**Three-Lobed
Set Theory:**

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

- By
Charles Carroll

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 horses probability of __winning__
the
race. In a high uncertainty race, sometimes the odds on the
first
four or five horsesor even all the horsesmay 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 dont 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 digressat any rate, the Ballentine logo is one representation of
a three-lobed set and thats 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 its a
tri-lobular
setlike 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 racing____and
of
handicapping__. Can one of your
mortal-lock-Non-Contenders jump
out of its circle of discarded horses and Winor 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 circlesWin Contenders, Money Contenders,
Non-Contenders. If you could get those three bubbles floating
separately for a race every now and thenand __know__
ityoud 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 spheresome 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 wheelsa 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
thats 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 aint easy. Its 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.
Im sorry to say I dont know where the idea originated, but it has
been in the literature for some time, notably in Dick Mitchells 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 (Ill 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 dont 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__
Sciencethis is __Art__. Even though were
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 Artand 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 linean Expected Line in which they predict (somewhat
like the Morning Line, but with significant differencesand 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 Dont 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 handor, maybe with a ten-dollar
calculator. While its 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, Ill 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
oddsand winning! Money isnt __everything__,
but its how
you tell youve won.