Standard Deviation: Your Risk Gauge
In the previous lesson, we learned that variance measures how spread out results are from the average. But variance has a problem: it's expressed in squared units, making it difficult to interpret. Enter standard deviation—the square root of variance that brings everything back to meaningful numbers.
What Is Standard Deviation?
Standard deviation (represented by the Greek letter σ, pronounced "sigma") tells you the typical amount by which your results will vary from the expected value. It's your measure of uncertainty.
Standard Deviation for Bets
σ = √(n × p × (1 - p))=SQRT(A1*B1*(1-B1))Where:
- σ (sigma) = standard deviation
- n = number of bets
- p = probability of winning (as a decimal)
Key Insight
A higher standard deviation means more volatility—your results will swing more widely. A lower standard deviation means more consistency—your results will cluster closer to the expected value.
Calculating Standard Deviation: Step by Step
Let's work through a practical example. You're placing 100 bets at a 52% win rate.
Step 1: Identify your variables
- n = 100 bets
- p = 0.52 (52% win rate)
Step 2: Calculate variance
Variance = n × p × (1 - p)
Variance = 100 × 0.52 × 0.48
Variance = 24.96
Step 3: Take the square root
σ = √24.96 ≈ 5.0 wins
Result: With a standard deviation of 5 wins, your results will typically vary by about 5 wins from your expected 52 wins.
Two Players, Same Average, Different Risk
Consider two NBA players, both averaging about 20 points per game over a season:
Player A (Consistent): Scores between 18-22 points in most games. Standard deviation: 1.13 points.
Player B (Volatile): Scores anywhere from 11-30 points. Standard deviation: 5.49 points.
Both players have the same average, but Player A is far more predictable. If you're betting on Player A to score over 19.5 points, you have a much clearer picture of the risk. Player B might have the same average, but the wide standard deviation means there's much more uncertainty in any single game.
Key Insight
Standard deviation is your risk gauge. Two bets can have the same expected value but vastly different risk profiles based on their standard deviation.
Standard Deviation for Player Performance
When analyzing player props, you'll often calculate standard deviation from actual game data rather than win/loss probabilities. The formula is slightly different:
Sample Standard Deviation
σ = √(Σ(xᵢ - μ)² / (n-1))=STDEV.S(A1:A82)Where:
- xᵢ = each individual performance value
- μ (mu) = mean/average performance
- n = number of observations
Tip
In Excel, use =STDEV.S(range) for sample data (most common) or =STDEV.P(range) for a full population. For player stats, you're almost always working with samples.
Example: Calculating Player Standard Deviation
A player's last 5 games: 25, 30, 20, 28, 22 points
Step 1: Calculate the mean
μ = (25 + 30 + 20 + 28 + 22) / 5 = 125 / 5 = 25 points
Step 2: Calculate squared deviations
| Game | Points | Deviation (x - μ) | Squared |
|---|---|---|---|
| 1 | 25 | 0 | 0 |
| 2 | 30 | +5 | 25 |
| 3 | 20 | -5 | 25 |
| 4 | 28 | +3 | 9 |
| 5 | 22 | -3 | 9 |
| Sum | 68 |
Step 3: Calculate standard deviation
σ = √(68 / 4) = √17 ≈ 4.12 points
This player's scoring varies by about 4.12 points from their 25-point average on a typical night.
Why Standard Deviation Matters for Bet Sizing
Standard deviation directly impacts how you should size your bets. Consider two strategies with the same expected value:
| Strategy | Bet Type | Expected Profit/Bet | Std Dev/Bet |
|---|---|---|---|
| A | Favorites at -110 | $2 | $10 |
| B | Underdogs at +200 | $2 | $25 |
Both strategies have the same expected value over time, but Strategy B will experience much larger swings. You might go on a 10-bet losing streak with Strategy B and lose $250, even though your edge is intact. With Strategy A, a 10-bet losing streak would cost you $110, which is easier to absorb.
Warning
High variance bets require larger bankrolls and longer time horizons to realize your edge. If you're working with a limited bankroll, prioritize lower-variance opportunities.
Excel Formulas Quick Reference
| Purpose | Formula | Example |
|---|---|---|
| Std dev for bets | =SQRT(n*p*(1-p)) | =SQRT(100*0.52*0.48) → 5.0 |
| Std dev from data | =STDEV.S(range) | =STDEV.S(A2:A83) |
| Population std dev | =STDEV.P(range) | =STDEV.P(A2:A83) |
| Variance from data | =VAR.S(range) | =VAR.S(A2:A83) |
📝 Exercise
Instructions
Calculate the standard deviation for the following betting scenario, then determine if the result falls within normal expectations.
You place 200 bets with a 54% win rate. You end up winning 98 bets.
Questions:
- What is the expected number of wins?
- What is the standard deviation?
- How many standard deviations below the mean is your result?
Key Takeaways
-
Standard deviation = √variance, bringing the measurement back to interpretable units
-
Lower σ = more predictable outcomes (consistent players, safer bets)
-
Higher σ = more volatile outcomes (streaky players, riskier bets)
-
Use
=STDEV.S()in Excel to calculate standard deviation from player data -
Factor standard deviation into bet sizing—high variance strategies need bigger bankrolls
In the next lesson, we'll explore the powerful 68-95-99.7 Rule that tells you exactly what percentage of outcomes fall within each standard deviation range.