Thaler and Ziemba on Efficient Betting Markets & Favorite/Longshot Bias

I’ve read it before (around 2005), but not since being exposed to Thaler’s other excellent work in behavioral economics a few years back. Ziemba (Dr. Z) is, of course, a legend for his work on arbitrage in place and show pools. I’ve always believed that betting markets are mostly efficient (especially regarding public information), but that certain public cognitive bias can be exploited to find long-term value. This article explores this area.

After re-reading it again, it’s still a very worthwhile read, and a solid introduction to the field. It’s chock full of rigorous examination of much of the “folklore” (the authors’ word) of the racetrack. It’s especially useful for conclusions regarding the public’s typically sharp handicapping, finding that “the racetrack betting market is surprisingly efficient,” which cuts at most of the common claims of the mainstream handicapping literature. It does however find inefficiencies (at least at the time), especially with the well-documented “Favorite/Longshot Bias,” which generally finds pricing errors at the very top (for example, 3/5 or less) and very bottom of the odds (for example, 20/1+). In my favorite part, the authors lay out the potential reasons for the bias:

Screenshot 2014-10-02 11.44.11

Indeed, just like with other decisions, bettors are motivated by a mix of both rational and irrational motivations. I especially like the serious consideration given to the process of betting and particularly, the added utility derived, especially from longshot betting. The short time horizons of most bettors also tend to influence irrational behavior, which also explains the increased severity of the favorite/longshot bias toward the end of racing cards. The goal of the sharper bettor is to find and exploit the irrational crowd decisions, while maintaining their own rationality.

Click here for full article

Image: Rachel Kramer, 2012.

Wise Dan: Let it Ride

I’ve tried to constantly beat Wise Dan on the turf, but instead, he always beats me. Not only have I lost money, but also the opportunity to wager on one of the most reliable horses in all of racing. So, out of curiosity, I decided I wanted to figure what he would have paid if I had fully embraced him from the beginning.

Let’s say a bettor put a minimum $2 on him back in August 2012 when he made the (now) permanent move to the turf. This bettor would have won only $5.00 that day, but let’s say he saw a turf monster in the making. So, wanting to make more, he decides to “Let it Ride” and re-invests his entire winnings each time Wise Dan runs on the turf, or he retires. For argument’s sake, he doesn’t bet Wise Dan when the Shadwell is moved to the polytrack last year knowing that there’s more risk with the surface change (a fair assumption, I think).

Sounds silly, and a bet that surely would have to catch up to you eventually. And, besides, what could it possibly pay? I mean, he’s been odds-on in every start since the Breeders’ Cup, so you can’t possibly make any money doing this. But, I was curious, so I opened up excel, typed in some odds, and let it do its magic.

If our hypothetical bettor had put $2 on Wise Dan and just let it ride through the streak, he would have made over $1,100 going into tomorrow. 

The result, of course, is very dependent on “letting it ride.” Pocketing just 20% of your winnings demolishes the return and leaves you with $75 pocketed and only a very Douglas-Adams-like $42.42 headed to tomorrow.

It would, of course, be much tougher to make these bets with $100 units (and rationally, I can’t imagine not taking profits) but, just for fun, here’s how it would have turned out:

Here’s the 20% pocketed at $100 units.

Can he do it again on Saturday? Well, he’s certainly done it before, and I’m officially done trying to beat him.  I’m not recommending this type of bet (one wipe out is catastrophic), but at least with Wise Dan, it would have paid very handsomely.

Scared Money & Multi-race Wagers

One reason I’m handicapping in public through this Belmont meet is to share the “inner game” of playing the races everyday. The game of betting is much more than just analytics; it is also a constant battle for self-discipline and emotional control. And this means more than not just staying strong through the lean times, but also maintaining proper perspective through the great times. In fact, this is one reason this game is so challenging, and why betting is growing more popular everyday. It not only requires analytical thought, but also strong self-discipline and constant learning.

One thing that often gets in the way is a phenomenon known as “scared money.” Essentially, it’s when you make any wager that you are afraid to lose. It’s related to “pressing,” or making bets because you really want a score right now.  In contrast, I find that when I’m playing patiently, I never expect any particular bet to hit, but I know that somewhere and sometime, the right number of bets will hit. Scared money–motivated by impatience–makes any one particular bet far more important than the long-term.

Scared money can be very deadly in in a multi-race wagers, such as the P3, P4 or P5. I find that if I am adding horses to a ticket only because I am afraid that the ticket is going to miss if I don’t, then I’m making a mistake. Even if the bet hits, it still was a bad bet. In contrast, like any set of wagers, each multi-race ticket needs to be part of a bigger long-term, value-seeking strategy.

Hindsight is always perfect, but in both making my wagers and reviewing my wagers, I always try to ask myself if I’m motivated by fear of missing the ticket, and whether adding additional horses actually adds value to the ticket. I’ll still screw up — although thankfully much less than I did when I was younger — but seeing and learning from mistakes is the key to avoiding the same pitfall in the future. But, then again, nobody said that playing the races was easy!





Gladwell on Taleb (and Niederhoffer)

It’s simply one of the best articles of the past 20 years: Malcolm Gladwell on the investment strategy of Nassim Nicholas Taleb.

I remember the first time I read it vividly; it substantially changed the way I think about the world. I had already read Taleb’s classic “Fooled by Randomness.” But when Taleb’s philosophy is placed against rival Niederhoffer’s, more insights are formed. Much is due to the skilled storytelling (as always) from Gladwell.

Click here for article

Image: John Morgan, Probability and Measure. Copyright 2009.

Podcast #4: Ellis Starr

I had a great conversation with Ellis Starr, National Racing Analyst for Equibase. He can be found on Twitter @ubercapper. If you’re not following him, you should!

We talked about many things related to handicapping. Highlights include:

  • Being involved in the very early days of the internet
  • Art v. Science of Handicapping
  • Changes in the Game
  • Record-keeping
  • Value
  • Confidence v. Arrogance
  • Emotional side of the game
  • Run-outs
  • Trusting yourself
  • Lifetime learning
  • Random Events
  • Revisiting past races
  • Wagering as a science
  • Handicapping by elimination
  • Uncertainty
  • Bell Curve of decision theory
  • Representative races
  • Multi-race strategies

Click here for the podcast. 

Book Review: Exotic Betting

Winning at the horse races is about two things. The first is handicapping the race — finding the questions, assessing uncertainty, and understanding the possibilities. The second is wagering — how to structure your bets to maximize your return given your handicapping of the race.  The mainstream handicapping literature on bet structuring is quite thin and one of its main entrants is our subject here, Steven Crist’s Exotic Betting.

At its core, Exotic Betting is  an introduction to exotic bet structuring. It is appropriate for the beginning to intermediate horseplayer. Crist discusses basic strategies for both within-race (exacta, trifecta, and superfecta) and multi-race (daily double, pick three, pick four, pick five, and pick six) wagers. For the most part, the strategies are sound and provide a good, launching pad for deeper thinking about the exotics. In particular, Crist mentions the single, most important piece of advice for the exotics bettor: Exotics can not be used as a means to profit from an overall lack of clarity. You simply can not use these bets as a replacement for difficult decision making. While you may occasionally reap the reward from this method, the bettor is typically not getting a return in accordance with the risk undertaken. And that is what exotic betting is about — finding ways to increase the return while managing risk — all based upon your opinion and analysis of the race.
Written on such a narrow topic, I would have preferred Crist to emphasize and detail strategies for maximizing potential return at appropriate levels of risk through the use of exotic wagering. Simply put, I wanted to read a discussion of when to add that extra horse to a trifecta or Pick 4 ticket. Unfortunately, Exotic Betting does not delve deeply into a fundamental dilemma of wagering.  For example, in devising his tickets for the Pick Four and Pick Six, he normally divides his horses into four groups – A’s (likely winners), B’s (horses that can win if the A’s fail), C’s (horses that could conceivably win, but are unlikely) and X’s (eliminations). Based on these classifications, he then creates tickets with various combinations of the non-eliminated horses to cover a vast range of possibilities. While Crist gives some examples of his “Chinese Menu” selection process (e.g. three from Group A with one from Group C), there is no discussion of the reasons why certain combinations are used. As a result, the reader is left wondering why he determined that potential financial rewards are best served by these combinations, and how to make these adjustments to their wagers. The same problem occurs in discussing the amounts to bet on certain combinations. In fashioning his tickets, Crist mentions that when he plays a Pick Four ticket with four A’s (the likeliest winners), he buys it four times to compensate for the lower payoff. Yet, much like the earlier discussion regarding the selection of combinations, no explanation is given on why or how these amounts were calculated. There is nothing worse than putting out capital at an undue amount of risk for the range and likelihoods of various returns, and, consequently, the horseplayer needs better tools to assess when he has either overplayed or underplayed their capital.

Exotic Betting is available used at Better World Books.


Podcast #1: Mark Cramer

Check out the debut edition of the All Day Racing podcast, featuring noted handicapping author, Mark Cramer!

Listen to Podcast #1:  Mark Cramer

We discuss:

  • Value — What is it? What isn’t it?
  • Belmont Stakes Review
  • False Favorites
  • Making Past Performances
  • Using Data Differently
  • Precision
  • Betting Personalities
  • Skipping races
  • Small-tracks and the joy of the day at the track


Rethinking Multi-Race Exotics

Having a ticket crafted out of various combinations of your “A”, “B,” and “C” rated horses is all the rage in wagering. Generally, you hit your ticket if all of your A’s win, or some combination of A’s & B’s, or A & C’s. Explained by Steven Crist in “Exotic Betting,” (full review here) and the basis for the DRF wagering calculator, this method lets you go deeper for less money in pick four, pick fives, and pick sixes. It is colloquially known as the “Chinese Menu” approach, in reference to Chinese food family-style menus that let you choose a couple of items from column A and B, respectively.

This method — now considered the mainstream approach — is flawed from a value perspective.  By eliminating tickets with multiple longshot horses, you cut out the rarest combinations and those that will pay the most. Many of these combinations can potentially scoop the pool at smaller tracks. Getting into these “soft spots” is where the outsized payoffs are. The proponents of the Chinese Menu approach need to show that the money saved by leaving these combinations off the tickets makes financial sense by giving up chances at year-changing payouts.  It is my experience that they do not.

I prefer the combinations of different levels of “unlikely” in order to maximize return. The greatest payoffs occur when you can combine “very unlikely” (in the eyes of the public, but still a contender) with “only slightly unlikely.”  The tighter the multi-race exotics, the better (Daily Double over Pick 3/Pick 3 over Pick 4 and 5), with the maximum amount of money pushed onto your opinion.  That said, there are many “soft spots” that can bring about outsized returns throughout the longer multi-race exotics.  Knowing how to play these well can make a significant difference in your bottom line.