Probability & Bankroll Math

The Science of Value Betting: Finding Positive Expected Value (+EV)

By WagerSensei AnalyticsUpdated August 20267 min read

In sports betting, value is the only sustainable edge over the bookmaker. You do not need to predict the winner of every match; you only need to wager when the probability of an outcome is higher than the implied probability reflected in the bookmaker's decimal odds.

1. Implied Probability and the Bookmaker Margin (Vig)

Decimal odds can be converted into implied probability using the formula:

Implied Probability (%) = (1 / Decimal Odds) × 100

In a fair two-way market (e.g. Over/Under 2.5 goals), the probabilities should sum to 100%. In reality, bookmakers set odds such that probabilities sum to 105%–110%. The excess percentage is the overround or vigorish.

2. The Expected Value Formula

A bet represents positive expected value (+EV) when:

EV = (Probability of Winning × Profit per Bet) - (Probability of Losing × Stake)

If EV > 0, placing this wager over a large sample size guarantees positive theoretical return.

3. Bankroll Staking: The Fractional Kelly Criterion

Even with positive expected value, incorrect bet sizing can lead to catastrophic drawdown. The Kelly Criterion determines optimal stake fraction f*:

f* = (b × p - q) / b

Where b = decimal odds - 1, p = true estimated win probability, and q = 1 - p.

Pro Tip: Professional bettors rarely use Full Kelly due to variance. At WagerSensei, our recommended staking model employs Quarter Kelly (0.25 × f*) or fixed unit sizing (1u–4u) to preserve bankroll longevity.

Track Our Verified Performance

All WagerSensei tips strictly adhere to +EV criteria with audited win rates, ROI, and closing-line value (CLV).