Simon Rowlands / 05 January 2010 Free Bet View Market

"The likelihood of good horses being in adjacent boxes is anything but random. Good horses go to good trainers, who often turn them into even better horses. Those trainers may even choose to stable their very best horses next to each other, for practical or sentimental reasons."

One interesting consequence of Kauto Star's brilliant victory in the King George VI Chase at Kempton on Boxing Day has been the revival of the "is he better than Arkle?" debate.

Arkle rewrote the record books in the mid-1960s, when he won three consecutive Cheltenham Gold Cups and put up several astonishing performances in handicaps. He is the jumper against which all other great jumpers since have been compared, and have been found wanting to date.

Greg Wood dealt with the subject on The Guardian website but managed to prove little, other than that journalists - even excellent ones, as Wood usually is - should stick to writing about what they understand.

Wood's assertion that "it is many millions-to-one against" the two best chasers in history occupying adjacent boxes betrays an ignorance of basic probability theory. There has to be a "best" chaser in history, so the question is only whether the "second-best chaser" happens to be berthed next to him.

The calculation is (1*(n-1)), and not (n*(n-1)), where "n" is the population of chasers in history, assuming that the likelihood of one good chaser being next to another good chaser is entirely random. The difference for a population of 300,000 of such an error is that between 299,999 to one and nearly 90 billion to one.

And, of course, the likelihood of good horses being in adjacent boxes is anything but random. Good horses go to good trainers, who often turn them into even better horses. Those trainers may even choose to stable their very best horses next to each other, for practical or sentimental reasons.

Readers seeking an illustration of this need look no further than Kauto Star himself and Denman. They are the two best jumpers of the last 20 years, they are both trained by Paul Nicholls, the best trainer of the last 20 years, and they live next to one another. A many millions-to-one chance? No.

Wood may have a wider point that the rating of Arkle deserves further scrutiny. But whether Phil Smith is the right man for the job deserves to be questioned.

I e-mailed Smith asking him for a fuller explanation of his methodology, but, at the time of writing, have not received a reply. I can only infer from his public utterances how he goes about doing his job, and I have to say I am not impressed.

In particular, his blog on the BHA website contains repeated references to "yardsticks" and of rating races "through" given horses. This type of handicapping - often described as "yardstick handicapping" - is limited, to say the least.

Smith, as a former mathematics teacher, should know very well that extrapolation from an individual to a larger population is a much riskier business than the reverse process of interpolation from a larger population to an individual.

"Extrapolation error", as it is known, is the main reason why yardstick handicapping is fundamentally flawed. No-one can be trusted to guess which horse the yardstick should be with the kind of accuracy that is being sought. Indeed, given how dynamic a horse's ability is under different circumstances, it is entirely possible that NO horse in a given race has run to the precise level it had run to previously, no matter how much we might wish it otherwise.

It is far better, as a general approach, to establish a race's overall strength in the context of the wider horse population and to allow that - and the result - to guide the assessments of performances of individual horses within that race. This is basic handicapping theory, not to mention plain common sense.

Take this season's King George VI Chase as an example. Using Timeform's ratings and differences at the weights as a guide, Kauto Star could have been rated as running to anything between 184 (with only him running to form) and 231 (with Ollie Magern running to his previous rating).

More realistically, Kauto Star would have run to 184, 200, 188 or 196, depending on which of the first four was assumed to be a true "yardstick". Now, that degree of variation, and the subjectivity it lends itself to, does not exactly inspire confidence!

Consider the alternatives, which include race standardisation - whereby the usual or expected strength of a race is adjusted for conditions, field size, margins between horses and so on - and assessments based on the prior ratings of all of the principals rather than of just one.

Both processes can be tested against the results of countless races, not just one, and shown to be accurate to an acceptable level. And both processes result in figures for Kauto Star that are in the region of the 191 rating Timeform awarded him, without any horse being used as a "marker".

It is disturbing that anyone in a position of seniority in handicapping circles should appear to be ignorant of such fundamentals. But I suspect it won't stop Smith making a song and dance about what he considers to be the "correct" assessment of a horse that ran nearly half a century ago.

* * *

Far removed from the stratospheric heights of Arkle and Kauto Star, my filly King's Miracle gets to run off a mark of just 48 at Kempton on Thursday.

From the outside, it may look as if she has been "plotted up" for the race, after three runs in maidens. The truth is that she ran so badly last time, and seemed so out of love with the game, that retirement was the favoured option for a while.

Hopefully she will show that it was worth giving her one last chance off a basement mark, but I will be watching with my fingers crossed rather than with them wrapped round a betting ticket.