Sport-Specific Distribution Guide
Now that you understand the theory behind Normal, Poisson, Negative Binomial, ZIP, and Hurdle distributions, let's apply them to real prop types across major sports. This lesson provides a practical reference you can use when analyzing any prop.
The Master Decision Framework
Before diving into sport-specific guidance, here's the universal workflow:
1. Is it continuous or count-based?
├── High-volume continuous (50+ yards, 15+ points) → Normal
└── Low-volume counts (0, 1, 2, 3 outcomes) → Continue...
2. Calculate VMR
├── VMR ≤ 1.3 → Poisson candidate
└── VMR > 1.3 → Negative Binomial candidate
3. Check for excess zeros
├── Observed zeros match prediction → Use distribution from Step 2
└── Observed zeros >> prediction → Continue...
4. Identify zero source
├── Structural (no opportunity) → ZIP
└── Any vs. none (player active) → Hurdle
NFL Distribution Guide
High-Volume Props → Normal
| Prop Type | Distribution | Rationale |
|---|---|---|
| Passing yards | Normal | High volume, roughly symmetric |
| Rushing yards (bell cows) | Normal | Consistent touches, ~100+ yard range |
| Receiving yards (WR1/WR2) | Normal | 50+ yard expected outcomes |
Normal P(Over)
P(Over) = 1 - Φ((line - μ) / σ)=1-NORM.DIST(line,mean,stdev,TRUE)Low-Volume Count Props → Poisson or Negative Binomial
| Prop Type | Distribution | VMR Check |
|---|---|---|
| Passing touchdowns | Poisson or NB | Check VMR; most QBs ≈ 1.0 |
| Rushing touchdowns (starter) | Poisson | Usually consistent, VMR ≈ 1 |
| Receptions (high-volume WR) | Poisson | 5+ targets expected, stable |
Zero-Heavy Props → ZIP or Hurdle
| Prop Type | Distribution | Rationale |
|---|---|---|
| Backup RB receptions | ZIP | Some games blocker-only (structural zero) |
| Pocket QB rushing yards | ZIP | Game plan determines scramble opportunity |
| TE targets (TE2) | Hurdle | Playing but may not be targeted |
| Rushing TDs (backup RB) | Hurdle | Active but goal-line work varies |
Key Insight
NFL Rule of Thumb: If the player's role varies game-to-game (sometimes involved, sometimes scripted out), lean toward ZIP. If the player is always active but the stat is just rare, lean toward Hurdle.
NBA Distribution Guide
High-Volume Props → Normal
| Prop Type | Distribution | Rationale |
|---|---|---|
| Points (starters) | Normal | 15+ expected, symmetric distribution |
| Rebounds (bigs) | Normal | 8+ expected, high volume |
| Assists (point guards) | Normal | 6+ expected, consistent opportunity |
| PRA combos | Normal | High combined volume |
Low-Volume Count Props → Poisson or Negative Binomial
| Prop Type | Distribution | VMR Check |
|---|---|---|
| 3-pointers made (shooter) | Poisson | Consistent attempts, VMR ≈ 1 |
| Steals | Poisson | Rare but stable rate |
| Turnovers | Poisson | Usually consistent |
Zero-Heavy Props → ZIP or Hurdle
| Prop Type | Distribution | Rationale |
|---|---|---|
| Bench player points | Hurdle | Either gets minutes or doesn't |
| Blocks (guards) | Hurdle | Zero common, but playing full minutes |
| 3PM (role player in platooned matchup) | ZIP | May be benched entirely vs certain lineups |
| Assists (non-PG) | Hurdle | Playing but assist opportunities rare |
Tip
NBA Rule of Thumb: NBA props are often higher-volume than NFL, so Normal is your default for star player stats. Reserve ZIP/Hurdle for bench players or rare events like blocks.
MLB Distribution Guide
Continuous/High-Volume Props → Normal (with caution)
| Prop Type | Distribution | Notes |
|---|---|---|
| Total bases | Normal | With large enough sample |
| Hits (high BA hitter) | Normal | If 2+ expected |
Warning
MLB props often have lower expected values than other sports. A hitter expecting 1.2 hits per game is better modeled with Poisson than Normal, despite hits being "common."
Count Props → Poisson or Negative Binomial
| Prop Type | Distribution | VMR Check |
|---|---|---|
| Strikeouts (pitcher) | Poisson | Usually consistent, VMR ≈ 1 |
| Hits allowed | Poisson | Stable rate per inning |
| Earned runs | Negative Binomial | Often clustered (big innings) |
Zero-Heavy Props → ZIP or Hurdle
| Prop Type | Distribution | Rationale |
|---|---|---|
| RBIs | Hurdle | Zero common, but player had at-bats |
| Stolen bases | Hurdle | Many games with zero, but player was on base |
| Home runs | Hurdle | Rare event, player active |
| Strikeouts (opener/reliever) | Hurdle | May only face 3-4 batters |
| Hits (bottom of order) | Hurdle | May get pulled for pinch hitter |
Key Insight
MLB Rule of Thumb: Most MLB player props are low-volume count data. Default to Poisson unless you see overdispersion (VMR > 1.3) or excess zeros. For RBIs and stolen bases, Hurdle is almost always appropriate.
NHL Distribution Guide
Moderate-Volume Props → Normal or Poisson
| Prop Type | Distribution | Rationale |
|---|---|---|
| Shots on goal (star forward) | Normal | 3+ expected, reasonably symmetric |
| Blocked shots (defenseman) | Poisson | Count data, usually consistent |
| Hits | Poisson | Consistent opportunity each game |
Zero-Heavy Props → Hurdle (Almost Always)
| Prop Type | Distribution | Rationale |
|---|---|---|
| Goals | Hurdle | Zero very common (~70-80% of games), but players are on ice |
| Assists | Hurdle | Similar to goals—rare but active players |
| Points (G+A) | Hurdle | Zero common for non-stars |
| Penalty minutes | Hurdle | Some players rarely take penalties, but opportunity exists |
| Power play points | Hurdle | PP time varies, but when on PP they're active |
Tip
NHL Rule of Thumb: Goals and assists are classic Hurdle candidates. The player is playing—they're just rare events. Don't confuse "rare" with "no opportunity."
Quick Reference: Distribution Selector
Use this tool to help determine the right distribution for your prop:
Negative Binomial Calculator
Try the interactive calculator for this concept
The Five-Question Checklist
Before betting any prop, answer these questions:
-
Is this high-volume continuous data? (50+ yards, 15+ points)
- Yes → Normal
- No → Continue
-
What's the VMR?
- VMR ≤ 1.3 → Poisson
- VMR > 1.3 → Negative Binomial
-
Are there excess zeros? (Compare observed to e^(-λ))
- No excess → Use distribution from Q2
- Yes excess → Continue
-
Why are there zeros?
- Player sometimes has no opportunity → ZIP
- Player always active, stat just rare → Hurdle
-
Does my mean projection match my π and λ assumptions?
- E[Y] should equal (1-π) × λ for ZIP/Hurdle
📝 Exercise
Instructions
Exercise: Match the Prop to the Distribution
For each prop, select the most appropriate distribution based on the guidance in this lesson.
Patrick Mahomes passing yards (expected: 285 yards, σ = 55 yards)
Connor McDavid goals (expected: 0.55 per game, zero in 68% of games)
Backup TE receptions (expected: 1.2 per game, VMR = 1.1, but he's a blocker-only in 40% of games)
MLB pitcher strikeouts (expected: 6.2 per game, VMR = 1.05, consistent starter)
An NBA backup center's blocks (expected: 0.8 per game, zero in 55% of games, but plays 12 minutes every game)
Running back rushing TDs (expected: 0.85, VMR = 1.75, games range from 0-3 TDs)