With the Kentucky Derby on the horizon and an office at the epicenter of the horse racing world, we would be remiss if we didn’t offer some insight into the peculiarities of thoroughbred wagering. One such curio is the presence of a favorite-longshot bias within the parimutuel betting market.
In general, bettors over-estimate the chance that a longshot will win and correspondingly under-estimate the chance that a favorite will win. While this phenomenon is nothing new (see Griffith, Odds Adjustments By American Horse-Race Bettors (1949)) it is interesting that the bias continues to this day.
To measure the favorite-longshot bias we recorded wagering pool volumes and payouts for 87497 entrants in 9793 races occurring in 2017. Assuming an efficient market the average return from betting on horses with long odds to win would be the same as betting horses with short odds to win, however, this is not the case.
Shown above is the average return on $2 win wagers grouped by their odds implied win probability (binned in groups of 3%). The error bars around each of these points are 1 standard error of the mean. The line at $2 gives a reference for breakeven and the line below that, at $1.64, is the expected return on $2 given a takeout of 18%.
Points on the far left, comprising runners valued at a low chance of winning, return less than runners valued at higher chances of winning. To illustrate, the second point from the left on the chart shows that wagering $2 to win on every runner going off at an odds implied win chance between 1.5% and 4.5% (66-1 and 22-1 on the tote) on average returned 1.34 dollars, which is probably a better-expected value than playing the Powerball, but far worse than going to the roulette wheel.
We can generate the same chart for place and show wagers. However, the odds implied chance of a horse placing can only be approximated from the wagering pool data since a horse’s chance of placing is the chance of winning plus the chance of coming in second and there is not a market for wagering on a horse to come in exactly second place. The same goes for show bets.
To work around this limitation, we will use Harville’s Formula to estimate the market implied chance of a horse placing and showing. While Harville’s Formula does have it’s own biases, namely, it relies on the win odds implied probabilities, which we just showed are biased, to approximate the place and show chance of a runner. Using Harville is also tenuous because, in reality, some horses have high chances of winning but disproportionately smaller chances of placing or showing than what Harville would imply. This observation is known as the Silky Sullivan Problem, coined after a horse notorious for finishing either at the back of the pack or coming extremely far off pace to win in dramatic fashion.
While the favorite-longshot bias continues to exist in horse racing, the Derby itself is an exceptional race. It is one of the few mile and a quarter races over the dirt each year, has twice as many entrants as an average race, and it commands wagering pool sizes far above those of most other races.
Perhaps the larger pools and increased handicapping focus on the Derby result in a more efficient market less prone to the favorite-longshot bias. Or, perhaps, we are still quick to remember Giacomo and Mine that Bird but forgetful of last year’s Thunder Snow.