Dr. Kupper is Emeritus Alumni Distinguished Professor of Biostatistics, Gillings School of Global Public Health, University of North Carolina at Chapel Hill. His research interests included the development and application of Statistical Methods for public health studies, particularly environmental, occupational, and women's health and quantifying health risks from exposure to environmental and workplace hazards.
Episode Description
With the arrival of spring, anticipation grows for the start of horse racing in the United States. The pinnacle of success in the sport is achieved by a horse that will win each leg of the Triple Crown, which includes the Kentucky Derby, the Preakness Stakes, and the Belmont Stakes. The excitement and anticipation of these three races are also associated with pre-race bookmaking and betting as well. But just how good are the bookmakers at setting the odds of victory? Do their favorites win, or will long shots emerge victorious? That's the topic on today's episode of Stats+Stories with guest Larry Kupper.
Full Transcript
John Bailer
With the arrival of spring, anticipation grows for the start of horse racing in the United States. The pinnacle of success is achieved by a horse that wins each race in the Triple Crown: the Kentucky Derby, the Preakness Stakes, and the Belmont Stakes. The excitement and anticipation surrounding these three races are also tied to pre-race bookmaking and betting.
How good are bookmakers at setting the odds of victory? Do their favorites win, or will long shots emerge victoriously?
To the excitement of fans and backers alike, I’m John Bailer. Stats + Stories is a production of the American Statistical Association, as well as Miami University’s Departments of Statistics and Media, Journalism, and Film. Rosemary Pennington is away.
Our guest today is Dr. Lawrence Kupper, Emeritus Alumni Distinguished Professor of Biostatistics at the School of Public Health, University of North Carolina at Chapel Hill. His research interests include the development and application of statistical methods for public health studies—particularly environmental, occupational, and women’s health—as well as quantifying health risks from exposure to environmental and workplace hazards.
On a previous episode, we talked with Larry about golf, but on today’s program, we’re going to talk with him about another of his passions: horse racing. He’s a longtime fan and follower of the sport. In his recent article in Significance magazine, “And They’re Off! Should Kentucky Derby Gamblers Slow Down?”, he explores outcomes from the three races in the Triple Crown.
Larry, it’s a delight to welcome you back to the podcast.
Larry Kupper
John, thanks again for having me. It really is an honor to participate in Stats + Stories. And as I’ve said before, you’re one of my favorite people, so that makes it even more special for me.
John Bailer
Oh, gosh—well, back at you. I attribute a lot of my success to having a great mentor and role model early in my career.
I’m curious, though—I didn’t realize you had this connection to horse racing. When did you first start following the sport?
Larry Kupper
Yes, I think the Kentucky Derby has always been the most popular of the three races for several reasons. First, it’s held in Louisville. It also features 20 horses, which makes it feel like a stampede. Then there’s the infield experience, and, by far, more money is wagered on the Kentucky Derby than on the other two races.
That said, all three races are fascinating in their own way.
John Bailer
And, in your article, you mentioned that there are, what—maybe only about 10 or 11 horses running in the other two races? I was struck by the difference, since the Derby typically has a median of about 19 horses.
Larry Kupper
That’s right. In the Kentucky Derby, if you’ve ever watched it, it really does look like a stampede. The other two races typically have about 10 horses. So the Derby is roughly twice as large a field, and that actually makes an incredible difference in what happens across the three races over time.
John Bailer
Yeah, I was also impressed to see how far back these races go. The Belmont Stakes—the oldest—dates to 1867, as you noted in your article, and then the Preakness and the Derby both started in the 1870s.
Larry Kupper
That’s exactly right—they go back a long time.
John Bailer
So, you mentioned we’d get into the gambling aspect, which I think is part of what makes this topic so compelling. How much money tends to be wagered on these races?
Larry Kupper
The thing is, I don’t always remember the exact numbers off the top of my head, but the amounts wagered are incredible. For example, about $320 million was wagered on the Kentucky Derby in 2024 alone. And across all horse racing in the United States, roughly $11.2 billion was bet in 2024. That’s an astonishing amount of money.
John Bailer
Can you talk a little bit about the types of bets people make on horse races?
Larry Kupper
That’s a great question. What’s fascinating is the wide variety of betting options available.
At the simplest level, you can bet on a horse to win. You can also bet on a horse to finish first or second—that’s called “place.” Or you can bet on a horse to finish first, second, or third—that’s called “show.”
Beyond that, there are more complex bets. An exacta means picking the horses that finish first and second in the correct order. A trifecta involves picking the first-, second-, and third-place horses in order. A superfecta adds a fourth-place finisher to that sequence.
There are also multi-race bets. A Daily Double requires picking the winners of two consecutive races. Then there are Pick 3, Pick 4, Pick 5, and even Pick 6 bets, where you’re selecting the winners of several consecutive races.
So, as you can see, there are a lot of options.
John Bailer
Holy cow. And with each layer of complexity comes a lower probability of success.
Larry Kupper
That’s exactly right. The more outcomes you’re trying to predict in sequence, the lower the probability of getting them all correct.
John Bailer
There’s also a payoff structure that comes into play when you’re thinking about placing a bet. What struck me was the distinction between the odds you see when placing a bet and what actually happens in terms of payouts at the end.
Could you talk a bit about the betting structure? I think some people—especially those with exposure to odds in a statistics or epidemiology class—might not have an intuitive understanding of how odds work in the context of gambling at the track.
Larry Kupper
Right, that’s a great point. In the United States, there’s a system called pari-mutuel betting. It works like this: for a particular race, people place bets into a shared pool.
You can start betting even before arriving at the track—many people place bets online. But the basic idea is that, for a given race, all the money wagered on a specific type of bet—say, betting on the winner—goes into a single pool.
Betting often begins in the morning. Gamblers may use information from experts, such as what’s called the “morning line,” which provides an initial estimate of the odds. For example, you might place a bet early in the day when a horse is listed at 5-to-1 odds. However, those odds are not fixed.
As more people place bets throughout the day, the odds change. They ultimately depend on how much money is wagered on each horse. By the time the race begins, the final odds reflect the distribution of all bets placed.
So, in pari-mutuel betting, the odds are determined by the bettors themselves—specifically, by how the total pool of money is divided among the horses.
John Bailer
So you have this large pool of money that’s collected, and then the people managing the pool take their cut—the “takeout,” as I learned from your article.
Larry Kupper
Yes, exactly—that’s right.
John Bailer
And then, based on the race outcome and the bets that people have placed, that determines the post-race payout structure—the dollar odds.
Could you define “dollar odds” for us?
Larry Kupper
What’s interesting is that when we were working on this paper, we had to decide on the best way to measure a horse’s chances of winning, placing, or showing.
In the United States, the minimum bet is typically $2, and odds are often expressed in formats like 3-to-2. However, we found that format difficult to work with from a statistical perspective. So, we converted everything to a $1 basis—what we call “dollar odds.”
For example, 3-to-2 odds become 1.5 in dollar odds, meaning $1.50 per $1 bet. Similarly, 9-to-5 odds become 1.8, and 4-to-2 becomes 2.0. We used this dollar-odds measure consistently for every race and every horse in our analysis.
John Bailer
And those odds tell you how much you win based on what you wager. So, for example, 2-to-1 odds mean that if you bet $1 and your horse wins, you get $2 in profit.
Larry Kupper
That’s exactly right. Let’s say you’re betting on a horse to win, and at post time the dollar odds are 6.0. If your horse wins, you would receive $6 in profit for every $1 you bet. Since the minimum bet is typically $2, that would mean $12 in profit on a $2 bet.
So, if you bet $10 at 6-to-1 odds, you’d earn $60 in profit. That’s how it works. In our study, we used these dollar odds at post time as our numerical measure for every horse in every race.
John Bailer
This is really interesting. When I first read your paper, I was thinking about odds in the context of disease—where higher odds suggest a higher likelihood of an outcome.
But with gambling and dollar odds, it’s essentially the inverse. The larger the odds, the larger the potential payout—but the lower the probability of winning.
Larry Kupper
That’s exactly right. The higher the odds, the lower the chance of winning—or of winning any money, for that matter.
John Bailer
Could you give a couple of examples of how dollar odds translate into probabilities of winning?
Larry Kupper
Yes, the dollar odds are related to probability in the following way: the dollar odds represent the ratio of the probability of not winning to the probability of winning.
If you rearrange that relationship, the probability of winning is equal to 1 divided by 1 plus the dollar odds. In other words:
If the dollar odds are 2, the probability of winning is 1/3.
If the dollar odds are 10, the probability of winning is 1/11.
So, the larger the dollar odds, the lower the probability of winning. That’s exactly what we examined in the paper. We looked at favorites, which have the lowest dollar odds, as well as long shots and heavy favorites.
John Bailer
You’re listening to Stats + Stories, and we’re talking with Larry Kupper about the Triple Crown of horse racing, which begins each spring with the Kentucky Derby.
Larry, you anticipated my next question—the “after the break” question. What did you learn? Where should I be putting my money this horse racing season? Although, keeping it in my wallet might be the safest option.
Larry Kupper
That’s a fair takeaway.
Our goals in this work were threefold. First, we wanted to see how dollar odds actually perform. Second, we wanted to examine how favorites and long shots fare. And third, we aimed to suggest possible optimal betting strategies.
In the Significance article, if you look at the figures, you’ll see that post-time dollar odds behave as expected. For example, one figure examines the proportion of horses finishing first as a function of their post-time dollar odds.
We looked at the percentage of winners among favorites—those with the lowest odds—then the second-lowest, third-lowest, and so on. The relationship is monotonic, just as you would expect: as the odds increase, the probability of winning decreases.
This pattern holds not only for winning but also for placing (finishing first or second) and showing (finishing first, second, or third). So overall, the post-time dollar odds behave in a very consistent and predictable way.
John Bailer
Were there any differences among the races that stood out?
Larry Kupper
Yes, there were some differences across the three races.
For example, over a 26-year period, about 38.5% of Kentucky Derby favorites won. In the Preakness Stakes, about 42% of favorites won, while in the Belmont Stakes, it was closer to 27%.
Overall, across all three races, only about 36% of favorites won during that period. So even when betting on favorites, the odds aren’t especially favorable.
Even when we looked at heavy favorites—those with odds of 2 or less—only about 41% won. So, in general, it’s still not very likely that you’ll win consistently.
John Bailer
What was the biggest surprise for you as you were doing this analysis—looking across the outcomes of all these races?
Larry Kupper
One of the biggest surprises for me was this: if I were actually placing bets, my strategy would differ by race.
If I were betting on the Kentucky Derby, I would bet on favorites—not long shots. But if I were betting on the Preakness or the Belmont Stakes, I would do the opposite and focus on long shots.
There are a couple of reasons for that. In the Kentucky Derby, the payoff is generally higher than in the other two races, and the probability of favorites winning is relatively strong—around 38%, which is close to the highest among the three races. So, with better payouts and solid winning chances, betting on favorites in the Derby makes sense to me.
In contrast, long shots tend to perform better in the Preakness and Belmont than they do in the Derby. Let me ask you—what do you think might explain that difference?
John Bailer
Oh man, I had a feeling I was going to get a comprehensive exam question in the middle of this. One thing that comes to mind is the number of horses running in each race.
Larry Kupper
Exactly—you nailed it. In the Kentucky Derby, if you’re betting on a long shot, that horse has to beat 18 or 19 other horses. But in the Preakness and Belmont, the field is much smaller, which gives horses more room to maneuver—whether on the inside or outside.
With fewer competitors, a long shot has a better chance. In fact, in the Preakness, about 18% of long shots finish in the top three, and in the Belmont Stakes, it’s about 19%. In the Kentucky Derby, that percentage is less than half of that.
The key point is that if you’re betting on long shots—say, a horse at 20-to-1 odds—you don’t need to win often to make money. Sometimes, it’s worth taking that chance.
John Bailer
So when you think about pre-race odds, how does that affect where horses start in the field—when they’re lined up?
Larry Kupper
The starting positions are determined randomly. Even if a horse has the best odds, it doesn’t necessarily get a preferred position—they use a random draw.
That said, it’s an excellent question, because starting position can still factor into betting decisions. For example, in the Kentucky Derby, with such a large field, if a horse is assigned an outside position—like 18 or 19—that can be a disadvantage.
What’s interesting is that bettors use a wide range of information when making decisions. They might consider weather and track conditions, the current health of the horses, past performance records, and details about the jockeys and trainers. They also look at morning-line odds, often informed by professional handicappers.
All of that information can be used to guide betting decisions before a race.
John Bailer
Are the starting positions known ahead of time? I’m thinking about how that factors into betting—there’s a draw beforehand, right?
Larry Kupper
Yes, exactly. The draw happens in advance, so the starting positions are known ahead of time. That means bettors can factor that information into their decisions.
In general, horses closer to the rail may have a slight advantage, although it depends on the race and conditions. It’s all part of what makes horse racing so interesting.
John Bailer
So, you’ve given us some takeaways. For the Kentucky Derby, you tend to favor betting on favorites because of the combination of payout and probability. And for the Preakness and Belmont, you lean a bit more toward long shots.
Larry Kupper
That would be my bottom line—yes, exactly. But you know what was interesting, John? The reviewer of our paper felt strongly that we should discourage gambling. He said the paper wouldn’t be published unless we addressed that point at the end.
So we did. We essentially said that gambling on horse racing is probably not a good idea for the average person. As we put it, “The surest way to end up with a small fortune gambling on horses is to start with a large one.”
We also included a quote—though I’m forgetting the exact source—that compared betting on horse racing to something like “animated roulette.” The point is, it can be fun to bet occasionally, but even professional gamblers likely struggle to make consistent money in the long run.
John Bailer
That reminds me of a quote I once read—that lotteries are a tax on people who don’t understand probability. That seems related to what you’re saying here. If it’s part of your entertainment, enjoy it—but keep it in perspective.
Larry Kupper
Exactly. Don’t go in and bet $10,000. The average person is going to lose money—there’s no question about that. But it can be fun to bet five or ten dollars now and then.
And like I said, if I were going to the Derby, I’d bet on favorites. If I were going to the Preakness or Belmont, I might take a chance on long shots, based on what the data suggest.
John Bailer
So, I have to ask—are you planning to have any stake in the races coming up?
Larry Kupper
Am I going to place any bets?
John Bailer
Yes—are you going to put a little money down?
Larry Kupper
That’s a good question. I’ve thought about it—maybe trying something online at some point. You can always bet off track these days.
John Bailer
Well, Larry, this has been a delight. It’s always a pleasure to talk with you. I’m afraid that’s all the time we have for Stats + Stories today.
Larry Kupper
John, it means so much to me that you invited me. I really can’t tell you how much I appreciate it. It’s been a lot of fun, and our personal connection means a great deal to me. I’m so glad to see you doing so well. Thank you again for everything.
John Bailer
Well, back at you. It’s always a pleasure to catch up and talk about the fascinating work you continue to do.
Larry Kupper
That’s right. I appreciate it. Thanks again, John.
John Bailer
You’re welcome.
Stats + Stories is a partnership between the American Statistical Association and Miami University’s Departments of Statistics and Media, Journalism, and Film.
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Be sure to listen for future editions of Stats + Stories, where we discuss the statistics behind the stories—and the stories behind the statistics.