The quirks of a three horse race
Why variability can be useful in competition
A few years ago, I interviewed Bill Benter, arguably the most successful bettor in history. During the 1990s, his team transformed horse racing prediction, using the lab-like conditions of races in Hong Kong to develop remarkably successul betting models. The resulting winnings would reportedly stretch to almost $1 billion.
I’d got in touch as I was researching my book The Perfect Bet, on the relationship between science and games of chance. In our conversation, Benter highlighted a range of statistical ideas that made his betting success possible. Like the importance of making your own predictions almost in a vaccuum, then combining them with crowd-sourced knowledge derived from market activity. And the challenges of managing bankroll risk in the face of uncertainty, or getting bets in without moving the market. These execution aspects of betting gets a lot less coverage than prediction, but – as in finance – they are often the difference between success and failure.
Benter also made a subtle, but important, point about competition. Specifically, he mentioned a crucial transition that happens when dealing with multiple competitors. I included it briefly it my book, but I think it’s worth taking a closer look.
Let’s start by imagining there are two horses in a race. The first is extremely reliable, always finishing in about the same time. The second is more scattergun; half the time it’s a bit faster than the first, and half the time it’s a bit slower. In a race between these two horses, it would therefore be a coin toss: it just depends on whether the second horse is having a good day.
Now suppose we add a third horse, which is even more scattergun. Half the time it’s rapid; half the time it’s rubbish. Which of the three horses is most likely to win? Well, if the third horse is having a good day, it will beat the other two, giving it a 50% chance of victory overall. And if it’s having a bad day, it will again be a coin toss between the first two horses. So overall, horse #1 and horse #2 will now each have a 25% chance of winning.
Notice that, on average, all the horses have the same performance. So if we looked only at their average race times, we’d conclude all should have an equal chance of victory. But in a multi-horse race, what matters is coming first. And that’s where the advantage of unreliability comes in: if the average performance is the same, it’s the most variable horse that is most likely to win.
The above is just an illustrative example, but the underlying logic can apply to a range of situations that involve multiple competitors and uncertain conditions, from job interviews to prizes. In a crowded field, it’s the high risk all-or-nothing strategy that has the best chance of succeeding.
When I first encountered this idea, I realised it was an approach I’d already used, even if I wasn’t aware of the theory behind it. Shortly before I got a book deal for The Perfect Bet, I’d won a major science writing prize. At the time, subjects like neuroscience and stem cell development were at the forefront of high profile science. Which presumably meant a lot of people would be submitting articles on these topics. Rather than compete with a crowded field, I instead wrote about a niche aspect of statistical estimation. I figured it was a necessary risk: it would either sink like a stone among the judges, or help me stand out against the competition.
It might seem a bit cynical to think of these situations so probabilistically. But I think the above ultimately leads to a hopeful message. If you try and please everyone by aiming for the middle ground, you’ll often lose out to someone who takes a risk. So it can pay to stay true to your strengths, and be the best take-it-or-leave-it version of yourself.
Even if there’s a chance it will sometimes put you in last place.