Chapter 13 Key Takeaways: Value Betting Theory and Practice

Key Concepts

Value betting is the systematic identification and exploitation of bets where your estimated true probability exceeds the implied probability from the odds. It is the intellectual core of professional sports betting --- without positive expected value, no amount of bankroll management or line shopping can produce long-term profit.
True probability estimation can be model-based (building an explicit prediction model from features), market-based (using sharp closing lines as the best available probability), or a hybrid that combines both. Most professionals use a hybrid approach where the model identifies the direction and the market validates the magnitude.
The Bayesian log-odds combination is the correct way to merge model and market probabilities. Working in log-odds (logit) space respects the multiplicative nature of odds and handles extreme probabilities correctly, unlike simple linear averaging.
Edge thresholds must account for estimation uncertainty, not just the point estimate. A 5% estimated edge with 10% uncertainty is less valuable than a 3% edge with 2% uncertainty. The ValueRating framework classifies bets from NO_VALUE to VERY_STRONG based on the lower bound of the edge confidence interval.
Multi-factor value scoring evaluates bets on six dimensions: edge size (0.35 weight), CLV track record (0.20), market efficiency (0.15), liquidity (0.10), portfolio diversification (0.10), and timing (0.10). Edge is necessary but not sufficient --- a high-edge bet with poor liquidity or high portfolio correlation may be inferior to a moderate-edge bet with better overall characteristics.
Bet tracking must be comprehensive: record odds at placement, closing odds, stake, result, your probability estimate, model version, sportsbook, and qualitative reasoning. Without this data, you cannot calculate CLV, identify market-specific strengths, or detect edge decay.
The sample size problem is severe. Confirming a 3% ROI edge at standard -110 juice requires approximately 4,268 bets at 95% confidence and 80% power. CLV converges far faster than win rate (approximately 20:1 speed advantage), making it the essential skill metric.
Regression to the mean means early results are unreliable. A 3% ROI bettor is only profitable 67% of the time over 200 bets. Trust the process (CLV), not the early outcomes.
Every edge has a lifecycle: discovery, exploitation, correction, adaptation. No edge lasts forever. The sports betting market is adversarial, with sportsbooks continuously improving their models and other sharp bettors competing for the same inefficiencies.

Key Formulas

Formula	Description
$P(A) = \frac{1}{1 + 10^{-\Delta / 400}}$	Elo win probability, where $\Delta$ is rating difference
$\text{Edge} = \frac{p_{\text{true}}}{p_{\text{implied}}} - 1$	Percentage edge on a bet
$\text{logit}(p) = \ln\!\left(\frac{p}{1-p}\right)$	Log-odds transformation
$p_{\text{combined}} = \text{inv\_logit}\!\left(w_m \cdot \text{logit}(p_m) + w_k \cdot \text{logit}(p_k)\right)$	Bayesian probability combination
$f^* = \frac{pb - q}{b}$	Full Kelly criterion ($b$ = decimal odds $- 1$, $p$ = win prob)
$\text{Brier} = \frac{1}{N}\sum_{i=1}^{N}(p_i - o_i)^2$	Brier score (lower is better)
$n \geq \left(\frac{(z_\alpha + z_\beta)\sigma}{\text{ROI}}\right)^2$	Required sample size for edge confirmation
$\text{CLV} = p_{\text{closing}} - p_{\text{placed}}$	Closing Line Value in implied probability

Quick-Reference Decision Framework

Use this 5-step process for every potential bet:

Step 1: Estimate True Probability

Run your model to get $p_{\text{model}}$
Obtain the no-vig closing probability $p_{\text{market}}$ from a sharp book
Combine using Bayesian log-odds: $p_{\text{combined}} = \text{inv\_logit}(w_m \cdot \text{logit}(p_m) + w_k \cdot \text{logit}(p_k))$

Step 2: Calculate Edge and Confidence

Edge = $p_{\text{combined}} / p_{\text{implied}}(\text{best odds}) - 1$
Compute 95% CI on edge using your probability uncertainty
Determine confidence that edge > 0 using the z-score of $(p_{\text{combined}} - p_{\text{implied}}) / \sigma_p$

Step 3: Apply Minimum Threshold

Standard markets: require 2% minimum edge (adjusted by confidence)
Props/less efficient markets: require 3% minimum edge
Live/fast-moving markets: require 4% minimum edge
If estimated edge falls below threshold at conservative end, pass

Step 4: Size the Bet

Compute full Kelly: $f^* = (pb - q) / b$
Apply Kelly fraction (typically 0.20-0.30)
Adjust by confidence level: $f_{\text{adj}} = f^* \times \text{fraction} \times \min(\text{confidence}, 1)$
Stake = $f_{\text{adj}} \times \text{bankroll}$

Step 5: Record and Monitor

Log all bet details (odds, closing odds, model probability, stake, book, timing)
Track rolling CLV over 100-bet windows
If rolling CLV drops below +1.0%, trigger a model review
Conduct quarterly reviews of performance by sport, market, and book

Self-Assessment Checklist

Before moving to Chapter 14, verify that you can:

[ ] Explain the difference between model-based and market-based probability estimation and when to use each
[ ] Implement the Bayesian log-odds combination method and explain why it is superior to linear averaging
[ ] Calculate edge, edge confidence intervals, and the probability that an edge is positive
[ ] Use the ValueRating framework to classify potential bets from NO_VALUE to VERY_STRONG
[ ] Describe the multi-factor value scoring system and explain why edge alone is insufficient
[ ] List the essential fields to track for every bet and explain why each is necessary
[ ] Calculate the required sample size to confirm a given ROI edge at specified confidence and power
[ ] Explain why CLV converges faster than win rate as a skill metric
[ ] Compute rolling CLV and interpret the results for edge decay detection
[ ] Describe the four stages of the edge lifecycle and give examples of each
[ ] Design a quarterly review process that evaluates performance across multiple dimensions
[ ] Implement the Kelly criterion with confidence adjustment and explain why fractional Kelly is preferred