Criteria for Calculating the Top Three Rated

A LITTLE LIGHT HISTORY
Twenty five years ago, when I first considered creating my own ratings, the most accurate ratings that one could buy came from the Timeform organisation in Halifax. Timeform ratings (as distinct from Timeform speed figures) are not based on time, but on collateral form expressed in pounds weight, using roughly the same methods as those that are employed by the official handicappers.

Much of Timeform's advertising rested on the claim that 50% of all races were won by one or other of Timeform's top-two rated. In making this claim, Timeform operated on the basis that if there were two joint top-rated horses, then the horse or horses immediately below them were second-top (rather than third-top) rated.

Here are a couple of fictitious examples:

Phils Boy 120      Joint top-rated
Dylan 120          Joint top-rated
Betsi Girl 120     Joint top-rated
Taxman 119         Second rated

St Pauli 120       Top-rated
Bamboozle 116      Joint second-rated
Welsh Warrior 116  Joint second-rated
The Wizard 116     Joint second-rated

Timeform have never allowed, and still don't allow subscribers to explore the statistical basis for their claims eg:

- What is the difference between their figures for handicaps and non-handicaps?

- What are the percentages for top-rated, those rated one pound behind the top-rated, two pounds behind the top-rated, three pounds...etc?

The only figures they are prepared to make public are that they score around 30% for top-rated horses, and 50% for horses in the top two.  Incidentally, I don't think that there is much to dispute in these claims.

When I started producing my own ratings, I decided to use Timeform as my benchmark. In other words I aimed to get at least 30% top-rated winners and 50% from my top two. I therefore defined my top-rated and second-top rated on the same basis as that used to this day by Timeform.

CONTINUOUS V DISCRETE
Traditional handicapping methods (including those used by Timeform) rely on expressing a horse's ability in pounds (weight), thus creating a ladder of ability where each figure represents a discrete, or separate, rung.

There is no provision for expressing the difference between two horses in ounces, or fractions of an ounce.

Traditionally, bookmakers' odds have also been expressed as a series of discrete values eg:

Even money, 11/10, 6/5, 5/4, 11/8, 6/4.

These correspond to probabilities of:

0.5, 0.476, 0.455, 0.444, 0.421, 0.4 (to three decimal places)

In short, discrete values have hitherto been the norm both in ratings and in bookies' odds.

However, the program that generates HOOF ratings produces, in the first instance, a calculation of each horse's chance of winning expressed as a probability, ie some value on a scale from 0 (no chance at all) to 1 (absolute certainty).

This scale is continuous. It's entirely possible that two horses could be separated by no more than, say, 0. 000000000000001. For practical purposes, I use a cutoff of three decimal places. So in theory, a horse rated 0.33 is higher in rank order than one rated 0.329.

However, most people want to use the output from the program to have a bet, and the natural 'language' of betting is, or until recently was, bookies' odds. Hence the TR_ODDS (true odds) column, and the two 'value bet' columns.

It follows that there has to be a way of converting probabilities (which are continuous) to bookies' odds (which are discrete). I have always had a very conservative policy with regard to this: a horse must have a probability value AT LEAST equivalent to the corresponding bookies' odds, in order to be given those odds in the true odds column.

Here's a simple example.

A horse rated 0.2 counts as a 4/1 shot
A horse rated 0.222 counts as a 7/2 shot

BUT a horse rated 0.214 (which means that its true odds are slightly shorter than 4/1) still counts as a 4/1 shot.

That's because 0.214 is less than 0.222, although it's obviously more than 0.2 Don't forget, the horse HAS to score a minimum of 0.222 to be rated a 7/2 shot.

JUDGE AND JURY
So in ranking horses for the purpose of determining the top three, I have always used the following principles:

1. The true odds column is judge and jury when determining a horse's rank. Thus two horses which appear in the TR_ODDS column as 3/1 shots are joint-rated, EVEN IF they have slightly different probability scores in the TR_PROB column.

2. Where horses are joint-ranked n, the horse or horses immediately below them are ranked n + 1.

Thus if there are two or more top-ranked horses, rated at, say, 9/4 true odds, and the next horse down is rated 3/1, that horse is ranked second.

If there are two or more top-ranked horses on 9/4, and two or more horses immediately below them on 3/1, and the next horse down is rated 5/1, then that horse is ranked third.

This can lead to a situation in which there are several horses in the top three.

Where this happens, it generally indicates that the race concerned is extremely tight and trappy, and that there are many with realistic chances.

It tends to entail more races in which one is obliged to back two or three in order to cover all potential value bets, with a corresponding increase in the number of losers. But by the same token, it has thrown up some incredible winners at huge prices which have more than covered the losses.

Here are some illustrative examples from a previous season's ratings:

Cheltenham:3.35
Handicap chase:13 rnrs
HORSE                TR-PROB TR-ODDS   V-30  V-PLUS
Whereareyounow(IRE)    0.158   11-2    17-2   11-1          Joint top-rated
Kelrev(FR)             0.156   11-2    17-2   11-1          Joint top-rated
Hand Inn Hand          0.109   17-2    14-1   18-1          Second-rated
Telemoss(IRE)          0.09    11-1    16-1   22-1          Joint third-rated
Hunters Tweed          0.084   11-1    16-1   22-1          Joint third-rated

...8 other runners rated below the top three

Cheltenham:4.10
Handicap hurdle:15 rnrs
HORSE                TR-PROB TR-ODDS   V-30  V-PLUS
Demi Beau              0.236   10-3    11-2    7-1          Top-rated
Distant Prospect(IRE)  0.099   10-1    14-1   20-1          Joint second-rated
Mambo(IRE)             0.091   10-1    16-1   20-1          Joint second-rated
Sud Bleu(FR)           0.084   11-1    16-1   22-1          Third-rated

...11 other runners rated below the top three

For the record, I frequently back two, and occasionally more in a race if they qualify as either v-30 or v-plus value bets.

Some people don't like this way of defining the top three, and I can see the attraction of applying rules for rank ordering which are, mathematically speaking, much more rigorous, and which lead to far fewer joint rankings.

My feeling in this case is that if someone uses a different system for rank ordering, and it works for them, then that's fine. There are only two things that count in this game. One is obviously the bottom line at the end of the season. The other is confidence in one's methods - the sort of confidence that enables one to ride out the really bad patches which inevitably occur from time to time.

WHAT OF THE COMING SEASON?
I must confess, as another full season on Betfair draws to a close, to being in something of a quandary. Betfair's scale of odds, although discrete, is more fine-grained than that used by traditional bookmakers. But the output from the HOOF program is still geared to transforming probabilities into traditional bookmakers' odds.

I'm also conscious of the fact that subscribers are using the ratings in different ways, with laying, place betting, and dutching regularly featuring in HOOF forum discussions.

As I said earlier, I tend to be conservative, and believe quite strongly that 'if it ain't broke, don't fix it'. In particular, I'm acutely aware of the fact that any change in the way I transform probabilities into odds will have a knock-on effect on rank ordering, with unknown consequences on the overall profitability of the ratings when the final audit is drawn up.

For the time being therefore, in defining the top three rated, I shall continue to use the criteria that have been in force for the past ten years.