12 min read
How to Calculate Expected Value (EV)
Learn the mathematical formulas and practical applications for quantifying betting edge
Understanding Expected Value
Expected Value (EV) is the most important concept in betting mathematics. It represents the average amount you can expect to win or lose per bet over the long run. Positive EV (+EV) bets are the foundation of profitable betting.
EV Formula:
EV = (Probability of Win × Amount Won) - (Probability of Loss × Amount Lost)
For decimal odds:
EV = (Probability × Decimal Odds × Stake) - Stake
Step-by-Step EV Calculation
Example 1: Simple Bet
Bet: R100 on Springboks at odds of 2.20
Your assessed probability: 50%
Step 1: Win amount = R100 × 2.20 = R220
Step 2: Net profit if win = R220 - R100 = R120
Step 3: EV = (0.50 × R120) - (0.50 × R100)
Step 4: EV = R60 - R50 = R10
This bet has a positive EV of R10 per R100 wagered (10% edge)
Example 2: Underdog Value
Bet: R100 on England at odds of 4.50
Your assessed probability: 28% (bookmaker implies 22%)
Step 1: Win amount = R100 × 4.50 = R450
Step 2: Net profit if win = R450 - R100 = R350
Step 3: EV = (0.28 × R350) - (0.72 × R100)
Step 4: EV = R98 - R72 = R26
Strong value bet with 26% positive EV despite being the underdog
ROI vs EV
Return on Investment (ROI) expresses EV as a percentage of the stake:
ROI = (EV / Stake) × 100%
In Example 2: ROI = (R26 / R100) × 100% = 26%
Common EV Misconceptions
- •Myth: "I lost, so the bet had negative EV"
Reality: Individual results don't determine EV. A +EV bet can lose and a -EV bet can win. - •Myth: "Higher odds always mean better value"
Reality: Value depends on probability accuracy, not odds size. A favorite can offer more value than an underdog. - •Myth: "Small edges aren't worth betting"
Reality: Professional bettors profit from 2-5% edges with proper bankroll management.
Practical Applications
Use EV calculations to compare betting opportunities. Always choose the bet with the highest EV, not the highest odds or perceived "safest" option. Track your estimated EV versus actual results to validate and refine your probability models.
