Calculating Probabilities with NORM.DIST
You don't need to understand the complex math behind normal distributions. Excel does all the work for you with one function: NORM.DIST
This is your primary tool for converting projections into betting decisions.
The Formula You Need
NORM.DIST (Cumulative)
=NORM.DIST(x, mean, standard_dev, TRUE)=NORM.DIST(24.5, 25.7, 6.7, TRUE)Where:
- x = the line you're evaluating
- mean = your projected average (μ)
- standard_dev = your projected standard deviation (σ)
- TRUE = tells Excel you want the cumulative probability
What it returns: The probability of the outcome being LESS THAN OR EQUAL TO x.
For Under Bets
Use the formula as-is. It directly gives you P(Under).
Probability of UNDER
P(Under) = NORM.DIST(line, μ, σ, TRUE)=NORM.DIST(24.5, 25.7, 6.7, TRUE)For Over Bets
Subtract from 1 to get P(Over).
Probability of OVER
P(Over) = 1 - NORM.DIST(line, μ, σ, TRUE)=1-NORM.DIST(24.5, 25.7, 6.7, TRUE)Key Insight
That's it. Plug in your numbers, get your probability, compare to market odds. If your probability is higher than implied odds, you have an edge.
Complete Example: LeBron Points Prop
Your projection: μ = 25.7 points, σ = 6.7 points
The line: Over 24.5 points (-110)
Step 1: Calculate your probability
=1-NORM.DIST(24.5, 25.7, 6.7, TRUE)
Result: 0.571 (57.1%)
Step 2: Calculate the market's implied probability
At -110 odds:
Implied probability = 110 / (110 + 100) = 52.4%
Step 3: Compare
| Your Probability | Market Implied | Edge |
|---|---|---|
| 57.1% | 52.4% | +4.7% |
Tip
Verdict: Your probability (57.1%) exceeds the market (52.4%) by 4.7%. This is a bet worth considering.
Example: Mahomes Passing Yards (Under)
Your projection: μ = 285 yards, σ = 90 yards
The line: Under 294.5 yards (-110)
Step 1: Calculate your probability
=NORM.DIST(294.5, 285, 90, TRUE)
Result: 0.546 (54.6%)
Step 2: Compare to market
| Your Probability | Market Implied | Edge |
|---|---|---|
| 54.6% | 52.4% | +2.2% |
Verdict: A smaller edge, but still +EV. Consider bet sizing based on confidence.
The Break-Even Threshold
At -110 odds, you need 52.4% probability to break even. This is your benchmark for every standard prop bet.
| Odds | Break-Even % | Formula |
|---|---|---|
| -110 | 52.4% | 110/(110+100) |
| -115 | 53.5% | 115/(115+100) |
| -120 | 54.5% | 120/(120+100) |
| -130 | 56.5% | 130/(130+100) |
| +100 | 50.0% | 100/(100+100) |
| +110 | 47.6% | 100/(110+100) |
Warning
Critical Rule: Never just ask "Is this over 50%?"
Always ask "Is this over the break-even probability for these odds?"
A 51% probability at -110 is still -EV because you need 52.4% to break even.
Building Your Probability Calculator in Excel
Here's a simple setup for evaluating props:
| Cell | Label | Value/Formula |
|---|---|---|
| A1 | Line | 24.5 |
| A2 | Your Mean (μ) | 25.7 |
| A3 | Your Std Dev (σ) | 6.7 |
| A4 | P(Over) | =1-NORM.DIST(A1,A2,A3,TRUE) |
| A5 | P(Under) | =NORM.DIST(A1,A2,A3,TRUE) |
| A6 | Odds | -110 |
| A7 | Break-Even % | =IF(A6<0,ABS(A6)/(ABS(A6)+100),100/(A6+100)) |
| A8 | Edge (Over) | =A4-A7 |
| A9 | Edge (Under) | =A5-A7 |
Just change cells A1, A2, A3, and A6 for each new prop, and you instantly see your edge.
Try the Calculator
Normal Distribution Calculator
Try the interactive calculator for this concept
Simulating Outcomes (Advanced)
Instead of calculating probabilities directly, you can simulate thousands of outcomes and count how many exceed the line.
Random Outcome from Normal Distribution
Random outcome ~ N(μ, σ)=NORM.INV(RAND(), μ, σ)Simulation Steps:
- Create a column with 1,000 rows
- In each cell, enter:
=NORM.INV(RAND(), 25.7, 6.7) - This simulates 1,000 games for LeBron with his 2023-24 stats
- Count how many exceed your line:
=COUNTIF(A1:A1000,">"&24.5) - Divide by 1,000 to get your probability
This method is useful for:
- Visualizing the distribution
- Complex scenarios with multiple adjustments
- Sanity-checking your NORM.DIST calculations
📝 Exercise
Instructions
You project a player to average 22 points (μ = 22) with σ = 5. The line is Over 20.5 points (-110).
What Excel formula calculates the probability of going OVER 20.5?
📝 Exercise
Instructions
Using the same projection (μ = 22, σ = 5), the probability of Over 20.5 is 61.8%. The odds are -110.
Should you bet the over?
📝 Exercise
Instructions
A prop has odds of -130 on the Over. You calculate P(Over) = 55%.
Is this bet +EV or -EV?
📝 Exercise
Instructions
You want to find the probability of UNDER 280 passing yards. Your projection: μ = 275, σ = 85.
What is the correct Excel formula?