantages of using a B2B provider like Kambi or Sportradar MTS?

(c) What factors should drive the decision (market timeline, available capital, competitive differentiation goals, technical talent)?

(d) Recommend a strategy and justify your choice.

Exercise D.5 --- Integrity Monitoring Case Analysis

A sportsbook's integrity team detects the following pattern: In a lower-division European soccer league, the same five customer accounts have placed significant bets on the correct score in three consecutive matches involving the same team. The bets were placed within 30 minutes of each other before each game, and all three bets won at odds between 8.00 and 12.00.

(a) Calculate the probability of three consecutive correct-score bets winning at those odds, assuming independence and fair odds.

(b) What does this pattern suggest, and what actions should the sportsbook take?

(c) What external organizations should be notified?

(d) How does this case illustrate the interplay between technology (anomaly detection), regulation (reporting requirements), and sports integrity (match-fixing prevention)?

Part E: Research & Extension

Each problem is worth 5 points. These require independent research beyond Chapter 39. Cite all sources.

Exercise E.1 --- History of US Sports Betting Legalization

Research and write a brief essay (500--700 words) tracing the history of sports betting regulation in the United States. Cover (a) the Wire Act of 1961 and its original intent, (b) PASPA (1992) and how it restricted state-level sports betting, (c) the Murphy v. NCAA Supreme Court decision (2018) and its reasoning, (d) the state-by-state expansion that followed, and (e) the current landscape and remaining challenges (federal regulation debate, interstate compacts, California/Texas).

Exercise E.2 --- The Economics of Same-Game Parlays

Research how same-game parlays (SGPs) have become a dominant revenue driver for US sportsbooks. Address (a) how SGPs differ from traditional parlays in terms of correlation modeling, (b) why the hold percentage on SGPs (20--45%) is dramatically higher than on straight bets, (c) how operators market SGPs to recreational bettors, (d) published estimates of the proportion of GGR attributable to SGPs, and (e) the ethical considerations of aggressively marketing a high-margin product.

Exercise E.3 --- Offshore vs. Regulated Sportsbooks

Research the ongoing tension between regulated and offshore (unlicensed) sportsbooks in the United States. Address (a) the estimated size of the offshore market relative to the regulated market, (b) why some bettors prefer offshore books (higher limits, better odds, cryptocurrency acceptance), (c) the consumer protection risks of betting with unlicensed operators, (d) what regulatory and enforcement approaches have been attempted, and (e) whether the regulated market can compete effectively by offering a better product.

Exercise E.4 --- Data Rights and Official League Partnerships

Research the role of "official data" in modern sports betting. Address (a) what official data means and why leagues (NFL, NBA, MLB) have sought to monetize it, (b) the difference between official and unofficial data for live betting purposes, (c) the mandates in some US states requiring operators to use official league data, (d) the financial terms of major data partnerships (Sportradar-NBA, Genius Sports-NFL), and (e) whether mandatory official data requirements serve consumer protection or league financial interests.

Exercise E.5 --- Responsible Gambling Technology

Research emerging technologies designed to promote responsible gambling. Address (a) AI-based behavioral detection systems that identify at-risk gamblers, (b) affordability check implementations (particularly in the UK), (c) self-exclusion databases and their effectiveness, (d) deposit limit and loss limit tools and their adoption rates, and (e) the role of operators, regulators, and third-party organizations in advancing responsible gambling technology.

Scoring Guide

Grading Criteria

Part A (Conceptual): Full credit requires clear, accurate explanations that demonstrate understanding of the underlying business and operational concepts and their relevance to both operators and bettors. Partial credit for incomplete but correct reasoning.

Part B (Calculations): Full credit requires correct final answers with all work shown. Partial credit for correct methodology with arithmetic errors.

Part C (Programming): Graded on correctness (40%), code quality and documentation (30%), and test coverage (30%). Code must execute without errors.

Part D (Analysis): Graded on analytical depth, logical reasoning, and appropriate application of industry concepts to real-world scenarios. Multiple valid approaches may exist.

Part E (Research): Graded on research quality, source credibility, analytical depth, and clear writing. Minimum source requirements specified per problem.

Solutions: Complete worked solutions for all exercises are available in code/exercise-solutions.py. For programming challenges, reference implementations are provided in the code/ directory.