Chapter 7 - The Law Of Probability-And Amendments Thereto

Knowing a few cold statistics steers a bettor's money to warmer horses.

Next to "I just bumped into a horse owner's brother,” the expression heard most around tracks is: "The law of probability favors Ragged Ann in the fifth."

Actually, the only law that favors Ragged Ann or any other horse is the law for the prevention of cruelty to animals. The fan who swears by the "law of probability" doesn't care if there actually is such a law and if so, who passed it. All he wants to know is how it works. Usually, he expresses it by saying a certain horse is "due."

There is no more reason, however, to believe a horse is "due" to win than there is to assume that a bowler who consistently rolls 270 or 280 is "due" to knock out a perfect game of 300.

A horse which runs second or third a few times may not be "due" to win. He may have reached his peak in any one of those races. The frantic owner may drop the horse in class but still he may lose because his form is fading. There is nothing to do then but to "unwind" him, give him a rest, and later start to train him again in the hope he can do better. Many players have gone deep into the "soup" because they backed a horse they believed was "due" rather than one which their best judgment told them was the most logical risk.

The fan gets his vague understanding of the "law of probability" by picking up half truths about chance probability as developed by statisticians. Chance probability which yields good results when applied to many fields cannot be transferred entirely to racing because in racing the variables are influenced by too many other factors. If horses were machines and if track conditions always were the same, then chance probability might be fairly reliable in pointing to winners. But some study of chance probability is useful in order to see in just what patterns the variables can be fitted. These variables, it must be kept in mind, include speed, distance, consistency, weight, etc.

It cannot be emphasized too strongly that statistical methods should be applied only to an analysis of mass data. As applied to racing, this simply means that a sufficient number of races should be studied to permit the trait or characteristic presumed to be present to reveal itself in definite form.

For example, let's assume a player wants to determine what chance the top-weighted horse in a race has of winning. The player doesn't worry about distance, consistency, track conditions or anything else. He just takes the horse which was assigned the most weight by the track handicapper. If he checks half a dozen races, he may find that all of such horses win, or all of them lose. The probability is that some will win and some lose.

The player, however, has no information of any value to him. But if he checks many races—several hundreds of them—he may find a pattern which will tell him whether top-weighted horses are good risks. Then, he can "refine" his study still further by noting the different types of races.

In fact, one man did this very thing and discovered the top-weighted horse wins most often in top allowance races, allowance stakes, and handicaps, except the extravaganzas such as the Kentucky Derby, Arlington Class, etc. What the player did, in effect, was to confirm the estimates of the track handicapper who, broadly speaking, assigns the top weight to the horse he regards as the best one in the race. The player, however, went further by limiting his activities to certain types of races only and also noted the horse's ability, as shown by past performances, to go the distance of today*s race if the distance was longer or shorter than in the horse's last race.

Another illustration of chance probability—as far as it can be applied to racing—can be shown by referring again to races in which the favorite is odds-on, that is, less than even money. It was shown that 70 per cent of these odds-on horses win.

This ratio was determined by studying hundreds of races in which there were odds-on favorites. But even that percentage can be improved, the same study showed. It was found that the percentage rises for muddy tracks or for tracks that were muddy but have not yet dried out sufficiently to be called just "slow." This percentage is also better if the race is a sprint—that is, a distance of six furlongs or less.

This knowledge that odds-on favorites win more times than they lose and that the percentage of winners increases on off tracks can be used by the player in two ways. He can use the winning percentage figure as the basis for developing some method for playing them that will yield results. Obviously, he is dealing with horses that will pay mutuel prices of less than $4.00 for each $2 ticket. He must take the price into consideration when he tries to figure out a method of play.

The second way in which the player can use the same information is to look carefully before playing against an odds-on favorite on a muddy track, especially if several of such horses have lost in previous races there. That doesn't mean that if two or three successive odds-on have lost that the next odds-on will win as certain as death and taxes. Such belief is what also helps to make players go into the "soup."

It must be remembered at all times that any form of chance probability is based on mass data—or for us, it is based on a check of many races. It predicts patterns that will emerge over a number of races and does not necessarily tell the possible outcome of any individual race. Just because three successive odds-on have lost doesn't mean a fourth will too. The fourth race merits a separate judgment.

Another way to explain the operation of chance probability is to take a set of figures from life insurance policies. If an insurance company issued policies on the lives of 1,000 children, all 12 years old, the company cannot predict which of those 1,000 children will live to reach age 50. The company, however, can tell very accurately how many of the 1,000 children will live to be 50.

Transferring that to this odds-on racing situation, the fan can tell that if he should check 1,000 races with odds-on, he will find that these top-heavy favorites have won 700 of the races. But the fan, then, can't predict which particular races of the next 1,000 that the 700 will win.

The same figuring can be applied to favorites of all kinds whether or not they are odds-on. Year in and year out, at all tracks, about 35 per cent of favorites will romp home first. Roughly, this means that one of every three races is won by the horse whose odds at post time are the lowest for any entry in the race. Since this pattern of one of every three favorites winning has gone on for years, the fan can assume that it will remain fairly constant.

If the pattern followed the exact rhythm of two losses and one win, two losses and one win, etc., there would be no racing because everybody would wait two losses and then play the favorite in the third race. Six or seven favorites may win today and only one, or none, tomorrow. And the chances are 25 to 1 that a card of eight races will be run without one favorite winning.

Perhaps, the best way to discuss chance probability is to consider the tossing of a coin into the air. A southern university, as an experiment, had a coin tossed more than 300,000 times and found that the percentage of heads and tails was even. In other words, if the coin is tossed hundreds of times the heads and tails will balance themselves.

While the coin was being tossed 300,000 times, let's assume that at the halfway mark, the score stood: heads, 125,000; tails, 25,000. (It is unlikely that the score would be that askew but let's assume it did happen.)

On throw 150,001, the odds of it coming head or tail still would be 50-50. In other words, at the start of each individual toss, the odds are always 50 per cent that it will be a head. The probability, however, is that at the end of the 300,000 toss, the score will stand even or very close to even.

Suppose, however, instead of tossing one coin that you toss two coins at the same time. The possible specific arrangements of the coins in any one throw are four. This can be seen by calling the coins A and B.

Both A and B could come down heads or could come down tails. Then A could come head and B tail or B could come head and A tail.

The combinations can be seen this way:

Coin A                                  Coin B
Head                                     Head
Head                                     Tail
Tail                                        Head
Tail                                        Tail

Translated into betting odds, it means that on any one toss of the two coins the odds are:

Once chance in four of throwing two heads.

One chance in four of throwing two tails.

Two chances out of four of throwing one head and one tail.

If three coins, instead of two, were tossed, the number of possible arrangements would be eight. That would mean one chance in eight of throwing all heads or all tails.

There is another figure which may set down the player if he doesn't interpret it correctly, and that is the payoff figure. Many players who follow some method talk glibly of the "average" mutuel paid by their selections. Sometimes this payoff may be a very respectable figure.

But again, figures in themselves can be misleading. Suppose a player following 100 races says he won 30 of those races and the "average" mutuel payoff was $10. That means he wagered a total of $200 (on the basis of $2 a bet) and got back $300.

But two or three of his 30 winners may have been boxcar numbers that boosted the average. Suppose he had a $20 winner, a $30 winner and a $40 winner. The three winners returned to him $90 of the $300. The other 27 winners paid him $210 or an "average" of only $7.40.

The player might reasonably expect then that the next 100 races would return him only the $7.40 "average" or total of $222.00. This time instead of $100 profit he would make only $22, keeping in mind the fact that he put up $200 of his own money. Thus, averages can be misleading. The vital statistic here is not the "average" mutuel, but the "mean" mutuel, the payoff that occurs most frequently in the 100 races.

Suppose of the 30 winners, three, as has been indicated, paid $20, $30 and $40. Three others, we will assume, paid less than even money, $3.90, $3.80 and $3.60. Of the other 24, let's assume that 38 paid not less than $6.40 and not more than $8. Of those 20, let's assume that 15 paid $7.20. The "mean" payoff, then, was $7.20, for this is the figure around which the most payoffs clustered.

The player can feel safer in using this "mean" figure than in using "averages." For it will give him a closer estimate of how much money to expect. If he hits any box-car mutuels he can regard them as "bonus."

Post-mortems on losing races often bring about as many incorrect conclusions as may arise from checking figures in business. For example, if there is a last-minute switch in jockeys, the player may say the new rider was the cause of the horse's losing. The player, of course, cannot say definitely that the jockey switch caused the horse to lose, but he is casting about for some reason and there was no other change from his original calculations.

Or if track conditions changed from the time the player made his selection until the horses went to the post, the player may blame that change for his loss. Just how big a part these changing conditions played in the horse's defeat also is subject to more speculation than accurate conclusion.

Thus when the player sets out to "figure" a race he should know what his figures mean. For three and three may be six but six can be made in other ways too, and it is the knowledge of all of these ways which constitutes the law of chance and makes it possible to stand in the payoff line more often.

In illustrating how the law of probability is applied to racing, some actually proven patterns were mentioned in this chapter. The next chapter discloses many more proven patterns determined from mathematical frequencies in race results over many seasons at all tracks.

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