Friday, 25 February 2011

Bounce Theory

In Britain and Ireland, a horse having its second run after a lengthy absence is sometimes referred to as a "bounce candidate". The concept is that freshness may have caused overexertion last time, leaving it sore and vulnerable to running poorly today.

Though some horses undoubtedly fit this pattern, the evidence may be just circumstantial. Horses with a history of absences from the track often have chronic physical problems which will resurface sooner or later. But they may not be affected on the second run back, it could just as easily happen on the third run, fourth run or later.

Not surprisingly, those who have investigated this particular "bounce" have found statistical support hard to find.

But the bounce theory as a holistic concept has little in common with this particular usage. Instead, it may be thought of as just a theoretical basis to understand the variance of racehorse performance over time.

All performance figures are affected by the randomness inherent in a race. A horse may get the ground or pace which suits it one day, but the next it may end up drawn badly or the victim of bad racing luck.

Some of these factors are obvious just by watching the race. But there is also an undercurrent of randomness in the physical state of any living being - just by dint of the fact that its health and wellbeing vary from day to day.

While handicappers have traditionally made great effort to improve and maintain the accuracy of their ratings, not until recently have some begun to investigate how past figures actually predict performance.

Phrased more technically, these far-sighted analysts have asked the question of the optimal weighting to apply to each particular rating in the array of a horse's past performances.

How much does recency matter? To what extent should we favour the consistency of an inferior horse over the peak ability of a superior one?

Many of these questions can be answered by sophisticated statistical techniques and neural networks. These powerful methods lie behind the great success of some of the most technically minded punters out there.

But what can we derive from the data that is useful to apply for those who don't have access to such information? How can we conceptualise the potential for variance in a horse's ratings over time - without using correlation coefficients or regression equations?

The bounce theory.

Because of the randomness of races and the varying physical state of racehorses, the performance rating of a horse in any particular race is just one expression of a whole array of figures it might have produced on the day.

So, the chance of it reproducing the figure depends on the the degree to which it was representative of the horse's mean output - at that specific point of its career.

When we look back at a video of the horse's last race, or consider the facts surrounding it, it may be totally obvious that its performance was a fluke. The horse may have benefited from a superior ride or raced on a favourable part of the track or lucked out in some other way.

But we don't necessarily have to know this. Neither does it have to be obvious. Instead, we could look back at its previous performances and infer that the latest might be aberrant because it is significantly different in merit.

In these circumstances, it is reasonably to expect that the horse will regress to a mean-level performance more often than not - that it will return to running to a figure closer to that which it had previously established as representative.

It is hugely important to understand that the use of the word "regression" in a mathematical context does not necessarily  have a negative connotation. The bounce theory also applies to a horse whose recent run was poorer than reasonable expectation; in this case, we might expect it to "bounce back to form". (Or, strictly speaking, towards form.)

Expressed formally, the bounce theory may be stated thus: "The tendency of a racehorse's performance level to regress to its notional mean."

The key word in this description of the bounce theory is "notional". A racehorse's career develops differently according to many factors, of which its age and experience are the most influential.

So, its mean, or expected performance level cannot be calculated by taking the average of its last three runs, or some other clumsy stricture.

Instead, the performance level of racehorses in general will change over time according to an age/experience curve: younger, inexperienced horses get better, older ones are more consistent or begin to decline.

While neural networks and techniques such as Markov chain analysis enable us to reach an estimate of a horse's likely performance by mathematical methods, this can still be limiting. There are many influences which defy strict statistical interpretation, such as how the trainer regards it or whether today's race is a particular target, for example.

Instead of getting bogged down in data analysis, many less technically oriented punters can use the bounce theory merely as a guiding principle; they can simply think of a racehorse's ratings as a notional progression.

When any of its performances depart sharply from reasonable expectation, a "bounce" or regression can be expected. In other words, the evidence of a horse's most recent run can be put into its proper context and seen just as a single point on the "best-fit line" of its career trajectory.

Of course, many intelligent punters already use the bounce theory. They just don't formalise it as such, or refer to it by name.

In essence, the bounce theory is a framework which encourages you to think in terms of expectation. And not to rely too much on the evidence of a horse's recent race, especially when you believe it was not truly representative.