Favourite-longshot bias: why long odds carry more margin
Favourite-longshot bias is the pattern where long odds return less per shilling staked than short odds in the same market. It arises when margin is added unevenly. In the example below, the same 8% total margin costs KES 32.26 per KES 1,000 on the favourite and KES 285.71 on the outsider.
The short answer
A market's margin is the amount by which the implied probabilities exceed 100%, as explained in the guide on calculating the bookmaker's margin. That total says nothing about how the excess is shared between the outcomes. If it is shared so that outsiders lose more of their value than favourites, long odds cost more per shilling. That unevenness is what the name favourite-longshot bias describes.
This guide shows the effect with arithmetic you can check. It does not claim how large the bias is in any real market, because no study or dataset was checked for it. Everything below rests on invented chances and stated assumptions.
The cost of one price
Take an outcome with a true chance p and a decimal price D. A KES 1 stake returns D with chance p and nothing otherwise, so the average return is p × D. The average cost per shilling is what is missing from 1.
The catch is that p is never known for a sports event. The fair-price idea is covered in the guide on the expected value of a bet; here we simply assume the chances so that costs can be computed exactly.
Illustrative example: a four-runner race
Illustrative example. Assume the true chances are 60%, 25%, 10% and 5%. They add to 100%. The fair prices are 1 ÷ 0.60 = 1.6667, 1 ÷ 0.25 = 4.00, 1 ÷ 0.10 = 10.00 and 1 ÷ 0.05 = 20.00.
Now suppose the market has a total margin of 8%, so the implied probabilities must add to 108%. There are many ways to build that 108%. Two simple ones follow.
Method A: margin shared in proportion
Multiply every true chance by 1.08. The implied probabilities become 64.8%, 27.0%, 10.8% and 5.4%, which add to 108%. Each price is 1 ÷ implied probability:
- 1 ÷ 0.648 = 1.5432
- 1 ÷ 0.270 = 3.7037
- 1 ÷ 0.108 = 9.2593
- 1 ÷ 0.054 = 18.5185
Check the favourite: 0.60 × 1.5432 = 0.9259, so the cost is 7.41%. Check the outsider: 0.05 × 18.5185 = 0.9259, also 7.41%. Every price has the same cost, 1 − 1 ÷ 1.08, which is KES 74.07 per KES 1,000. Under this method there is no favourite-longshot pattern.
Method B: margin shared as equal probability points
Add 2 percentage points to every true chance. The implied probabilities become 62%, 27%, 12% and 7%, which add to 108%, the same total margin. The prices are 1 ÷ 0.62 = 1.6129, 1 ÷ 0.27 = 3.7037, 1 ÷ 0.12 = 8.3333 and 1 ÷ 0.07 = 14.2857.
The return per shilling on each outcome is true chance ÷ implied probability, because p × (1 ÷ q) = p ÷ q. For the favourite, 0.60 ÷ 0.62 = 0.9677. For the outsider, 0.05 ÷ 0.07 = 0.7143.
| Outcome | True chance | Fair price | Price, method A | Price, method B | Cost per KES 1,000, A | Cost per KES 1,000, B |
|---|---|---|---|---|---|---|
| Runner 1 | 60% | 1.6667 | 1.5432 | 1.6129 | KES 74.07 | KES 32.26 |
| Runner 2 | 25% | 4.00 | 3.7037 | 3.7037 | KES 74.07 | KES 74.07 |
| Runner 3 | 10% | 10.00 | 9.2593 | 8.3333 | KES 74.07 | KES 166.67 |
| Runner 4 | 5% | 20.00 | 18.5185 | 14.2857 | KES 74.07 | KES 285.71 |
Both columns come from the same 8% total margin. In method B the cost per KES 1,000 is 1,000 × (1 − p ÷ q), for example 1,000 × (1 − 0.7143) = KES 285.71. The longest price carries almost nine times the cost of the shortest (285.71 ÷ 32.26 = 8.86).
Why equal points hit long prices hardest
Two extra percentage points are a small slice of a 60% chance and a large slice of a 5% chance. Compare the implied probability with the true chance:
| Outcome | True chance | Implied probability, B | Implied ÷ true | Price cut below fair |
|---|---|---|---|---|
| Runner 1 | 60% | 62% | 1.033 | 3.23% |
| Runner 2 | 25% | 27% | 1.080 | 7.41% |
| Runner 3 | 10% | 12% | 1.200 | 16.67% |
| Runner 4 | 5% | 7% | 1.400 | 28.57% |
The outsider needs a 7% chance just to break even at 14.2857 (1 ÷ 14.2857), but its assumed chance is 5%. The break-even bar is 40% above the real chance. For the favourite the bar is 3.3% above.
What it looks like on a KES 100 stake
Illustrative example
Under method B, KES 100 on Runner 4 at 14.2857 returns KES 1,428.57 when it wins, a profit of KES 1,328.57. It wins with the assumed chance of 5%, so the average return is 0.05 × 1,428.57 = KES 71.43 and the average cost is KES 28.57. The same KES 100 on Runner 1 at 1.6129 returns KES 161.29 with a 60% chance, an average of KES 96.77 and a cost of KES 3.23.
The long price also gives a very wide spread of results: 19 times in 20 the stake is lost in full. How that feels over a series of bets is explained in the guide on variance and losing streaks.
Why the total margin cannot show this
Add the implied probabilities in either method and you get 1.08. The check in the guide on what overround is gives the same answer for both, so the total margin hides how the cost is spread. Only the true chances, which nobody can observe for a sports event, would reveal it.
Regulation 23(1) of the Gambling Control (Conduct of Gambling Operations) Regulations, 2026 requires a licensee to clearly display betting odds, rules and terms. That lets you see every price and the total margin. It does not oblige a licensee to publish true chances or to share margin in a particular way, and none of the sources read here set a rule on that.
How to use the idea safely
- Work out the total margin of the market by adding every implied probability and subtracting 1.
- Remember that this total is an average-style figure. A single long price can cost more than the total suggests, and a short price can cost less, when margin is uneven.
- Treat any long price as a small chance of a large return, not as a bargain. The cost per shilling and the chance of winning move in different directions.
- Count the cost over the amount staked across a month, not per bet, and keep it inside the budget you set.
If long prices are combined into one bet, the effect compounds. The guide on why accumulators carry more margin shows the multiplication. Betting is not a way to make money: every price carries a cost. 18+. Gambling is addictive. Play responsibly.
Questions and answers
What does favourite-longshot bias mean?
It means that, per shilling staked, bets on outsiders (long odds) cost more on average than bets on favourites (short odds) in the same market. The cause in this guide's example is how the margin is shared out across the prices.
Does this guide say how big the bias is in real markets?
No. It shows the arithmetic with invented chances and stated assumptions. It makes no claim about the size of the effect in any real market or sport, because no primary study was checked for this guide.
Can I see the bias by adding up the implied probabilities?
No. The total of the implied probabilities gives the overall margin, but it does not show how the margin was split between outcomes. Two markets with the same total can cost very different amounts on a long price.
Does a longer price mean a worse bet?
Not by that fact alone. The cost of a price is 1 minus (true chance times price), and the true chance is never known for a sports event. The example only shows that, if margin is added as equal probability points, the long price takes the largest relative cut.
Why does this matter for accumulators?
Each leg of an accumulator multiplies the payback of the legs before it. If long-priced legs carry a larger cut, the combined cost rises faster, which is covered in the guide on why accumulators carry more margin.