Sports
The Favourite-Longshot Bias in Nine-Runner Fields
Multi-runner markets like horse racing exaggerate a bias you can measure: longshots return less than their odds imply, favourites a little more.
Key takeaways
- A nine-runner field prices nine outcomes, so the overround compounds across every one of them.
- Normalising by the book total is the only way to compare runners on a like-for-like basis.
- Proportional de-vigging taxes every runner equally in relative terms, which is where the distortion enters.
- The bias signature is monotone across the field, not a spike on one runner.
- Longshots need the most data and get the least, which is why the effect is easiest to see in simulation.
Fields multiply the effect
In a two-way market a bias is subtle. In a nine-runner field it compounds: every runner is priced, the overround is spread across all of them, and small mispricings at long odds add up. That makes fields a good teaching surface for the favourite-longshot bias.
The arithmetic is unforgiving. A two-way book carrying 4.8% overround is asking for one extra unit of margin across two prices. A nine-runner book at the same per-runner margin sums to well over 120%, because the excess is charged nine times. The raw implied probabilities in a field routinely total 1.2 or more, and comparing any single runner's raw implied figure to a model probability without normalising first is meaningless.
That normalisation step is where the interesting decisions live. How you distribute the removal of 20 percentage points across nine runners determines what each runner's fair price looks like — and different methods disagree most on the runners furthest from the favourite.
Normalise before you compare anything
Work a small example. Suppose a field's raw implied probabilities are 0.34, 0.22, 0.15, 0.11, 0.09, 0.07, 0.05, 0.04 and 0.03. They sum to 1.10, so the book carries 10% overround.
Proportional de-vigging divides every entry by 1.10: the favourite falls from 0.340 to 0.309, and the longest runner falls from 0.030 to 0.027. In absolute terms the favourite gave up 31 points of a percent and the longshot gave up 3 — but in relative terms both gave up exactly 9.1%, which is the assumption proportional de-vigging makes.
That assumption is the crux. If the market's margin is in fact concentrated at the long end — which is what the favourite-longshot bias asserts — then proportional de-vigging leaves the longshots still overpriced and the favourite slightly underpriced in the fair line you derived. The method you pick decides what you will conclude about the bias you set out to measure.
Read the four-probability table
For each runner the horse-racing lab shows raw implied, margin-adjusted, model and observed probabilities. Comparing margin-adjusted to model probability isolates where the priced field disagrees with the generative truth — and the pattern usually tilts against the longshots.
Because the runners are synthetic, you can dial the bias up or down and watch the table respond, which is far clearer than trying to infer it from real tote data.
Look for the shape of the disagreement, not its size. If margin-adjusted exceeds model probability for the last four runners and falls short for the first two, with the crossover somewhere in the middle, that is the bias signature: a monotone tilt across the field. If one runner disagrees sharply and its neighbours do not, that is noise on a small sample, and it will not survive a re-seed.
Why the long end is hardest to measure
The runner you most want to study is the one you can least afford to study. A 3% runner wins roughly three times in a hundred races, so a thousand simulated races give you about thirty wins to estimate the rate from — a 95% interval spanning perhaps 2% to 4.3%, which is wide enough to hide almost any bias you might be looking for.
The favourite in the same thousand races wins about 340 times, and its rate is pinned down to within a point and a half. So the table you are reading is precise exactly where the effect is smallest and vague exactly where it is largest.
This is the practical reason the bias is easier to demonstrate in a lab than in historical data: you can generate a hundred thousand races overnight, and you know the truth you are trying to recover. Real tote data offers neither luxury, which is why the literature on the effect has argued about it for decades.
Frequently asked
Why do field implied probabilities sum to more than 100%?
Because each runner's price carries margin, and a nine-runner book charges that margin nine times. Totals of 115–125% are ordinary. You must normalise to a fair set summing to one before comparing any runner to a model probability.
Does proportional de-vigging distort a field?
It assumes the margin was applied evenly in relative terms — every runner gives up the same percentage of its probability. If a market actually loads more margin onto longshots, proportional de-vigging leaves them still overpriced in the fair line you derive.
How do I tell a real bias from noise in the table?
A bias is monotone across the field: the disagreement grows steadily as prices lengthen. Noise is local — one runner out of line while its neighbours behave. Re-seed the run; the monotone pattern persists and the spike does not.
Why is the longshot row always the least reliable?
Because it has the fewest wins to estimate from. A 3% runner produces about 30 wins per 1,000 races, giving a confidence interval wide enough to conceal the very effect you are measuring. Raising the race count is the only fix.
Try it yourself
Everything in this article is something you can run and tweak in the lab — with your own settings and a reproducible seed.
Open the lab →