Are horse racing betting markets actually efficient?

A prediction and a probability are not the same object

Start with the sentence at the top. The favourite was beaten, so the market was wrong.

A horse priced at around a one-in-three chance is expected to lose roughly two times in three. When it loses, the price has not failed. The price told you, in advance, that this was the more likely outcome. Treating a beaten favourite as a market error is like treating a forecast of a thirty percent chance of rain as wrong because it stayed dry.

A prediction names a winner and can be right or wrong. A probability describes a distribution and can only be judged across many races. Racing talk slides between the two constantly, usually within one sentence.

You cannot grade a probability from one race. You can only grade it from a few thousand.

Efficient means at least three things

Eugene Fama's 1970 review in the Journal of Finance gave the phrase its working definition: a market is efficient when prices fully reflect available information. That definition has done enormous work in economics, and it is narrower than the way the word gets used in a betting shop.

In practice people mean one of three things, and the argument usually happens because two people mean two of them.

Information efficiency. Whether the things that are known about a race are already in the price. Trainer form, ground, the stable's intentions, the money.

Calibration. Whether the probabilities are numerically honest. Do horses priced at a one-in-four chance win about a quarter of the time. This is measurable and it is the one we test.

Profitability. Whether anything is left after the margin, the commission and everybody else's cleverness. This is the only one that pays for anything, and it is the hardest to establish.

A market can be beautifully calibrated and still leave nothing on the table. A market can be poorly calibrated in some corner and still be unprofitable once costs are paid. Proving one of these three says very little about the others.

What our own data says about calibration

We measured the same races twice, at the exchange price and at the bookmakers' starting price, on 1,997 races and 18,529 runners, with the overround normalised the same way on both sides. Two reviewers re-ran it independently.

The Betfair calibration slope came out at 0.974, with a 95 per cent confidence interval of 0.925 to 1.023. That interval contains 1.000, which is the value a perfectly calibrated price would have. On this sample the exchange price is not statistically distinguishable from exactly right.

The bookmakers' starting price on the same races came out at 1.095, interval 1.041 to 1.148. That interval excludes 1.000. The contrast is the finding, not either number alone: on identical races one of these prices is indistinguishable from calibrated and the other is measurably not.

The margins sit either side of the same gap. The exchange carries 0.2% of built-in margin. The bookmakers' starting price carries 19.2%.

And on the favourite study, across 60,671 races, actual wins against the wins implied by the favourites' own prices came out at 0.997. The racing did very nearly what the prices said it would.

The pattern we keep running into

Almost every promising racing idea we have tested has died the same way, and it is not the way people expect. The effect is usually real. It just turns out to already be in the price.

Steamers are the cleanest example. Horses that shorten do win more often than horses that drift, and the money moves a long way in the last hour. Then you compare a steamer and a drifter at the same final price, and the advantage disappears. The move was telling you where the horse would end up, and the price at the end already knew.

Draw bias goes the same way. Ratings go the same way: across 30,088 races the top-rated horse won at 0.998 of the rate its price implied, which is to say the rating ranked horses well and told you nothing the price had not.

Obvious information being useful does not mean it stays useful after the market has priced it.

So what is left

If the price already carries the form, the money and the ratings, the honest place to look is where the price is being asked to summarise something awkward. Races where the structure is unusual. Races where the pace could collapse. Races where two horses are genuinely inseparable and the market has had to pick one.

That is not a claim to have found anything. We have 0 systems that have cleared our validation bar, out of 227 examined, and we publish that number precisely because it is the unflattering one.

What is Betfair Starting Price covers the price these tests are measured against. Do steamers win more often is the full market-move study. The system audit lists what we have examined and what survived.

See how the same discipline is applied to today's card.