Knowing you have a “Value Bet” is one thing. Knowing the likelihood of actually walking away with a profit after 100 or 1,000 bets is another.
Even with a mathematical edge, variance can cause losing sessions. Our Profit Probability Calculator goes beyond simple Expected Value (EV). It applies statistical analysis (binomial distribution) to your win rate and odds, showing you the exact percentage chance that you will finish your betting series “in the green.” It also calculates the 95% Confidence Interval, giving you a realistic range of best-case and worst-case scenarios.
Profit Probability
Variance CalculatorHow to Use the Calculator
This tool is essential for bankroll planning and understanding the Law of Large Numbers. Here is how to interpret the data:
- Enter Number of Bets (N): The sample size you want to simulate (e.g., 100 bets for a weekend, or 1,000 bets for a month).
- Enter Stake & Odds:
- Flat Stake: Your standard bet size (e.g., $10).
- Avg Decimal Odds: The average price you bet at. (Use 1.91 for standard -110 lines).
- Input Win Rate (%): Your historical or estimated strike rate (e.g., 55%).
- Analyze the Results:
- Profit Probability: The likelihood that your total profit will be greater than $0.
- 95% Confidence Range: Ideally, you want the entire range (Low to High) to be positive. If the lower bound is negative, there is still a significant risk of loss.
Real-World Examples: The Impact of Volume
The most important lesson this calculator teaches is that volume cures variance. A small edge is risky in the short term but powerful in the long term.
Example 1: Short Term (High Risk)
You are a skilled sports bettor with a 54% Win Rate on standard point spreads (Odds 1.91 / -110). You plan to place 50 bets.
- The Math: Over just 50 bets, variance plays a huge role.
- The Result: The calculator shows a Profit Probability of ~64%. This means there is still a 36% chance you will lose money, even though you are a winning bettor!
Example 2: Long Term (Low Risk)
You keep the same stats (54% Win Rate, 1.91 Odds), but you increase the volume to 1,000 bets.
- The Math: The Law of Large Numbers smooths out the bad luck.
- The Result: Your Profit Probability jumps to over 95%. The 95% Confidence Interval will likely show a range that is almost entirely profitable (e.g., +$200 to +$1,500). This proves that to realize your edge, you must stick to the strategy over the long haul.
Frequently Asked Questions (FAQ)
What is the difference between EV and Profit Probability?
Expected Value (EV) tells you the average amount you would win per bet if you played infinite times. Profit Probability tells you the likelihood of actually realizing that profit over a finite number of bets (e.g., “I have an 80% chance of being profitable this month”).
What is the “95% Confidence Range”?
This is a statistical term. It means that if you repeated this betting session 100 times, in 95 of those times, your final bankroll change would fall within this range. It effectively shows you your “Best Case” and “Worst Case” scenarios excluding extreme statistical anomalies.
Why is my Profit Probability not 100% if I have a positive edge?
Because of Variance. Even a casino, which has a mathematical advantage, can lose money to a player in a short session. To get your probability closer to 100%, you need to increase the number of bets (sample size) to allow your edge to overcome the standard deviation.