Workbook Exercises and Practice

Now it's time to apply everything you've learned about the Poisson distribution. These exercises will help you build muscle memory for the 3-step process and develop intuition for count-based props.

Exercise 8.1: Build a Poisson Prop Calculator in Excel

Create a spreadsheet with these columns:

Key Formulas

Assuming Line is in C2 and λ is in D2:

P(Under) = =POISSON.DIST(INT(C2), D2, TRUE)
P(Over)  = =1 - POISSON.DIST(INT(C2), D2, TRUE)

Implied probability from American odds in E2:

=IF(E2<0, ABS(E2)/(ABS(E2)+100), 100/(E2+100))

Edge calculation (if Side is in F2, P(Over) in G2, P(Under) in H2, implied in I2):

=IF(F2="Over", G2-I2, H2-I2)

Test Case

Expected Output:

• P(Over) = 61.3%
• Edge = +1.3%
• EV ≈ +$3.25 per $150 risked

Exercise 8.2: Multiple Outcome Analysis

Using λ = 2.3 for Patrick Mahomes passing TDs, calculate probabilities for each outcome and identify potential edges.

Your Task

Fill in this table using Excel:

Exercise 8.3: Overdispersion Detection

For each player, compute mean, sample variance (VAR.S), and VMR. Determine which player is better suited for Poisson vs. Negative Binomial.

Player Data (TDs per game, last 15 games)

Player A (Consistent): 1, 0, 1, 1, 2, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1

Player B (Boom-or-Bust): 0, 0, 3, 0, 2, 0, 0, 0, 3, 1, 0, 2, 0, 0, 3

Your Task

Calculate for each player:

1. Mean (AVERAGE)
2. Sample Variance (VAR.S)
3. VMR (Variance / Mean)
4. Recommended model

Exercise 8.4: λ Adjustment Template

Build a simple template and run it for the following prop:

Prop: Gerrit Cole Over 7.5 Strikeouts at -115

Given Information

• Season average: 7.2 K/start
• Last 5 starts: 9, 8, 6, 10, 7 (averaging 8.0)
• Opponent (Rays): Below average K rate, difficult to strike out
• Game is in Tampa (dome, no weather factor)

Your Template

Exercise 8.5: Full Prop Analysis Workflow

Work through a complete analysis:

Prop: Backup RB Anytime Touchdown Scorer at +125

Given Information

• Player is a goal-line specialist
• Season average: 0.65 TDs/game
• This week: Facing bottom-5 run defense
• Team is 7-point favorite (positive game script)
• Starting RB is healthy (no extra opportunity)

Your Task

1. Build λ using the adjustment template
2. Calculate P(Over 0.5) = P(scoring at least 1 TD)
3. Calculate market implied probability
4. Determine edge
5. Calculate EV per $100 bet
6. Make your decision: Bet or Pass?

Chapter Summary: Key Takeaways

The Big Takeaways

1. Poisson is best for rare, discrete events where 0/1/2 outcomes are common

2. Your edge typically comes from estimating λ better than the market — Books can run POISSON.DIST too

3. Two Poisson shortcuts matter constantly:

   • Var(X) = λ
   • P(X=0) = e^(-λ)

4. Tail probabilities are often mispriced in "exact count" markets

5. Check for overdispersion with VMR to know when Poisson is likely to miss the tails

Quick Reference: Excel Formulas

What's Next

In Chapter 9, we'll introduce the Negative Binomial distribution, which adds flexibility when variance exceeds the mean. This is essential for modeling boom-or-bust players.

Chapter 10 explores correlation and covariance—because props don't exist in isolation, especially in same-game parlays.

Chapter 11 will cover Zero-Inflated Poisson (ZIP) and Hurdle distributions for when structural zeros are a factor.