Favourite-Longshot Bias and What It Means for Acca Builders

The favourite-longshot bias is the long-documented tendency for bets on long shots to return less per pound than bets on favourites. In bookmaker terms, a 20/1 outsider is typically worse value than the implied probability suggests, while a short-priced favourite is slightly better value than its price suggests, once margin is accounted for. For accumulator builders, it matters in two ways: how you strip margin out of prices, and which legs you are willing to pay for.

This article summarises what the literature says, says what we cannot claim, and works through an example.

What the research says#

The earliest widely cited finding is from horse racing. Griffith (1949) in the American Journal of Psychology reported that horses with short odds won more often than their betting odds implied, while long shots won less often. Thaler and Ziemba (1988) reviewed racetrack and lottery markets in the Journal of Economic Perspectives and described the bias as one of the standard anomalies in the literature.

Why it exists is still argued over. The main explanations are:

Snowberg and Wolfers (2010), in the Journal of Political Economy, tested the risk-love and misperception explanations using a dataset of 5,610,580 US horse race starts from 1992 to 2001. They concluded that misperception of probabilities, in line with prospect theory, better explains the bias than risk-love. Their working paper is available from the NBER.

Shin (1993) in the Economic Journal built a model in which bookmakers set prices knowing that some bettors are better informed, and estimated the incidence of insider trading from UK horse racing data. The model implies that margins are loaded more heavily on longer prices. See the bibliographic record.

Cain, Law and Peel (2003), in the Bulletin of Economic Research, tested for the bias across several betting markets, found it in each, and noted that its exact shape is not identical across markets. Record here.

What we do not claim#

• Most of the headline evidence is from horse racing, where data are plentiful.
• How large the bias is in football 1X2, BTTS or goal-line markets varies by study, period and bookmaker. We cannot give you a trustworthy number, so we do not.
• Bookmaker pricing has changed since many of these studies were written. A bias that was present once may be smaller or different now.
• Finding the bias in prices is not the same as finding a profitable strategy. Margin still applies.

Treat the bias as a reason for caution, not as a rule.

A worked example: how de-vig method changes a long shot#

Take a match priced 1.25 / 6.50 / 12.00 for home, draw and away. The implied probabilities total 103.7%. Here is what each de-vig method gives.

Proportional scaling gives the long shot the highest probability. The other two methods take more margin from the long shot and give more to the favourite.

Now compare edges. Suppose you find a price of 13.00 on the away side.

The same price shows an edge or a loss depending on the method. If the bias is real, the second row is closer to the truth, and a proportional-scaling model will systematically find edges on long shots that are not there. In a balanced market (2.10 / 3.50 / 3.60) the three methods differ by about half a percentage point or less, which is why the method matters most for lopsided matches. See how to read implied probability and remove the margin.

Štrumbelj (2014), in the International Journal of Forecasting, compared ways of converting odds to probabilities, and later papers describe his result as Shin-based probabilities predicting outcomes better than basic normalisation. That does not make Shin right in every market, but it does mean the simplest method is not the safest.

What this means for accumulator builders#

1. An accumulator is itself a long shot#

A six-leg acca at 5.36 is a bet with a 13.9% chance in our worked example. It is a long shot by any definition. Whether or not the bias applies to the legs, the combined price is a longer price than any individual leg, and it carries the compounded margin in the hidden cost of accumulators. The bias is a smaller effect than that compounding, and it points the same way.

2. Beware of stretching legs to long prices#

If the bias exists, the legs that cost you the most are the ones with the longest prices. A leg at 12.00 can look attractive in an acca because it lifts the payout, but it is where the market's shading is likely to be heaviest. ArtificialAcca's generator sets a minimum and maximum odds per leg to keep legs in a sensible range.

3. Do not read the bias as a case for stacking short prices#

Short prices carry margin too. A 1.15 favourite with an 87.0% implied probability needs a true probability above 87.0% to have positive expected value, and every short leg adds margin on top of a small payout. See common acca mistakes for the cost of padding.

4. De-vig carefully#

If you estimate edges, state your de-vig method and test whether the conclusion survives a change of method. When the result depends on the method, there is no edge worth acting on.

How ArtificialAcca handles it#

Our engine de-vigs proportionally, anchors on the market with a weight of at least 70%, and takes the best price available. This is simple and transparent, and it has the weakness described above: it can understate favourites and overstate long shots. We describe that limitation in how the model works. If we change method, we will say so there.

The effect of the blend is to dampen our reliance on the goals model. The generator's leg-odds limits keep most legs away from the extremes where the bias would matter most. Neither protects fully. You can see each leg's probability and odds in the generator, and check outcomes on the results page.

Further reading#

• Griffith, R. M. (1949). Odds adjustments by American horse-race bettors. American Journal of Psychology, 62(2), 290-294.
• Thaler, R. H. and Ziemba, W. T. (1988). Parimutuel betting markets: racetracks and lotteries. Journal of Economic Perspectives, 2(2), 161-174.
• Shin, H. S. (1993). Measuring the incidence of insider trading in a market for state-contingent claims. Economic Journal, 103(420), 1141-1153.
• Cain, M., Law, D. and Peel, D. (2003). The favourite-longshot bias, bookmaker margins and insider trading in a variety of betting markets. Bulletin of Economic Research, 55(3), 263-273.
• Snowberg, E. and Wolfers, J. (2010). Explaining the favorite-long shot bias: is it risk-love or misperceptions? Journal of Political Economy, 118(4), 723-746.
• Štrumbelj, E. (2014). On determining probability forecasts from betting odds. International Journal of Forecasting, 30(4), 934-943.

18+ only. Academic findings about betting markets describe averages and do not promise results for any bet. Accumulators lose more often than they win. If gambling is a concern, visit BeGambleAware.org or call 0808 8020 133.