Three-Lobed Set Theory:

(Not) A Mickey-Mouse Approach To Odds-Making

Charles Carroll

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There is a little wrinkle in the process of creating an odds line that is probably too complicated to include in any preliminary discussion, such as the first articles in this series, so it was just mentioned there in passing.  When I make an odds line by hand, probably more often than not, the percentage given to each horse does not actually represent that horse’s probability of winning the race.  In a high uncertainty race, sometimes the odds on the first four or five horses—or even all the horses—may be estimated “Win” probabilities.  Just as often, however, only two or three horses may be Win probabilities, a few others may be in-the-money probabilities, and still others are “not-in-this-lifetime” camels.

This discussion can get arcane in a hurry if you start thinking about probabilities and dealing with them mathematically, with the idea of computerizing it (as I did a while back).  Without going to the numbers here, if you work with them a while (for that matter, if you just watch races for a while), you will probably come to the conclusion that in most races there are Win Contenders, Money Contenders, and Non-Contenders.  While anything can happen in a race, Win Contenders and Money Contenders are not necessarily the same set of horses. Sometimes they are almost separate “sets.”

Remember “set” theory?  Most everyone remembers drawing those overlapping circles in high school, even if we don’t remember what the heck they were for.  You may also remember Ballentine Beer, with the logo of three, slightly interlocking rings, like a cloverleaf, which Army drill sergeants used to give out to good shots, but I digress…at any rate, the Ballentine logo is one representation of a “three-lobed set” and that’s the image here.  If all horses were Win Contenders, there would only be one circle, and all their probabilities of winning would comprise it.  Or, if all horses were either Win Contenders or Money Contenders, there would be two circles interlocking to varying degrees, like the way they portray looking through binoculars on a movie screen.  But, there is the third case of Non-Contenders, so it’s a “tri-lobular set”—like binoculars after a few too many Ballentines.

The fact that these three circles interlock, Ballentine fashion, shows that certain members are shared.  The interlocking area represents the uncertainty of racingand of handicapping.  Can one of your mortal-lock-Non-Contenders jump out of its circle of discarded horses and Win—or pop into the Money circle to Place or Show?  Mine can.  Can one of your Win Contenders lose?  The fact that the word “Contenders” is plural guarantees it.  These interlocking areas of the sets represent those horses that share these crossover possibilities.  Now picture these circles changing in size, and the degree to which they interlock, depending upon the nature of the race, the capabilities of the horses, jockeys, trainers, etc.—but, most of all, your own handicapping.  This is a little out-there, but if you wanted, you could view handicapping as the task of reducing the overlap between those three circles—Win Contenders, Money Contenders, Non-Contenders.  If you could get those three bubbles floating separately for a race every now and then—and know it—you’d be one rich dude, Dude.

“High uncertainty” races are those in which the three circles move together and, occasionally, they may form one sphere.  Remember the mid-summer race at Churchill Downs, where the combined stud fees of the ten horses in the gate could cancel the national debt for certain third-world nations?  That race might be represented by a sphere—some horses may be more likely to win on a particular day, but when it gets down to it, any horse could fire.

I come from a “mixed-meet” state, where Quarter Horses make up at least a third of most race cards, so I get to see a lot of highly competitive races, where the “set diagram” often looks like a pumpkin on wheels—a lot of well-bred, hot horses making up a big Win Contender bubble.  Here too, and across the country, in some of the cheesier Thoroughbred races, you may see the same diagram, but with Non-Contenders filling the biggest part of the pumpkin.  This is one reason you may already love cheesy Thoroughbred races.

The really useful thing about this Ballentine “set theory” image (which, if you turn it upside down, resembles Mickey Mouse), is that when you are making a conventional odds line, as discussed at the beginning of this series, it is usually a Win odds line, since that’s all anybody ever talks about, as I did in Part 1.  However, every odds line is actually composed of Win Contenders, Money Contenders, and Non-Contenders.  How do you deal with that in an odds line?

The short answer is:  it ain’t easy.  It’s not something you are going to do with a pencil in the margin of your Form.  It requires a computer to do it quickly, but if you can do it in the background, without any effort (that is, after it is programmed), it is a really nifty baseline to use in planning bets against the public odds.  [It also happens to be such a seriously brain-bruising exercise that I do not know anyone who has done it well who is going to divulge their exact algorithm.]  There is a relatively simple way, however, where you can weight your odds if you make them by hand.  I’m sorry to say I don’t know where the idea originated, but it has been in the literature for some time, notably in Dick Mitchell’s books as well as others.  There are several variations of it and, if you pursue it, you may want to try a couple of different approaches or make up one of your own.

As with any odds line, the first step is to rank the horses.  You can do it with the “mental templates” described in Part 1, or there may be something inherent in your method that quantifies the horses.  In my case, I represent each horse with a speed figure (I’ll get into that someday, but for now, be assured that the figure represents a whole lot more than raw speed).  If you do end up with a number representing a horse, you have the essential ingredient for automating this process either with your own program, spreadsheet, or database, if you wish.  If not, you can still do as described in Part 1 and estimate a probability for winning for each horse, but don’t bother yet translating that to odds.  Instead, look at your ranked horses in order and decide which are contenders.  (There is a lot more to be said about Win-, Money-, and Non-Contenders, but for now, just Win Contenders.)  If you have your horses ranked in order, you may want to draw a line to separate the contenders from the non-contenders.

If you come from a background in science, you already know this, but maybe I should say it:  this is not “Science”—this is Art.  Even though we’re dealing with numbers and talking about computers, we are not applying any rigorous tests or much or anything beyond opinions and experience, when we use this approach.  But, experience shows that it works pretty well.  Simply drawing the line between Contenders and Non-Contenders requires some art on your part and you have to at least define them to suit yourself in order to do it.  The basic approach is to weight the odds on the Contenders and what you are doing is, basically, accounting for the tendency of the crowd to “pile on” contenders.  The amount that I recall seeing recommended most often is dividing 80% of all probability between the Contenders (in proportion to your original ranking percentage) and simply relegating 20% to all the rest without worrying about distribution.

You can see that if you have three contenders in a 12-horse race, this would tend to load them up on shorter odds, while five or six contenders would generally spread the odds more thinly.  If you become adept at this, you may not want to apply a rigid rule at all but, instead, use a sliding scale that you adapt to fit the particular race as you see it.  Again, this is Art—and maybe a bigger canvas than you want to fool with, but the most valuable thing that a “value bettor” can have is their own “fair odds” line in order to evaluate value in the odds offered by the public.  I have some good friends who are masters of the game who go a step further and use a third odds line—an “Expected Line” —in which they predict  (somewhat like the Morning Line, but with significant differences—and a lot more accurately) what the public odds should be.  This gives them a finer level of analysis of what is represented by the actual public odds, and it is especially useful as a warning flag for false overlays, or cases of “JDFR” —“Just Don’t Feel Right.”  With that level of experience and play, a good sense of “JDFR” can save occasional blunders.

Believe it or not, some people actually do the basic part of this approach by hand—or, maybe with a ten-dollar calculator.  While it’s not a required course, it has a real place in the “Earn-While-You-Learn” University of Horse Racing.  As I said in the first of this series, it is also a great refresher course, and when I feel myself getting jaded by the routine of computer handicapping, I’ll stop and do it for fun.  Some people may say that money is the only thing, but even though it is not my daily routine, there is a special satisfaction in handicapping a race by eye and by hand, assigning artful percentages to Win, Money, and Non-Contenders, vying with those percentages against the public odds—and winning!  Money isn’t everything, but it’s how you tell you’ve won.


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