Case Study: Are Closing Lines Really Efficient?

Executive Summary

The proposition that closing betting lines are efficient --- that they represent the market's best, unbiased estimate of the true probability of each outcome --- is one of the most important claims in sports betting theory. If closing lines are efficient, then Closing Line Value (CLV) is a valid measure of bettor skill, and any strategy that consistently beats the closing line has genuine long-term edge. If closing lines are systematically biased, then CLV is a flawed metric and the entire framework for evaluating bettor performance must be reconsidered. This case study tests the efficiency of NFL closing lines using a synthetic dataset of 2,720 games spanning five seasons. Through calibration analysis, the Brier score decomposition, and tests for specific biases (favorite-longshot, home-away, and primetime effects), we find that closing lines are remarkably well-calibrated overall but exhibit small, persistent biases in specific contexts. These findings have practical implications for how bettors should use CLV and where they should focus their search for value.

Background

What Does "Efficient" Mean?

In financial economics, a market is said to be efficient if prices fully reflect all available information. Applied to sports betting, an efficient closing line is one where the implied probability (after removing the vig) accurately predicts the frequency of outcomes over a large sample.

Formally, a closing line is well-calibrated if, for all probability thresholds p:

P(outcome = 1 | implied_probability = p) = p

In other words, among all games where the closing line implies a 60% chance of the favorite winning, the favorite should win approximately 60% of the time. Deviations from this ideal reveal systematic biases that bettors can potentially exploit.

There are several levels of efficiency to consider:

1. Unbiasedness: Does the closing line systematically overestimate or underestimate outcomes in any category?

2. Calibration: Across the full range of probabilities, do outcomes match predictions?

3. Profitability: Can any systematic strategy (based on publicly available information at closing time) generate positive returns after the vig?

These are increasingly strong tests. A market can be well-calibrated without being profitable to bet into (because the vig absorbs the edge). Our analysis examines all three.

The Dataset

We constructed a synthetic dataset modeled on publicly available NFL results and closing lines from the 2019-2023 seasons. The dataset contains:

• 2,720 regular-season games (272 games per season x 5 seasons x 2 sides per game = 5,440 team-game observations, though we analyze at the game level)
• Closing spread, moneyline, and total for each game from a composite of four sportsbooks
• No-vig closing probabilities calculated using the multiplicative removal method
• Actual game results: final scores, margins, and binary outcome indicators

The data was generated to reflect documented patterns in NFL betting markets, including known biases and efficiency characteristics, so that the analysis demonstrates realistic findings.

The Analysis

Test 1: Overall Calibration

Our first test bins the 2,720 games by the no-vig closing implied probability of the favorite and compares the actual win rate within each bin.

Results:

Interpretation:

The calibration is impressive. In every bin, the actual win rate is within 2 percentage points of the bin midpoint, and in most bins the deviation is under 1 percentage point. The largest deviation occurs in the 80-90% bin, where the actual win rate of 79.8% is 5.2 percentage points below the midpoint of 85.0%. However, this bin contains only 94 games, and the 95% confidence interval for the true win rate is approximately 71.5% to 88.1%, which comfortably includes 85%.

Brier Score:

The overall Brier score for the closing-line implied probabilities is 0.2134. For context:

• A naive model predicting 50% for every game would produce a Brier score of 0.2500.
• A perfect model (knowing every outcome) would score 0.0000.
• Published estimates for NFL closing-line Brier scores in the academic literature range from 0.210 to 0.220.

Our score of 0.2134 is squarely in the expected range, confirming that the synthetic data replicates the calibration properties of real NFL closing lines.

Test 2: Brier Score Decomposition

The Brier score can be decomposed into three components: reliability (calibration error), resolution (the model's ability to distinguish outcomes), and uncertainty (the inherent unpredictability of outcomes).

Decomposition Results:

The reliability component of 0.0008 is extremely small, confirming excellent calibration. The resolution of 0.0374 indicates that the closing line does meaningfully differentiate between games where the favorite has a high probability of winning and games that are close to a coin flip. The bulk of the Brier score comes from the irreducible uncertainty of NFL outcomes --- football is simply a noisy sport where even the best predictions leave substantial room for upsets.

Test 3: The Favorite-Longshot Bias

To test for the favorite-longshot bias, we compare the actual return on investment (ROI) for bets on favorites versus underdogs at various price points.

Moneyline ROI by Odds Range:

Interpretation:

The favorite-longshot bias is clearly present. As we move from favorites to underdogs, the ROI becomes increasingly negative. Heavy favorites (-300 to -201) have an ROI of -1.8%, which is close to the theoretical vig cost. Moderate underdogs (+121 to +150) have an ROI of -7.1%, and large underdogs (+201 to +300) show a devastating ROI of -14.3%.

This means that the closing line, while well-calibrated overall, contains a systematic bias: longshot probabilities are inflated relative to their true frequency. A bettor who blindly bet every favorite would lose less to the vig than a bettor who blindly bet every underdog.

However, this does not mean favorites are profitable to bet. The -1.8% ROI on heavy favorites still represents a loss. The bias is real but insufficient to overcome the vig in most cases.

Test 4: Home-Away Bias

We test whether the closing line systematically misprice home and away teams.

Spread Cover Rates:

Interpretation:

Home underdogs show the highest cover rate at 52.4%, consistent with well-documented findings in the literature. However, the 95% confidence interval (49.1% to 55.7%) includes 50%, so even over 892 games this result is not statistically significant at conventional levels.

Away favorites show the lowest cover rate at 47.6%. The direction is consistent with a bias where the market slightly overvalues prominent teams traveling to play lesser opponents, but again the confidence interval includes 50%.

Profitability Test:

Blindly betting all home underdogs at -110 over the five-season period:

• 892 bets x $100 = $89,200 wagered
• 467 wins x $90.91 = $42,455 profit from wins
• 425 losses x $100 = $42,500 in losses
• Net: -$45 (essentially break-even)
• ROI: -0.05%

The home underdog edge, if it exists, is too small to generate profit after the vig. The market has priced it in almost exactly.

Test 5: Primetime Game Bias

Primetime games (Thursday Night Football, Sunday Night Football, Monday Night Football) receive disproportionate public attention and betting volume. We test whether closing lines for primetime games are less efficient.

Results:

Interpretation:

There is a clear gradient: primetime games have slightly higher (worse) Brier scores and lower favorite cover rates compared to the Sunday main slate. This pattern is consistent with the hypothesis that public attention inflates the lines on primetime favorites (typically the more popular teams scheduled in marquee slots), creating marginal value on primetime underdogs.

The underdog moneyline ROI improves from -6.4% on early Sunday games to -2.8% on Thursday Night Football. While none of these are profitable after the vig, the difference between -6.4% and -2.8% is substantial and suggests that the closing line is slightly less efficient for primetime games.

Test 6: Can CLV Predict Profitability?

To validate CLV as a skill metric, we simulated 100 bettors with varying levels of skill, each placing 300 bets over the five-season dataset. "Skill" was modeled as the ability to predict closing line movements: skilled bettors bet early on the side that the line will eventually move toward, while unskilled bettors bet randomly.

Results (Simulated):

The correlation between average CLV and ROI across the 100 simulated bettors is r = 0.87, confirming a very strong relationship. Bettors in the top CLV quintile are profitable 85% of the time over 300 bets, while those in the bottom quintile are almost never profitable.

Key Findings

1. NFL closing lines are remarkably well-calibrated. The Brier score of 0.2134 and the near-zero reliability component confirm that closing probabilities accurately predict outcome frequencies across the full range of implied probabilities.

2. The favorite-longshot bias is present but insufficient to profit from. Longshots are systematically overpriced relative to favorites, but the vig absorbs the potential edge in most cases. The bias is most pronounced for underdogs of +200 or longer.

3. Home underdog and primetime biases exist but are marginal. Home underdogs cover slightly above 50% and primetime underdogs offer slightly better value, but neither pattern is consistently profitable after the vig.

4. CLV is a validated predictor of profitability. The simulation confirms an r = 0.87 correlation between CLV and ROI, supporting the use of CLV as the primary metric for evaluating bettor skill.

5. The market is efficient enough to make blind contrarian strategies unprofitable but not so efficient that informed bettors cannot find edges. This is the hallmark of semi-strong form efficiency.

Practical Implications

For bettors, these findings suggest several actionable conclusions:

Use CLV as your primary diagnostic. The strong CLV-ROI correlation validates CLV as a skill measure. Track your CLV on every bet and evaluate your process based on CLV trends, not short-term win rate.

Do not blindly bet favorites or underdogs. The favorite-longshot bias is real but not exploitable through simple strategies. You need a model that identifies specific mispricings, not a blanket approach.

Look for value in primetime and high-profile games. These markets attract disproportionate public money, which can inflate lines beyond fair value. The marginal reduction in efficiency for these games represents opportunity.

Respect the closing line. The market's calibration is excellent. If you consistently find yourself on the wrong side of the closing line (negative CLV), it is more likely that your process is flawed than that the market is wrong.

Focus on the margins. The market is efficient enough that edges are measured in 1-3% of implied probability, not 10%. Small advantages in line shopping, timing, and market selection compound over hundreds of bets into meaningful profit.

Discussion Questions

1. If the closing line is well-calibrated, why do sportsbooks still generate significant profit? How does the relationship between calibration and the vig work?

2. The favorite-longshot bias has been documented for decades. If it is well-known, why does it persist? What market forces sustain it?

3. Our simulation found that bettors need approximately 300+ bets to reliably distinguish skill from luck using CLV. A recreational bettor places 100 bets per season. How should they evaluate their performance given this sample-size constraint?

4. If the market becomes more efficient over time (as technology and information access improve), what happens to the edges available to sharp bettors? Is there a theoretical limit to market efficiency?

5. Design an experiment to test whether opening lines or closing lines produce better Brier scores. What would the result imply about the value of the information incorporated during the life of the market?