Many bookmakers offer a refund if your horse finishes 2nd for certain races. These can be very profitable as the odds of a horse coming in second are similar to the odds of it winning, effectively creating an arbitrage opportunity. Naturally there is a balance between choosing a horse with low odds and choosing a horse that has the lowest qualifying loss. In this article I hope to enlighten you on the best horses to pick as well as show you the best bookmakers for these offers.
Empirical Correlation of Win Probability vs 2nd place Probability
In the chart below I have collated some data that shows the implied probability of a horse winning vs coming in 2nd place, taken from the betfair odds. The data was taken from races where there are greater than 8 horses. Any lower and the probabilities get skewed, and it also isn’t applicable as most 2nd place refunds are on races with 12+ horses.
Aside from heavily backed horses with a probability greater than 20% there is more or less a 1:1 correlation between the win probability and the 2nd place probability. This is as you would expect for a race with many horses and since most races that have the 2nd place refund have a favourite at odds of 5.00 or more then this correlation is fine for our analysis.
Expected Value of the Refund
Let the Betfair fractional odds of a horse be donated by X. This represents the true odds of a horse winning, something I shall explain in detail in a future article. The bookmaker overround, bookmaker fractional odds divided by Betfair fractional odds, will be denoted by OR. If we lay the bet off, the qualifying loss with 2% commission will be:
QL = (0.98*Stake+0.98*X*Stake)/(0.98+X/OR) – Stake
Where ‘Stake’ is how much we’ve bet on the horse. If you’re interested in how I derived this formula please read my article on Matched Betting. Since we know that the appoximate chance of the horse coming in second is 1/(X+1) and assuming we get an 80% yield from the free bet then the expected value is:
EV = (0.98*Stake+0.98*X*Stake)/(0.98+X/OR) – Stake + 0.8*Stake/(X+1) = (0.98*Stake+0.98*X*Stake)/(0.98+X/OR) – Stake*(1 – 0.8/(X+1))
Below is a graph showing how the EV varies for a £10 stake (click the image to view fullsize). Note that the values are invalid for odds below 4/1.
The red, blue, green, yellow and purple line represent an bookmaker to Betfair fractional odds ratio of 1.00, 0.95, 0.9, 0.85 and 0.8 respectively. Like with other matched betting activities, keeping the qualifying loss low is essential to making this offer profitable. The graph shows that the EV of a 5/1 horse with a fractional odds ratio of 0.95 is equivalent to the EV of an 8/1 with a fractional odds ratio of 1.00. That is to say that in this example a 5% decrease in the bookmaker payout is equivalent to a 60% decrease in the probability of the horse coming in 1st/2nd!
There are also other horse refund offers that bookmakers like to entice punters with:
- Some bookmakers e.g. Skybet offer three or more places for the refund. This obviously offers extra value over two places which means there is nearly always a horse that will be profitable.
- Beaten by a length – I don’t have a lot of data on this however I suspect that the probability is small since most horse races tend to have a horse that steams along and wins by several lengths. There are practical tips to make it worthwhile however. Ideally you will want to find a match on a favourite horse and not risk more than about £1 per £25 bet. You will also want a race with few horses i.e. less than 8 and have a short race e.g. 7 furlongs. This will increase the chances of the horses being more bunched up as they cross the finishing line.
- Faller insurance – Based off this article it would appear that there is around a 5% chance of the rider falling off their horse. From this I would really only attempt this offer if you can get super tight odds e.g. backing at 3.5 and laying at 3.55 otherwise it unlikely to be very profitable in the long run.
- Extra places – This is a whole topic in itself which I will discuss in another article. In short these extra place offers on each way bets mean that we can potentially win on both our back bet and our lay bet. These are nearly always worth doing given the potential reward available.
If you have any queries leave a comment below.