How smart is the betting public? There are conflicting views on this question. In recent years, the claim has been advanced that the 'crowd' is smart, that it gets it more right, or close to right, than any individual can.

But some experts are starting to question this belief. Among them is Charles Carroll, one of the greatest speed-rating gurus in world racing.

Carroll, an American, is currently working on applying his speed ratings to Australian racing. He's the author of the best-selling book, Handicapping Speed. Carroll, an anthropologist by profession, developed a profitable method of calculating speed in both thoroughbred and quarter horse racing.

Carroll has done significant work, too, in the area of making a personal odds line. The following is an edited extract from Carroll's recent writings on this vital subject for any keen punter.

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 as "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.

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. 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 'trilobular 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 racing, and 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?

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 of Win Contenders, Money Contenders and 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.

The really useful thing about this 'set theory' image is that when you are making a conventional odds line it is usually a win odds line, since that's all anybody ever talks about. 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 formguide. 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. 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 programme, spreadsheet, or database, if you wish.

If not, you can still 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 Contenders, Money Contenders 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 per cent of all probability between the contenders (in proportion to your original ranking percentage) and simply relegating 20 per cent 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 his 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 and 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 accurate) 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.

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 Contenders, Money Contenders 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.

Making your own odds line 'by hand' is an excellent tune-up for your personal handicapping.

However, once you've tuned up, you may prefer to computerise it. Computerising the line frees you to put your attention where it almost has to be today: planning your bets against the moving target of the public odds.

The days when you could pick up a formguide and be excited simply because you think you have figured out which horse is going to win are long gone. The job, now, is to constantly roll with the public's odds. You search for 'value', and avoid being stiffed.

So before you start computerising and leave the nuts and bolts behind, you should spend a little time just looking over an odds table. It can be both an educational and a humbling experience.

A couple of weekends ago, at Hollywood Park, the entry of Bienamado and Single Empire, with McCarron and Desormeaux aboard respectively, went off at 1/10. That is ONE-to-TEN. Odds about as far 'on' as they can go.

If you are handicapping a race with 10 or 12 horses in it, how bold do you have to be as a handicapper to set an odds line with a horse rated at 1/10? If you have been to the races more than once, you know something about 'racing luck' and its converse, racing bad luck.

I'd venture a guess that simple racing bad luck can affect more than 10 per cent of any horse's performance capability. The horse next to it in the gates can rear up. Fabulous horses can stumble at the start. Great horses get boxed in by lesser horses. Jockeys go too wide, or try to squeeze too close to the rail.

"You name it, it happens. There is a greater than 10 per cent chance that any given horse will get less than a perfect trip. How much, then, do you have to like a horse to say that although it may have to overcome a bad trip, it still has a 90.91 per cent probability of winning?

I cannot imagine ever making a horse 1/10 in my own odds line giving that horse a greater than 90 per cent probability of winning in a field greater than two - much less betting on it.

Which brings up an interesting point: just how far 'on' would you be willing to go when setting odds on a  stand-out horse and - assuming you are even a tinsy bit conservative - why is the public willing to go so much further?

It sometimes seems that newer, grander notions of 'the crowd' have crept into our basic concepts of the sport. I sometimes suspect this was a subtle influence of the Dr. Z syndrome, which included a basic premise: 'The crowd is smart, so let them do the handicapping and analyse them'.

Well, the crowd is not that smart. In fact, the idea is sort of self-contradictory. If the crowd was really smart, there would be no overlays for 'Z-market analysers' or more normal run-of-the-mill handicappers. You don't have to look far for evidence.

One of the quickest proofs is the crowd's 'piling on' overbet underlays.

One of the fundamentals is that before the race is run, no matter how good you are, NOBODY, not you, not the crowd, knows exactly what the true odds of the race are.

Since there is always some error in the 'fair odds' that you estimate, you will eventually go broke if you accept only 'fair odds'. In order to buffer against the inherent errors of your pre-race odds line, you have to sit on your money for fair odds as well as underlays.

Underlays can happen in any odds range; they don't have to be 'odds on'. In fact, it's probably more common in more normal odds ranges. A horse you make 10/1, with no prayer as a contender, catches the crowd's eye and drops to 4/1, becoming a drastic underlay."

Learn more about Charles Carroll on the Internet:

By Richard Hartley Jnr