Why Portfolio Theory Applies to Betting
The Core Insight: A weekend with 8 individual bets isn't just 8 separate decisions—it's a portfolio. The bets interact through correlation, and your total risk/reward depends on how you allocate across them, not just whether each is +EV individually.
Modern Portfolio Theory (MPT), developed by Harry Markowitz in 1952, revolutionized investing by proving that diversification reduces risk without sacrificing returns. The same mathematics applies perfectly to sports betting—but almost no one uses it.
Most bettors think in single bets: "Is this +EV? Yes. Bet." But professionals think in portfolios: "How does this bet interact with my other positions? Does it increase or decrease my overall risk-adjusted return?"
Modern Portfolio Theory Fundamentals
The Three Pillars of MPT
Expected profit from each position
= Edge × Odds
Variance of possible outcomes
= Standard Deviation
How positions move together
= -1 to +1
The Efficient Frontier
In investing, the "efficient frontier" is the set of portfolios that offer the highest return for each level of risk. In betting, we can construct the same curve by combining bets with different odds and correlation profiles.
| Portfolio Type | Expected Return | Risk (Std Dev) | Sharpe Ratio | Best For |
|---|---|---|---|---|
| All Favorites (-200 avg) | +2.1% | 8.2% | 0.26 | Grinders |
| Mixed (70% Fav / 30% Dog) | +3.8% | 14.5% | 0.26 | Balanced |
| Efficient Frontier Optimal | +4.2% | 12.8% | 0.33 | Sharp Bettors |
| All Longshots (+250 avg) | +5.5% | 28.4% | 0.19 | Risk Seekers |
Key Insight: The "Efficient Frontier Optimal" portfolio has the BEST Sharpe ratio (return per unit of risk) by strategically combining uncorrelated bets. This is where round robins shine—they let you build these optimized portfolios.
Understanding Correlation in Betting
Correlation is the secret weapon of portfolio construction. Two bets that are positively correlated will often win or lose together, providing no diversification benefit. Negatively correlated or uncorrelated bets smooth out variance dramatically.
| Bet Pair | Correlation | Diversification | Portfolio Effect |
|---|---|---|---|
| Chiefs ML + Chiefs -6.5 | +0.95 | Very Low | Nearly identical exposure |
| NFL Team Total O + Game Total O | +0.78 | Low | Correlated scoring outcomes |
| NFL Game + NBA Game (same day) | +0.05 | High | True diversification |
| Favorite ML + Underdog ML (diff game) | -0.15 | Very High | Hedge-like protection |
| Over (high-scoring game) + Under (low-scoring) | -0.08 | Very High | Balanced total exposure |
The Correlation Matrix
Typical correlations between bet types (NFL):
| Spread | ML | Total O | Total U | Team O | 1H Spread | |
|---|---|---|---|---|---|---|
| Spread | 1.00 | 0.85 | 0.15 | -0.15 | 0.32 | 0.68 |
| Moneyline | 0.85 | 1.00 | 0.12 | -0.12 | 0.28 | 0.55 |
| Total Over | 0.15 | 0.12 | 1.00 | -1.00 | 0.78 | 0.45 |
Building Your Bet Portfolio
Step 1: Define Your Risk Profile
- • Target: 2-4% weekly return
- • Max drawdown tolerance: 10%
- • 80% favorites, 20% underdogs
- • Round robin 2s and 3s
- • Target: 4-8% weekly return
- • Max drawdown tolerance: 20%
- • 60% favorites, 40% underdogs
- • Round robin 2s, 3s, and 4s
- • Target: 10-20% weekly return
- • Max drawdown tolerance: 40%
- • 40% favorites, 60% underdogs
- • Round robin 3s, 4s, and 5s
Step 2: Select Your Assets (Bets)
A well-diversified betting portfolio should include multiple "asset classes":
Core Holdings (60-70%)
- • NFL/NBA spreads at -110
- • Game totals at -110
- • Small favorites (-150 to -200)
- • Consistent edge, low variance
Satellite Holdings (30-40%)
- • +EV underdogs (+150 to +300)
- • Player props with edge
- • Cross-sport diversification
- • Higher return potential, higher variance
Step 3: Determine Position Sizing
Use the Kelly Criterion to determine optimal allocation, but remember: Kelly assumes you know your true edge perfectly. In practice, use fractional Kelly (1/4 to 1/2) for each position.
| Bet Type | Est. Edge | Full Kelly | 1/4 Kelly | Portfolio % |
|---|---|---|---|---|
| NFL Spread (-110) | +3.0% | 3.3% | 0.8% | 15% |
| NBA Total (-110) | +2.5% | 2.8% | 0.7% | 12% |
| NFL Underdog ML (+180) | +5.0% | 2.8% | 0.7% | 10% |
| NHL Puckline (+145) | +4.0% | 2.7% | 0.7% | 8% |
| Round Robin Reserve | — | — | — | 55% |
Round Robins: The Portfolio Insurance
Round robins aren't just a "safer parlay"—they're a structured way to build correlation-aware portfolios. Different combination sizes create different risk/reward profiles.
Example: 5 Picks, Different Portfolio Structures
Picks: NFL Spread A (-110), NFL Spread B (-110), NFL Underdog ML (+180), NBA Total (-110), NHL ML (-150)
| Structure | # Bets | $ Per Bet | Total Risk | Max Win | Break-Even |
|---|---|---|---|---|---|
| 5-Team Parlay | 1 | $100 | $100 | $2,847 | 5/5 (100%) |
| Round Robin 4s | 5 | $20 | $100 | $1,892 | 4/5 (80%) |
| Round Robin 3s | 10 | $10 | $100 | $1,127 | 3/5 (60%) |
| Round Robin 2s | 10 | $10 | $100 | $485 | 2/5 (40%) |
| Optimal Mix (2s + 3s) | 20 | $5 | $100 | $806 | ~2.5/5 (50%) |
The Optimal Mix: Combining 2-team and 3-team round robins gives you the best risk-adjusted return. You profit with just 2-3 winners, but still capture upside when you hit 4-5. This is the "efficient frontier" of round robin betting.
Simulating Portfolio Outcomes
Use the Monte Carlo Simulator to model 10,000+ possible outcomes for your portfolio. This reveals the true distribution of results—not just expected value, but the full range from worst-case to best-case.
Sample Portfolio: 52-Week Simulation Results
$1,000 bankroll, 5% of bank per week, 55% win rate at -110
5th Percentile
$642
-35.8% worst case
25th Percentile
$892
-10.8% unlucky
Median (50th)
$1,156
+15.6% typical
95th Percentile
$1,687
+68.7% lucky
Key Metrics to Track
Sharpe Ratio
(Expected Return - Risk-Free Rate) / Standard Deviation. Higher is better. Target: 0.3+ for betting portfolios.
Max Drawdown
The largest peak-to-trough decline. Tells you how much pain to expect. Target: Less than 30% of bankroll.
Risk of Ruin
Probability of losing your entire bankroll. Must be under 5% for survival. Use quarter-Kelly to minimize.
Win Rate Distribution
How often you have profitable weeks. Target: 55%+ weekly profit rate for sustainable growth.
The 5-Step Portfolio Construction Process
Define Weekly Budget & Risk Tolerance
Use Risk of Ruin Calculator to determine total weekly allocation (typically 5-10% of bankroll). Define max acceptable loss for the week.
Select 5-8 Uncorrelated +EV Bets
Mix sports (NFL, NBA, NHL), bet types (spreads, totals, MLs), and risk profiles (favorites, underdogs). Check correlation matrix to ensure diversification.
Size Positions with Kelly
Use Kelly Criterion Calculator for each bet. Apply 1/4 Kelly for safety. Allocate remaining budget to round robin combinations.
Structure Round Robin Combinations
Use Round Robin Calculator to build 2s and 3s for balanced risk. For aggressive portfolios, add 4s. Avoid 5+ team combinations—they're lottery tickets.
Simulate & Validate
Run your portfolio through Monte Carlo Simulator 10,000 times. Check Sharpe ratio, max drawdown, and risk of ruin. Adjust until metrics are acceptable.
Real Example: NFL Sunday Portfolio
Bankroll: $5,000 | Weekly Budget: $500 (10%)
Core Positions (45% = $225)
- • Chiefs -3.5 (-110): $75
- • Eagles -6.5 (-110): $75
- • Ravens/Bengals O47.5 (-110): $75
Satellite Positions (20% = $100)
- • Dolphins ML (+165): $50
- • Texans ML (+180): $50
Round Robin Structure (35% = $175)
2-Team Combos (10 bets × $10):
All 10 possible 2-team parlays
3-Team Combos (10 bets × $7.50):
All 10 possible 3-team parlays
Outcome Scenarios
2/5 Winners
Loss: -$186
3/5 Winners
Profit: +$124
4/5 Winners
Profit: +$512
5 Common Portfolio Mistakes
Correlated Positions Disguised as Diversification
Betting Chiefs spread AND Chiefs ML isn't diversification—it's concentrated risk. Check the correlation matrix.
Using Full Kelly Sizing
Full Kelly is mathematically optimal but practically suicidal. Use 1/4 Kelly to survive inevitable estimation errors.
Ignoring Transaction Costs (Vig)
Each leg in a round robin carries vig. More legs = more vig drag. Keep combinations to 2s and 3s.
Chasing Losses with Larger Positions
Portfolio theory demands consistent sizing. A bad week doesn't change the math—stick to your allocation percentages.
Not Rebalancing as Bankroll Changes
If your bankroll grows 50%, your position sizes should grow 50%. Use the Unit Size Calculator weekly.
Key Takeaways
- Think in portfolios, not bets—your weekly slate is a collection of correlated assets, not independent wagers
- Diversification reduces risk—uncorrelated bets across sports, bet types, and favorites/underdogs smooth out variance
- Round robins are portfolio insurance—2s and 3s give optimal risk-adjusted returns by requiring fewer winners to profit
- Use quarter-Kelly sizing—protects against edge estimation errors while still maximizing long-term growth
- Simulate before you bet—Monte Carlo shows the full distribution of outcomes, not just expected value