Advanced Moneyline Strategy

This guide assumes you understand basic probability and are comfortable with quantitative approaches to betting. If you're looking to move beyond gut instinct and into systematic edge-finding, here's how to structure your thinking.

Bayesian Probability Updates

Most bettors have a starting belief about win probability—maybe from power ratings or market consensus. But information changes constantly. Bayes' theorem lets you update your estimate systematically when new information arrives.

The Formula

$P(\theta | \text{data}) = \frac{P(\text{data} | \theta) \cdot P(\theta)}{P(\text{data})}$

Where:

• $\theta$ = the outcome you're estimating (e.g., "Celtics win")
• $P(\theta)$ = prior probability - what you thought before new information
• $P(\text{data} | \theta)$ = likelihood - how probable this new data is, assuming your prior is correct
• $P(\text{data})$ = evidence - overall probability of seeing this data
• $P(\theta | \text{data})$ = posterior probability - your updated belief after new information

Concrete Example

Setup:

• Your model says Celtics have 60% chance to win tonight
• Breaking news: Jayson Tatum (their star) is questionable with ankle injury
• Historical data: Teams lose ~8% win probability when their best player sits

Calculation:

1. Prior: $P(\text{Celtics win}) = 0.60$
2. Evidence: Tatum injury report suggests 50% chance he sits
3. Impact if he sits: Win probability drops to $0.60 - 0.08 = 0.52$
4. Impact if he plays: Win probability stays $0.60$

Updated estimate: $P(\text{Celtics win | injury report}) = 0.50 \times 0.52 + 0.50 \times 0.60 = 0.56$

Your new probability is 56% instead of 60%.

Now compare to the line:

• If the line still implies 60% (Celtics -150), you might have value on the opponent
• If the line already moved to imply 56% (Celtics -127), the market already priced it in

Key Insight: Don't just react to news. Quantify how much it should move your estimate, then check if the market overreacted or underreacted.

Correlated Parlays

Standard parlay math assumes independence. If two bets each have 50% win probability, a two-leg parlay should have 25% win probability ($0.5 \times 0.5 = 0.25$).

But what if those bets are correlated?

Understanding Correlation

Positive correlation: If Bet A wins, Bet B is more likely to win Negative correlation: If Bet A wins, Bet B is less likely to win

Example: Same-Game Parlay

Independent bet math:

• Lakers moneyline: 60% chance
• Lakers -5.5 spread: 55% chance
• If independent: $0.60 \times 0.55 = 33\%$ parlay probability

But they're correlated!

If the Lakers win outright (moneyline), they're very likely to cover -5.5. Let's say:

• If Lakers win by 1-5 points: 15% of their wins
• If Lakers win by 6+ points: 85% of their wins

Real parlay probability:

1. Lakers win by 6+: $0.60 \times 0.85 = 51\%$ (both bets hit)
2. Lakers win by 1-5: $0.60 \times 0.15 = 9\%$ (ML hits, spread misses)
3. Lakers lose: 40% (both bets miss)

Parlay actually wins 51% of the time, not 33%!

The Sportsbook's Response

Books know about correlation. They adjust same-game parlay odds to compensate. You might get +150 instead of the +200 you'd expect from independent bets.

But: If you can model correlations better than the book, you can find mispriced parlays.

Pro Tip: Build a correlation matrix of common bet combinations. Track how often Lakers ML + Lakers spread both hit vs. what independence would predict.

Sharpe Ratio: Measuring Risk-Adjusted Returns

If you're making multiple bets over time, you don't just care about profit—you care about how much risk you took to get that profit.

The Formula

$\text{Sharpe} = \frac{E[R] - R_f}{\sigma}$

Where:

• $E[R]$ = expected return (average profit per bet)
• $R_f$ = risk-free rate (usually 0 for betting)
• $\sigma$ = standard deviation of returns (how much your results vary)

Higher Sharpe = Better risk-adjusted performance

Practical Example

Strategy A: Betting Heavy Favorites

• Average return: 2% per bet
• Standard deviation: 10%
• Sharpe: $\frac{0.02}{0.10} = 0.20$

Strategy B: Betting Moderate Underdogs

• Average return: 4% per bet
• Standard deviation: 30%
• Sharpe: $\frac{0.04}{0.30} = 0.13$

Analysis:

• Strategy B has higher expected return (4% vs 2%)
• But Strategy A has better risk-adjusted return (0.20 vs 0.13)
• You can bet more of Strategy A because it's less volatile

Why This Matters

You have $10,000 bankroll. Which strategy do you bet more on?

Strategy A (high Sharpe): Bet 3-5% per game ($300-500)

• Less volatile = can bet bigger without risking ruin

Strategy B (low Sharpe): Bet 1-2% per game ($100-200)

• More volatile = need smaller bets to survive variance

Key Takeaway: Don't just chase the highest ROI. A consistent 3% ROI beats a volatile 5% ROI if you can compound the 3% with bigger bets.

Kelly Criterion for Moneylines

Kelly tells you the optimal bet size to maximize long-term bankroll growth given your edge.

The Formula

$f^* = \frac{p(b+1) - 1}{b}$

Where:

• $f^*$ = fraction of bankroll to bet
• $p$ = your estimated win probability
• $b$ = decimal odds minus 1

Step-by-Step Example

Scenario:

• You think Suns have 45% chance to win
• Line: Suns +150 (+150 American = 2.50 decimal)
• Your bankroll: $5,000

Step 1: Convert odds to b

$b = \text{decimal odds} - 1 = 2.50 - 1 = 1.5$

Step 2: Apply Kelly formula

$f^* = \frac{0.45(1.5 + 1) - 1}{1.5} = \frac{0.45(2.5) - 1}{1.5} = \frac{1.125 - 1}{1.5} = \frac{0.125}{1.5} = 0.083$

Full Kelly says bet 8.3% of bankroll

Step 3: Calculate dollar amount

$0.083 \times 5000 = 415$

Bet $415 on this game.

Fractional Kelly (Recommended)

Full Kelly is aggressive. Most pros use Half Kelly or Quarter Kelly:

• Half Kelly: $0.083 \times 0.5 = 4.15\%$ → Bet $208
• Quarter Kelly: $0.083 \times 0.25 = 2.1\%$ → Bet $104

Why use fractional Kelly?

• Reduces bankroll swings
• Accounts for uncertainty in your probability estimate
• Still captures most of the growth

When Kelly Says Don't Bet

If your probability equals or is less than implied probability, Kelly tells you not to bet.

Example: Suns +150 (implies 40%)

• You think: 40% chance → $f^* = 0$ (no bet)
• You think: 38% chance → $f^* < 0$ (negative edge, definitely don't bet)

Warning: Kelly assumes your probability estimate is accurate. If you're overconfident, Kelly will make you bet too big and lose money faster.

Portfolio Allocation Across Multiple Bets

When you have multiple +EV bets on the same slate, you can't just Kelly each one individually. You need to consider how they interact.

The Core Insight

$\mathbf{f}^* = \Sigma^{-1}(\mu - r)$

This formula accounts for:

• $\Sigma$ = covariance matrix (how correlated your bets are)
• $\mu$ = expected returns vector
• $\mathbf{f}^*$ = optimal allocation for each bet

Practical Application

Scenario: You have 4 +EV bets tonight:

1. Lakers ML (+120) - 5% edge
2. Celtics ML (-110) - 3% edge
3. Nuggets ML (+150) - 6% edge
4. Warriors ML (-130) - 2% edge

If independent: Kelly says bet ~3% on each = 12% total bankroll

But they're on the same night:

• All NBA games are somewhat correlated (weather, refs, betting trends)
• If one favorite wins, other favorites are slightly more likely to win
• Correlation factor: ~0.15

Adjusted allocation: Bet ~2.5% on each = 10% total bankroll

The rule of thumb: If betting multiple games on one slate, reduce each individual Kelly by 15-25% to account for correlation.

Practical Tip: Don't deploy more than 10-15% of your bankroll in a single night, even with multiple +EV bets. Gives you cushion for variance.

Dynamic Hedging

Lines move. Sometimes you need to adjust your position mid-game or before tip-off.

When to Hedge

Scenario 1: Line moves in your favor

You bet Nuggets +180 early. By game time, line is +140.

Options:

• Do nothing (you already have the best line)
• Bet more if you still like the edge
• Small hedge on the other side to create a middle

Scenario 2: Line moves against you

You bet Warriors -5 early. By game time, line is -8.

This suggests:

• Sharp money came in on the opponent
• New information (injury, lineup change)
• Your original read might be wrong

Hedge calculation:

Original bet: $200 on Warriors -5 at -110 (to win $182)

To lock in profit:

• Bet opponent +8 for $100
• If opponent loses by 6-7: win both (+$282)
• If Warriors win by 8+: lose hedge, win original (+$82)
• If opponent wins or loses by ≤5: lose original, win hedge (+$91)

You've guaranteed profit between $82-282 depending on outcome.

Key Decision: Only hedge if you've lost confidence in your original read. Otherwise, you're giving up EV.

Tracking Realized vs Expected Results

You need to know if you're running bad (variance) or betting bad (poor model).

What to Track

For each bet:

• Your estimated win probability
• Actual result (W/L)
• Expected value
• Actual profit/loss

After 100+ bets:

Calculate your win rate by probability bucket:

Analysis:

• Small differences (-4%, +3%) = normal variance
• Large differences (-15%+) = your probability estimates are off

Chi-Square Test

$\chi^2 = \sum \frac{(\text{observed} - \text{expected})^2}{\text{expected}}$

If $\chi^2$ is very large relative to sample size, your model needs calibration.

Example: If you're consistently winning 47% when you estimated 52%, your probabilities are inflated. Recalibrate.

Final Thought

Advanced betting is about systematic edge extraction:

1. Bayesian updates = process new information correctly
2. Kelly sizing = bet the right amount given your edge
3. Sharpe optimization = choose strategies with best risk-adjusted returns
4. Portfolio management = manage correlation across multiple bets
5. Performance tracking = validate your model is actually working

But remember: garbage in, garbage out. The best math can't fix bad probability estimates. Focus on improving your model first, then optimize bet sizing.