Player Props Analyzer
Model any player prop over/under using normal distribution. Input player's average and game-to-game standard deviation to find mispriced lines.
Interpretation: Player is below the line by 0.1 standard deviations. Very close to the line — coin flip territory.
Normal distribution assumes symmetrical variance. For player props, consider outliers (injury risk, blowout, weather). Use this as a baseline, not the final answer.
How Player Prop Modeling Works
A player prop is an over/under on a single player's statistic — passing yards, points, receptions, made threes. Pricing one takes exactly two inputs: a projection (what you expect the player to produce in this specific matchup) and a spread (how much the stat varies from game to game, measured by standard deviation). This calculator treats the stat as a probability distribution centered on your projection. It computes the z-score — how many standard deviations the bookmaker's line sits from your mean — converts that into over and under probabilities with the normal CDF, and then compares your probability to the implied probability of the offered odds. The difference is your expected value.
Distribution choice depends on the stat type. High-volume, near-continuous stats — passing yards, rushing and receiving yards, NBA points — are well approximated by a normal distribution: their averages are large and outcomes are roughly symmetric around the mean. Low-count discrete stats — receptions, made threes, blocks, steals, touchdowns — are integer counts, and counts follow a Poisson distribution far better than a normal one. Poisson needs only one parameter, the expected count λ, and its standard deviation is approximately √λ: a player projected for 6 receptions has a natural spread of about 2.4. As a rule of thumb, when the projection is above roughly 10 the normal model is fine; below about 6 the Poisson probabilities diverge enough to change a betting decision — the worked example below shows a 2.7-point gap on a receptions line.
Juice matters more on props than almost anywhere else. A standard prop at −110/−110 (decimal 1.91 both sides) carries about 4.5% hold, and many books post props at −115 or even −120 both sides, pushing the hold to 7–9% — roughly double the cost of main spreads and totals. At 1.87 the break-even win rate is 53.5%: your model does not just need to disagree with the line, it needs to disagree by enough to clear the margin. Before trusting an edge, strip the vig from both sides of the prop with the no-vig calculator to see what the market itself believes after the juice is removed.
Projection quality decides everything downstream. Build the baseline from the player's last 10–20 game logs, then adjust for minutes and usage, opponent strength, pace, home/away splits, and weather in outdoor sports. Shop the same prop across several books — prop lines vary more between operators than main markets do, and half a point on a receptions or threes line moves the probability materially. Once you have a probability you trust, run the stake and long-run profit numbers through the expected value calculator.
Player Prop Formulas
Normal model (yardage, points): z = (Line − Projection) / σ P(Over) = 1 − Φ(z) P(Under) = Φ(z) Poisson model (receptions, 3PM, blocks, TDs): P(X = k) = (λᵏ × e⁻λ) / k! σ ≈ √λ P(Over k.5) = 1 − P(X ≤ k) Pricing: Fair odds = 1 / P EV per $1 = P × offered odds − 1
Worked Examples
Projection 280 yds, σ = 85, line 275.5, Over offered at 1.87. z = (275.5 − 280) / 85 = −0.05, so P(Over) ≈ 52.1% and fair odds ≈ 1.92. EV = 0.521 × 1.87 − 1 ≈ −2.6%. Projecting above the line is not enough — the juice eats a sub-1σ edge. Pass.
Projection λ = 6.0 receptions, line 5.5, Over offered at 1.91. Poisson gives P(X ≥ 6) ≈ 55.4%, fair odds 1.80 → EV = 0.554 × 1.91 − 1 ≈ +5.9%. A normal approximation (σ = √6 ≈ 2.4) would claim 58.1% — overstating the edge by 2.7 points. Distribution choice matters at low counts.
Frequently Asked Questions
Should I use a normal or a Poisson distribution for player props?
Use the normal distribution for high-volume stats such as passing, rushing and receiving yards or NBA points, where averages are large and outcomes are roughly symmetric around the mean. Use Poisson for low-count stats such as receptions, made threes, blocks or touchdowns, because those are integer counts. With Poisson the standard deviation is roughly the square root of the projected count, and for lines below about 6 the two models give noticeably different probabilities — enough to flip a betting decision.
Where do I get a projection and standard deviation for a player?
Start from the player's game logs — the last 10 to 20 games is a workable sample. The average of that sample is your baseline projection and the game-to-game standard deviation is your spread input. Then adjust the projection for context: minutes and usage, opponent defense, pace, home/away splits and weather for outdoor sports. The bookmaker's line itself is a strong prior — if your number is wildly different, re-check your inputs before assuming you found an edge.
How much juice do sportsbooks charge on player props?
A standard prop priced at -110/-110 (decimal 1.91 both sides) carries about 4.5% hold, and many props are posted at -115 or -120 both sides, pushing the hold to 7-9% — roughly double what main spreads and totals cost. At odds of 1.87 the break-even win rate is 53.5%. Alternate lines and boosted props usually carry even more margin, so your projected edge has to clear the juice before a prop is worth betting.
Why does the calculator sometimes show value on the Under?
The model is symmetric: if your projection sits below the bookmaker's line, the Under covers more of the probability distribution than the Over. The tool flags Under value whenever your modeled Under probability exceeds the implied probability of the offered odds. Keep in mind both sides carry juice, so a small probability edge on either side can still be a pass once the margin is accounted for.
How reliable is the normal-distribution assumption for props?
It is a baseline, not the truth. Real prop outcomes have fat tails and asymmetry: early injuries and blowouts truncate the downside, yardage stats skew right because of long plays, and minutes risk in the NBA adds variance the model does not see. Treat the output as a first filter, then adjust for game script, injury news and role changes before betting.