Which Statistical Distribution for Player Props: Normal vs Poisson | DMP Learn

Which Distribution Should You Use?

What You'll Learn

The previous two lessons covered the normal distribution and the Poisson distribution. This lesson ties them together with a practical decision framework: given any player prop, how do you know which math to use? You'll learn a simple flowchart that handles every common prop type, plus a quick reference table for the most popular markets across NFL, NBA, MLB, and NHL.

---

The Decision Flowchart

When you're evaluating a player prop, ask these three questions in order:

Question 1: Is the stat continuous or discrete?

Continuous stats can take any value, including decimals. Passing yards, fantasy points, total bases (effectively continuous at scale), rebounds, assists. Even though the final box score shows whole numbers, the underlying performance is continuous — a quarterback could theoretically throw for any yardage total.

Discrete count stats are small integers. Touchdowns scored (0, 1, 2), home runs (0, 1), goals scored (0, 1, 2). These are counts of rare, individual events.

• If continuous → Normal distribution is your starting point. Proceed to Question 2 for a variance check.
• If discrete count → Poisson is your starting point. Proceed to Question 3 for an overdispersion check.

Question 2 (Continuous stats): Is the variance manageable?

Not all continuous stats follow a clean bell curve. Check the player's game-to-game consistency:

• Coefficient of Variation (CV) under 30% → Normal distribution fits well. CV = (Standard Deviation / Mean) × 100. Most assist and rebound props fall here.
• CV between 30-50% → Normal distribution is usable but less precise. NBA points props often fall here. Your probability estimates will be rougher.
• CV above 50% → The stat is too volatile for the normal distribution to give reliable probabilities. This is rare for commonly bet continuous props, but it happens with some receiving yard props for inconsistent targets.

Question 3 (Discrete count stats): Is the Variance-to-Mean Ratio close to 1?

Poisson assumes variance equals the mean (VMR ≈ 1.0). Calculate the VMR from the player's recent game log:

VMR = Sample Variance / Sample Mean

• VMR between 0.8 and 1.3 → Poisson works. Standard equidispersion assumption holds.
• VMR above 1.3 → The player is overdispersed (boom-or-bust). Poisson will underestimate both zero-count and high-count probabilities. Use the Negative Binomial distribution instead, which adds a second parameter to capture the extra variance.
• VMR below 0.8 → Rare, but it means the player is underdispersed (more consistent than Poisson predicts). Poisson is conservative here — it slightly overstates tail probabilities.

---

The Quick Decision Table

---

The Negative Binomial: When Poisson Isn't Enough

For most discrete count props, Poisson works. But some players — particularly boom-or-bust types — produce outcomes that are more spread out than Poisson allows.

The Negative Binomial distribution is a generalization of Poisson that adds a "dispersion parameter" to account for extra variance. It has two parameters instead of one:

• Mean (μ): Same as Poisson's lambda — the expected count
• Dispersion (r or alpha): Controls how much extra variance exists beyond what Poisson allows

When to reach for Negative Binomial:

• VMR > 1.3 in the player's game log
• The player has a pattern of either going off or putting up zeros (touchdown-dependent running backs, streaky home run hitters)
• Your Poisson model consistently mispredicts the player's outcomes

Practical impact: For an anytime TD scorer prop, Poisson with λ = 0.8 gives P(X ≥ 1) = 55.1%. But if the player is overdispersed (VMR = 1.6), the Negative Binomial might give P(X ≥ 1) = 49.2%. That 6-point difference can flip a bet from +EV to -EV.

Spreadsheet formula:

=NEGBINOM.DIST(k, r, p, cumulative)

Parameterizing r and p from the mean and variance requires a bit more setup. The VMR lesson walks through this in detail.

---

Edge Cases and Judgment Calls

Pitcher strikeouts (6-8 K range): This is the gray zone between Poisson and Normal. Either distribution gives reasonable results. A practical approach: use Poisson if the pitcher averages under 7 Ks, Normal if above 8, and check both if in between. If they give meaningfully different probabilities, the true answer is somewhere in the middle — which means the edge probably isn't large enough to bet.

NBA 3-pointers made: Technically a discrete count, but high-volume shooters (averaging 3-4 makes per game) produce distributions that look roughly normal. For players averaging under 2.0 3PM, stick with Poisson. For elite shooters above 3.5, Normal works fine.

Combo props (PRA, P+A, P+R): These add multiple stats together, and the sum of many random variables tends toward a normal distribution regardless of the individual components (Central Limit Theorem). Use Normal for all combo props.

Game totals and team totals: Team-level stats aggregate many players, so Normal distribution applies. Individual pitcher/team K totals, team run totals, team point totals — all Normal.

---

A Practical Workflow

Here's how to put this all together when evaluating a prop:

1. Identify the stat type — continuous or discrete count?
2. Pick the starting distribution — Normal or Poisson
3. Check the fit — CV for Normal, VMR for Poisson
4. If the fit is poor — upgrade to Negative Binomial (for overdispersed counts) or acknowledge reduced confidence (for high-CV continuous stats)
5. Calculate probability — use the appropriate formula or spreadsheet function
6. Compare to the sportsbook's implied probability — devig the line and compare
7. Size your confidence — better-fitting distributions → more confidence in your edge estimate

---

How DMP Handles This

DMP's modeling pipeline doesn't use a one-size-fits-all approach. The platform evaluates each prop's statistical characteristics as part of its 14-signal scoring system. Props where the underlying stat fits a known distribution cleanly score higher for modelability, which factors into the overall confidence score you see on the platform.

This is one reason why some prop types consistently show up as +EV candidates on DMP more often than others — the math is more reliable for well-distributed stats, which means the fair probability estimates are more precise.

---

Key Takeaways

• Start with the stat type: continuous → Normal, discrete count → Poisson.
• Check the fit: CV for Normal, VMR for Poisson. If the fit is poor, adjust your distribution or reduce your confidence.
• VMR > 1.3 means the player is overdispersed — switch from Poisson to Negative Binomial.
• Combo props and team totals are almost always Normal (Central Limit Theorem).
• The gray zone (6-8 K pitchers, high-volume 3PM shooters) can go either way — check both distributions and only bet if they agree.
• Better distribution fit → more reliable probability → more confident EV estimate.

---

Next lesson: Understanding Variance-to-Mean Ratio →