The favourite–longshot bias: test it, don't assume it
Long shots have often returned less per unit staked than favourites, but whether that holds depends on market structure, the test you use and the period. The lesson is to test it in your exact market — not to always back favourites.
Learning objectives
- Define the favourite–longshot bias in terms of expected returns, not win rates.
- Compare three explanations (bettor preferences, insiders, risk-averse bookmakers with disagreement) and what each predicts.
- Explain why market competition and test design change whether the bias is found.
- Show how the choice of de-vig method embeds an assumption about the bias.
What the bias is — and what it is not
The favourite–longshot bias (FLB) describes a pattern in returns: the expected loss per unit staked is larger on long shots than on favourites. Writing r = p × o − 1 for the expected return of each selection, an FLB means r falls as the odds o rise.
r(o) = p(o) × o − 1, FLB ⇔ r decreases as o increasesIt is not the statement that favourites win more often — they do by definition. A strategy that wins 75% of its bets can still lose money if the prices are short enough. Win rate without price says nothing about value.
Another way to see it: the bookmaker's margin need not be spread evenly. In the worked example below, the same 4.03% overround is consistent with every outcome returning −3.87% (an even spread) or with the favourite returning −2.39% and the long shot −9.42% (Shin's spread); the quoted prices look identical either way. The FLB is a statement about how that margin is distributed across the odds range — and only outcome data can reveal it, because the quoted prices alone are consistent with any distribution.
Why it might exist
- Bettor preferences. Some bettors enjoy the chance of a big payout and over-back long shots, so books can shade those prices more.
- Insiders. In Shin's model, a bookmaker who fears better-informed bettors protects itself most on long shots, producing a bias. This model underlies the Shin de-vig method.
- Risk-averse bookmakers and disagreement. Whelan shows that when bettors disagree about probabilities and competitive bookmakers are risk-averse, a favourite–longshot pattern can arise without assuming bettors love risk Whelan (2024).
Competition and test design change the answer
Put together: a bias can be real in one market structure and absent in another, one test design can hide it, and one good season can manufacture it. None of these studies shows that backing favourites is profitable in competitive markets.
Your de-vig method already assumes an answer
Proportional de-vigging spreads the margin evenly, which implicitly assumes no FLB: every outcome has the same expected return. Shin and power de-vigging take more margin from long shots, which assumes an FLB. The worked example puts numbers on this. Only outcome data from your market can tell you which assumption fits — and lesson 12 explains how to run that test without fooling yourself.
How to test it in your own market
- Fix the market exactly: competition, bookmaker or exchange, market type (90-minute 1X2), and which snapshot (opening, a fixed time before kick-off, or closing).
- Normalise first: convert prices to de-vigged probabilities and test whether outcomes match them across odds bands, rather than regressing on raw inverse odds.
- Measure returns by band: average p × o − 1 per odds band, with standard errors. Long-shot bands are very noisy; the synthetic long-shot rule had a standard error of 11.74 points on 295 bets.
- Split by time: estimate on earlier seasons, confirm on later ones, and look at every season separately rather than only the pooled figure.
- Count your tests: every league, band and snapshot you try is another chance of a false positive (lesson 12).
- Check execution: a bias in a market where stakes are capped or accounts are restricted may not be exploitable at all.
Worked example
Worked example · Three de-vig methods, three views of the bias
A hypothetical lopsided match, Kestrel Park v Dunmore, priced 1.40 / 4.80 / 8.50. We ask what expected return each outcome would have if each method's fair probabilities were the truth.
- Raw implied probabilities
1/1.40, 1/4.80, 1/8.5071.43% / 20.83% / 11.76%; book sum 104.03% (overround 4.03%) - Proportional
Divide by 1.040368.66% / 20.03% / 11.31% - Shin
Shin de-vig, z ≈ 0.020569.72% / 19.62% / 10.66% - Power
Power de-vig, k ≈ 1.050970.22% / 19.23% / 10.55% - Expected return if proportional is true
p × o − 1−3.87% on every outcome: no bias by construction - Expected return if Shin is true
p × o − 1Favourite −2.39%, draw −5.82%, long shot −9.42% - Expected return if power is true
p × o − 1Favourite −1.70%, draw −7.68%, long shot −10.32% - Synthetic favourites backtest
Back every synthetic event priced at a market probability of 65% or more372 bets, 280 wins (75.27%, Wilson 95% interval 70.64%–79.38%), profit −26.05 units, ROI −7.00%
Under every method the favourite's expected return is still negative after the margin; the methods disagree only about how the loss is shared. The FLB is therefore a claim about relative losses that must be measured, not assumed — and in the synthetic world, where no bias was built in, a high win rate on favourites simply lost money.
Practice · See the bias assumption inside each method
Open the Remove the Margin lab with 1.40 / 4.80 / 8.50. Note the long shot's fair probability under each method, then compute p × 8.50 − 1 for each.
Lab 2 · Remove the margin
Synthetic · deterministic| Method | Home | Draw | Away |
|---|---|---|---|
| Raw implied (with margin) | 71.43% | 20.83% | 11.76% |
| Proportional | 68.66% (1.456) | 20.03% (4.993) | 11.31% (8.842) |
| Additive | 70.09% (1.427) | 19.49% (5.131) | 10.42% (9.595) |
| Power k = 1.0509 | 70.22% (1.424) | 19.23% (5.199) | 10.55% (9.478) |
| Shin z = 0.0205 | 69.72% (1.434) | 19.62% (5.097) | 10.66% (9.384) |
- Proportional: Divides every implied probability by the book sum. Simple, but assumes the margin is spread in proportion to probability.
- Additive: Removes an equal amount from every outcome. Easy to explain; it can push long shots below zero.
- Power: Raises every implied probability to a common power. Takes relatively more margin from long shots.
- Shin: Derived from Shin's insider-trading model. Takes more margin from long shots; performed well in Štrumbelj (2014).
Reading the result. The methods agree on the favourite more than on long shots. None of them recovers the “true” probability: they are different assumptions about how the bookmaker spread its margin. Differences of a point or two can decide whether a price looks like value, so state which method you used.
Educational calculator. Uses only the numbers you enter or seeded synthetic data — no live prices, no staking, no real money.
Show what you should find
Overround is 4.03%. The long shot gets 11.31% (proportional), 10.66% (Shin), 10.55% (power) and 10.42% (additive). Its implied expected return is −3.87% if proportional is right, −9.42% if Shin is right and −10.32% if power is right. The methods differ by up to 0.89 of a point of probability on the long shot alone (11.31% versus 10.42%) — the same order of size as the effect an FLB test is trying to detect.
Common mistakes
- ✗ Concluding 'always back favourites'.Favourites still carry the margin, and in competitive markets Hegarty & Whelan (2026) found little bias. Test your exact market and period.
- ✗ Judging a strategy by its win rate.The synthetic favourites rule won 75.27% and lost 7.00%. Value depends on price, not hit rate.
- ✗ Testing FLB by regressing outcomes on raw inverse odds.That design is biased against finding the bias Hegarty & Whelan (2024). Use normalised probabilities.
- ✗ Trusting one significant season.Single-season 'inefficiencies' are common even in efficient markets Winkelmann et al. (2024). Require multiple seasons and out-of-sample tests.
When it fails
Supporting research
- Whelan (2024): Risk aversion and favourite–longshot bias in a competitive fixed-odds betting marketEconomica · Peer-reviewed theoryA theoretical mechanism — risk-averse bookmakers plus bettor disagreement — that can produce a favourite–longshot pattern without risk-loving bettors.
- Hegarty & Whelan (2026): Market structure and prices in online betting markets: theory and evidenceOxford Economic Papers · Peer-reviewed empiricalEvidence that the bias appears in less competitive bookmaker markets and is small in competitive ones.
- Hegarty & Whelan (2024): Comparing two methods for testing the efficiency of sports betting marketsSports Economics Review · Peer-reviewed methodsInverse-odds regression tests are biased against finding the bias; normalised-probability tests behave well.
- Winkelmann et al. (2024): Are Betting Markets Inefficient? Evidence From Simulations and Real DataJournal of Sports Economics · Peer-reviewed empiricalApparent pricing biases in single seasons do not persist systematically, and significant single-season results are likely even in efficient markets.
Check your understanding
Practice only: saved on this device, no XP and no account record.