---
title: "Are Betting Markets Efficient? Evidence from European Football Championships"
authors:
  - name: "Alexis Direr"
    affiliation: "Laboratoire d'Économie d'Orléans (LEO), Université d'Orléans; Paris School of Economics"
date: "2011-07"
doi: "10.1080/00036846.2011.602010"
keywords: [decision-making under risk, information, market efficiency, betting markets, favourite-longshot bias, European football, fixed-odds]
jel_codes: [D81, G14]
language: en
type: research-article
journal: "Applied Economics"
---

# Are Betting Markets Efficient? Evidence from European Football Championships

**Author**
- Alexis Direr — Laboratoire d'Économie d'Orléans (LEO), Université d'Orléans, and Paris School of Economics — *direr@ens.fr*

**DOI**: [10.1080/00036846.2011.602010](https://doi.org/10.1080/00036846.2011.602010)

**Keywords**: decision-making under risk, information, market efficiency, betting markets, favourite-longshot bias, fixed-odds betting.
**JEL codes**: D81, G14.

---

## Abstract

This article investigates the degree of efficiency of the European Football online betting market by using odds quoted by 12 bookmakers on 21 European championships over 11 years. We show that systematically picking out odds inferior to a threshold delivers a rate of return of 4.45% if best odds are selected across bookmakers and 2.78% if mean odds are used. This amounts to backing overwhelmingly favourites whose probability of winning exceeds 90%. Our results only exploit information contained in odds, are robust to the use of real-time data and different sample periods and hold under risk neutrality and expected utility preferences for realistic degrees of risk aversion. Transaction costs reduce profitability but only for small stake bets.

---

## 1. Motivation and contributions

The paper tests weak-form efficiency in the European football online betting market — the largest in Europe — using a uniquely large dataset of fixed-odds quotes. The central question is whether a simple, odds-only betting rule can deliver positive risk-adjusted returns that bettors and bookmakers have failed to arbitrage away. The setting offers cleaner identification of efficiency violations than financial markets, because bets have only two payoffs delivered a few days forward, the asset-pricing model is minimal, and learning conditions are favourable (Thaler and Ziemba 1988; Erev and Haruvy 2010).

The paper makes the following contributions.

1. **Documenting a profitable, odds-only betting rule.** Backing every outcome whose best odd is below a threshold around 1.19–1.21 generates a positive, statistically significant return without any forecasting model, complex econometrics, or covariates beyond the quoted odd itself. This contrasts with the broader sport-forecasting literature, in which neither statistical systems nor experts consistently outperform the market (Stekler, Sendor and Verlander 2010; Snowberg and Wolfers, forthcoming).

2. **Scale of the dataset.** The study uses 79,446 matches across 21 championships in 11 European countries from 2000 to 2011, with around 1,800,000 individual bookmaker odds. This is roughly an order of magnitude larger than the datasets used in prior football studies (Kuypers 2000: 3,382 matches; Dixon and Pope 2004: 6,629; Goddard and Asimakopoulos 2004: 8,144), enabling reliable inference on infrequent short-odds bets.

3. **Distinguishing fixed-odds from pari-mutuel pricing.** Most favourite-longshot bias evidence comes from pari-mutuel horse racing where mispricing is mechanically imputable to bettor behaviour. In a fixed-odds setting, bookmakers set prices and need not balance the books, so a decreasing odd–return profile may reflect optimal bookmaker pricing in the presence of biased bettors or insider traders (Shin 1991, 1992; Levitt 2004). The paper shows the bias is large enough in this fixed-odds market to generate net profit opportunities — implicating both sides of the market.

4. **Robustness battery.** Profitability is shown to survive: out-of-sample tests on rolling windows, real-time threshold computation, expected-utility preferences with realistic risk aversion, and transaction costs (for sufficiently large stakes). This rules out several standard explanations for apparent return anomalies in financial markets.

---

## 2. Data

**Source.** All match results, dates and bookmaker odds are downloaded from `football.data.co.uk`. Odds are recorded for the three possible outcomes (home win, away win, draw) of each match.

**Coverage.**
- 79,446 matches.
- 21 national championships across 11 European countries.
- 11 seasons, from 2000–01 through 2010–11.
- 12 online bookmakers accessible to British gamblers: Bet365, Blue Square, Bwin, Gamebookers, Interwetten, Ladbrokes, Sportingbet, Sporting Odds, Stan James, Stanleybet, Victor Chandler and William Hill.
- ≈ 1,800,000 odds in total (≈ 598,775 match–bookmaker triplets).

**Championships.** Top four leagues of England and Scotland; top two leagues of Germany, Italy, Spain and France; top leagues of Netherlands, Belgium, Portugal, Turkey and Greece. The fifth English league is excluded because data start only in 2005. All other championships are present from the first season onwards to avoid selection bias.

**Two odd measures.** For each match outcome, the paper uses (i) the **best odd** across all bookmakers covering the match, and (ii) the **mean odd** (arithmetic mean across all quoting bookmakers). The mean-odd return corresponds to the realistic case of a bettor who shops around to detect betting opportunities but executes the trade at their regular bookmaker.

**Bookmaker coverage by season.** The number of recorded bookmakers grows from 5 in 2000–01 to 10 in the most recent seasons. Match coverage per bookmaker is reported in Appendix A of the paper.

**Market structure.** European football betting is a fixed-odds market: bookmakers post odds several days before the match (typically Wednesday for the weekend) and rarely revise them during the betting window. Bookmakers do not balance the books, so prices need not reflect supply and demand for each outcome.

---

## 3. The mean return at different odds

Using best odds and pooling all seasons, championships and outcome types, the paper plots the mean rate of return as a function of odds, with 95% confidence intervals (Figure 1). Two facts emerge.

1. **A favourite-longshot bias is present.** Returns decrease with odds, although the relationship is noisier than in racetrack data and flattens out for odds above 3.5. This pattern is consistent with several mechanisms: risk-loving expected-utility bettors (Quandt 1986), probability weighting of small chances as in Prospect Theory (Snowberg and Wolfers, forthcoming), and bookmaker price-skewing in response to insider trading (Shin 1991, 1992).

2. **Short-odds bets earn a positive return.** Bets with odds below 1.21 yield approximately 4% with best odds. The 95% confidence interval excludes zero. For odds below 1.17, the positive return is statistically significant at the 99% level. With mean odds, returns are around 2% and only statistically positive for odds below 1.17.

### Confidence intervals on short-odds bets (extracted from Table B)

| Odd bracket | N bets | Win freq. (%) | Return best odds (%) | Return mean odds (%) | 95% CI |
|:---:|:---:|:---:|:---:|:---:|:---:|
| [1, 1.17) | 614 | 91.53 | +4.37 | +2.72 | ± 2.39 |
| [1.17, 1.21) | 504 | 86.71 | +3.90 | +1.84 | ± 3.53 |
| [1.21, 1.25) | 989 | 80.09 | −0.73 | −2.96 | ± 3.06 |

The pattern strongly suggests that the market underprices overwhelmingly favourite outcomes.

---

## 4. A simple odds-based betting rule

The headline strategy is: place a unit stake on every outcome whose best odd is at or below a threshold $\bar{q}$.

### 4.1 Instant returns by threshold

The instant return profile (Table 1) is hump-shaped. The maximum return is reached at $\bar{q} = 1.19$:

| Odd threshold | Number of bets | Win frequency (%) | Return best odds (%) | Return mean odds (%) |
|:---:|:---:|:---:|:---:|:---:|
| 1.17 | 614 | 91.53 | 4.37 | 2.72 |
| 1.18 | 659 | 91.35 | 4.40 | 2.73 |
| **1.19** | **661** | **91.38** | **4.45** | **2.78** |
| 1.20 | 1,111 | 89.38 | 4.16 | 2.32 |
| 1.21 | 1,118 | 89.36 | 4.15 | 2.33 |
| 1.24 | 1,455 | 87.97 | 3.61 | 1.72 |

The threshold $\bar{q} = 1.19$ generates 661 bets over 11 seasons (≈ 60 per season) and a 91.38% win frequency. Any threshold in [1.17, 1.21] yields a return greater than 4% with best odds. Restricting to bets in [1.16, 1.19) — a refinement of the rule — increases the return to 7.20% with best odds and 5.26% with mean odds, but the paper retains the simpler one-threshold rule for transparency.

### 4.2 Annualized rates of return

Bettors are assumed to stake £1 on every qualifying bet, reinvest the proceeds when possible (with a three-day no-reinvestment buffer), and withdraw end-of-season gains. Geometric mean of annual returns over the 11 seasons (Table 2):

| Odd threshold | Annualized return — best odds (%) | Annualized return — mean odds (%) |
|:---:|:---:|:---:|
| 1.18 | 78.73 | 43.94 |
| 1.19 | 77.47 | 43.18 |
| 1.20 | 103.54 | 51.79 |
| **1.21** | **106.11** | **52.54** |
| 1.22 | 63.11 | 22.96 |

The optimal threshold for the annualized criterion is $\bar{q} = 1.21$, slightly above the 1.19 found for instant returns — a consequence of the reinvestment opportunity. With a £1 unit stake, the average season-total stake is £4.80 and the average season-end gain is £9.90, implying an average annualized return of 106% with best odds (52% with mean odds).

---

## 5. Transaction costs

Transaction costs depend on the payment infrastructure and on the size of stakes.

- **Search costs** for best odds are negligible (free comparison websites).
- **Bank transfers** are free but slow (3–5 business days), making them inadequate for shopping across bookmakers in the short pre-match window.
- **Card deposits** are instant; some bookmakers charge a small percentage fee.
- **Money transfer sites (MTS)** are the realistic infrastructure for arbitrage across bookmakers. Two are studied: Moneybookers (1% fee, capped at £0.41, on transfers to bookmakers; £1.48 withdrawal) and Neteller (free transfers to bookmakers; £5 withdrawal).

### Annualized returns net of transaction costs (threshold 1.21)

| Stake | No costs | Moneybookers | Neteller |
|:---:|:---:|:---:|:---:|
| £10 | 106.11% | 75.06% | 93.01% |
| £100 | 106.11% | 94.74% | 104.81% |

Flat fees materially erode small-stake returns but become negligible for stakes ≥ £100. Even the worst case (Moneybookers, £10 stake) remains well above the mean-odds return of 52.54%, confirming the rule is profitable at realistic stakes. With a £100 unit stake and reinvestment, a typical season involves 102 qualifying bets, a £440 total stake, and an end-of-season gain of approximately £819 (Moneybookers) or £857 (Neteller).

---

## 6. Robustness

### 6.1 Persistence across seasons (Table 5)

Instant returns at threshold 1.19 are positive in 10 out of 11 seasons with best odds (9 out of 10 with mean odds). The unweighted mean instant return is **5.01%** (best odds) / **3.34%** (mean odds), with a 91.73% mean win frequency. Returns do **not** decline over time — the last three seasons (2008–09 to 2010–11) are among the most profitable, with returns of 12.39%, 8.79% and 7.80% respectively for best odds. Roughly eleven years of high profitability have not been arbitraged away.

### 6.2 Out-of-sample testing with real-time thresholds (Table 6)

For each season $t$, the optimal threshold is recomputed using only data up to season $t-1$, and applied to season $t+1$ and to all remaining seasons.

| Test | Best odds (%) | Mean odds (%) |
|:---:|:---:|:---:|
| Full-sample threshold (Section 4) | 5.01 | 3.34 |
| Real-time threshold, applied to next season only | 4.33 | 2.90 |
| Real-time threshold, applied to all remaining seasons | 5.04 | 3.29 |

Real-time updating reduces returns moderately (5.01% → 4.33% with best odds) but does not eliminate them. Interestingly, freezing the threshold once estimated outperforms full annual updating on average, suggesting that frequent re-optimization captures noise.

---

## 7. Optimal staking under risk aversion

A natural objection is that the rule's risk could deter rational arbitragers, sustaining the apparent inefficiency. The paper tests this with a calibrated portfolio choice exercise. Risk-averse expected-utility bettors with isoelastic utility $u(c) = c^{1-\sigma}/(1-\sigma)$ allocate wealth $w$ between cash (zero rate) and one or several simultaneous bets. With zero risk-free rate, no return autocorrelation and isoelastic utility, the multi-period problem collapses to the static one (Mossin 1968).

For a single bet with probability $p$ and odd $q$:

$$\alpha^* = \arg\max_\alpha \, p\, u(w - \alpha + \alpha q) + (1-p)\, u(w - \alpha)$$

Multi-bet versions (2, 3, 4 simultaneous bets) are detailed in Appendix D and exploit independence across matches.

### Optimal stake as % of wealth (Table 8)

| Odd class | Type | Instant return | $\sigma=1.5$ | $\sigma=5$ | $\sigma=10$ |
|:---:|:---:|:---:|:---:|:---:|:---:|
| [1.13, 1.15) — 1 bet | best | 9.97% | 54.47 | 20.54 | 10.79 |
| [1.13, 1.15) — 4 bets | best | 9.97% | 99.91 | 80.14 | 44.12 |
| [1.15, 1.17) — 1 bet | best | 5.92% | 25.96 | 8.51 | 4.33 |
| [1.18, 1.21) — 1 bet | mean | 0.44% | 3.36 | 1.02 | 0.51 |
| [1.18, 1.21) — 4 bets | mean | 0.44% | 26.43 | 8.06 | 4.04 |

Even in the worst case — a single mean-odds bet with 0.44% return and $\sigma=10$ — bettors still allocate 0.5% of wealth to wagering. With multiple concurrent bets (a frequent occurrence: only 29% of qualifying bets come in isolation), risk aversion is much less of a deterrent. Risk therefore cannot rationalize the persistence of the anomaly.

---

## 8. Conclusion

A purely price-based betting rule — back every outcome with odds below a threshold of roughly 1.19–1.21 — generates positive and statistically robust returns in the European football online betting market over 2000–2011: 4.45% per bet (instant) and 106% annualized using best odds. The evidence directly contradicts weak-form efficiency in this fixed-odds market. The bias documented in racetrack favourite-longshot data is here large enough to generate exploitable profits, even after accounting for transaction costs and realistic risk aversion.

The mispricing implicates both sides of the market: bettors fail to chase the available short-odds returns, and bookmakers leave themselves exposed to systematic losses on heavy favourites. This is at odds with Levitt (2004), who shows bookmakers optimally exploit bettor biases in the NFL gambling market.

The result is also relevant for the broader market-efficiency debate in finance (Shleifer 2000; Schwert 2003). Tests of efficiency typically rely on a contestable asset-pricing model; the betting setting requires almost no model. The persistence of an exploitable, simple, odds-only rule is therefore unusually informative about the limits of arbitrage and about market participants' rationality.

### Limitations and research extensions

The author lists several extensions that would refine the rule without changing its qualitative content:

- Excluding odds below 1.16, where returns are sub-optimal, in favour of an interval rule (e.g. 1.16–1.19), which raises the instant return to 7.20% (best odds) / 5.26% (mean odds).
- Allowing the threshold to vary by country, league, or by home/away outcome.
- Exploiting possible serial correlation of wins.
- Sizing stakes with the optimal-staking model from Section 7 rather than a flat unit.

The analysis is restricted to weak-form efficiency (information contained in odds). Semi-strong tests using public information (recent form, home advantage, etc.) are left to the empirical-forecasting literature cited in the paper.

---

## Main references

Asimakopoulos, I., Goddard, J. (2004). Forecasting football results and the efficiency of fixed-odds betting. *Journal of Forecasting* 23(1), 51–66.

Barber, B. M., Odean, T. (2001). Boys Will Be Boys: Gender, Overconfidence, and Common Stock Investment. *Quarterly Journal of Economics* 116(1), 261–292.

Cain, M., Law, D., Peel, D. (2000). The favourite-longshot bias and market efficiency in UK football betting. *Scottish Journal of Political Economy* 47, 25–36.

Deschamps, B., Gergaud, O. (2007). Efficiency in Betting Markets: Evidence from English Football. *Journal of Prediction Markets* 1, 61–73.

Dixon, M. J., Pope, P. F. (2004). The value of statistical forecasts in the UK association football betting market. *International Journal of Forecasting* 20, 697–711.

Fama, E. F. (1991). Efficient Capital Markets: A Review of Theory and Empirical Work. *Journal of Finance* 25, 383–417.

Kuypers, T. (2000). Information and Efficiency: An Empirical Study of a Fixed Odds Betting Market. *Applied Economics* 32, 1353–1363.

Levitt, S. (2004). How Do Markets Function? An Empirical Analysis of Gambling on the National Football League. *Economic Journal* 114, 2043–2066.

Mossin, J. (1968). Optimal Multiperiod Portfolio Policies. *Journal of Business* 41, 215–219.

Pope, P. F., Peel, D. A. (1989). Information, Prices and Efficiency in a Fixed-odds Betting Market. *Economica* 56, 323–341.

Quandt, R. E. (1986). Betting and Equilibrium. *Quarterly Journal of Economics* 101, 201–207.

Shin, H. S. (1991). Optimal Odds Against Insider Traders. *Economic Journal* 101, 1179–1185.

Shin, H. S. (1992). Prices of State-Contingent Claims with Insider Traders, and the Favorite-Longshot Bias. *Economic Journal* 102, 426–435.

Snowberg, E., Wolfers, J. (forthcoming). Explaining the Favorite-Longshot Bias: Is it Risk-Love or Misperceptions? *Journal of Political Economy*.

Sorensen, P. N., Ottaviani, M. (2008). The Favorite-Longshot Bias: An Overview of the Main Explanations. In *Handbook of Sports and Lottery Markets*, eds. D. B. Hausch and W. T. Ziemba, North-Holland, 83–101.

Stekler, H. O., Sendor, D., Verlander, R. (2010). Issues in Sports Forecasting. *International Journal of Forecasting* 26(3), 606–621.

*The full reference list appears in the PDF.*