Please note I did not write this but I found it very interesting.
Extract from
http://sportales.com/equestrian/chaos-theory-and-the-strike-rate-of-horse-racing-selection-systems/I have been monitoring a large number of horseracing selection systems for an extended period of time. Although some are my invention, most are the creation of others. I have found them all to be cyclic with respect to their short-term strike rates in that they, alternatively, go through winning and losing periods. During their losing periods, the selection systems lose at least as much as they win during their winning periods. Over the long-term, all of the systems would break even if it wasn’t for the bookmaker’s over-round or betting exchange’s commission. Once when the bookmaker’s over-round and the betting exchange’s commission have been taken into account, however, all system’s lose long term.
Let us consider the cyclic nature of systems.
Why?
Because if we can anticipate when a system’s losing periods will begin, we will then be in a position to avoid them. This will allow us to only place bets during periods when the system is most likely to win and to thus make a profit from our betting activities.
Now, we would expect a selection system to be cyclic with regard to the short-term strike rate.
Why?
Because it would be unreasonable to expect that the short-term strike rate of a system is static. It is therefore reasonable to expect some variation.
Let us suppose that the short-term strike rate increases until it reaches 100% and remains there.
Would this be reasonable?
No.
Why?
Because it would result in an increase in the long-term strike rate of the system. Such a rise isn’t likely because the long-term strike rate is determined by the average odds of the selections generated by the system. This is because betting exchange markets are approximately perfect. Since the average odds of the selections generated by a system remain fairly constant, the long-term strike rate must also remain fairly constant. Therefore, if the short-term strike rate of a system begins to increase, there will be a tendency for it to decrease in the near future in order that the long-term strike rate is maintained.
Let us now suppose that the short-term strike rate of the system decreases until it reaches 0% and remains there.
Would this be reasonable?
No.
Why?
Because it would result in a decrease in the long-term strike rate of the system. Such a fall isn’t likely because the long-term strike rate is determined by the average odds of the selections generated by the system. This is because betting exchange markets are approximately perfect. Since the average odds of the selections generated by a system remain fairly constant, the long-term strike rate must also remain fairly constant. Therefore, if the short-term strike rate of a system begins to decrease, there will be a tendency for it to increase in the near future in order that the long-term strike rate is maintained.
So, from the above, in theory at least, the most likely behaviour that we would expect to see in the short-term strike rate of a system is cyclic i.e. sinusoidal – a steady and periodic rise and fall in the system’s short-term strike rate. This behaviour is approximately in-keeping with Mean Reversion theory which states that the short-term mean has a tendency to gravitate towards the long-term mean. The Mean, in this case, is the short-term strike rate of a system.
In practice, we do observe a rise and fall in the short-term strike rate of a system but it only approximates to sinusoidal behaviour. The reason for stating that it only approximates to sinusoidal behaviour is that if the short-term strike rate were perfectly sinusoidal, the short-term strike rate peaks and troughs would be equally spaced and of equal height. If this were the case, then a system would be perfectly predictable. Sadly, the peaks and troughs are un-equally spaced and are of un-equal heights. As such, a system is not perfectly sinusoidal and therefore not predictable.
Now, if the short-term strike rate of a system does obey the principles of Mean Reversion, then we would expect to see the short-term strike rate fall only after it has risen above its respective long-term strike rate. Likewise, we would only expect to see the short-term strike rate of system increase after it has fallen below its respective long-term strike rate. In practice, and in general, both of these traits are observed.
So, let’s recap: A system’s strike rate is approximately sinusoidal but irregularly so. The irregularity prevents us from profiting from our betting activities since irregularity implies unpredictability and unpredictability isn’t conducive with profiting from betting activities. However, the behaviour of a system’s strike rate is largely in keeping with Mean Reversion theory. Therefore, to some extent, at least, we are able to determine, approximately, when a system’s strike rate is likely to go into decline. As a result, we are able to avoid at least some losing periods at least some of the time. This avoidance of losing periods may give us an edge such that we are able to make a profit from our betting activities.
Now, this is where I put an off-the-wall theory on the table for discussion and possible further investigation by those who have a mind to.
When the short-term strike rate of a typical system is plotted against time, we find that there are periods when the short-term strike rate increases uniformly, there are periods when the short-term strike rate decreases uniformly and there are periods when the short-term strike rate becomes somewhat erratic. Now, although this behaviour may be typical of a random system, it is also typical of a Chaotic behaviour as well.
For those who are not familiar with Chaos, Chaotic behaviour and Chaos theory, it is the identification of order in data which appears to be random. Chaotic behaviour was first identified and studied by Edward Lorenz in 1961 whilst he was working on the problem of weather prediction.
If the short-term strike rates for a large number of selection systems are plotted against time, although the graphs obtained are all different, they are also somewhat similar in that the behaviour that they display is very similar. The graphs all depict periods when the short-term strike rate increases uniformly, periods when the short-term strike rate decreases uniformly and periods when the short-term strike rate becomes somewhat erratic.
From Chaos theory, we know that if a system is chaotic, rather than random, then the equation which gives rise to, and controls the phenomenon, has a ‘sensitive dependence on the initial conditions’. In other words, even if the initial conditions are changed only slightly, its behaviour, over time, is vastly different to the behaviour that it would have displayed had the initial conditions not been changed.
Now, we know that every selection system behaves differently. However, this would be allowed under Chaos theory because the differing behaviour of differing systems could be due to differing initial conditions that each system is subject to. This opens up the possibility that even though differing systems behave differently, they may all be subject to the same mathematical equation and the differing behaviour is due to the differing initial conditions for each of the differing systems.
Another feature of Chaos theory is that there may be attractors associated with Chaotic behaviour. This phenomenon was first observed by Lorenz. Basically, it is a point about which the chaotic behaviour oscillates. In the case of our selection systems’ strike rates, the attractor may well be their respective long-term strike rates about which the short-term strike rate oscillates.
So, there we have it. It is entirely possible that the behaviour of the short-term strike rate of a system may not be random. It may, in fact, be Chaotic.
If this is the case, then all we have to do is to identify an equation that mimics the behaviour of our system and then use it to predict its future behaviour. I say ‘all we have to do’ with my tongue firmly in my cheek. I’ve been working on the problem for ‘quite some time’ and have got precisely nowhere.
This could mean that, although selection systems do behave chaotically, I am not a sufficiently good mathematician to identify an equation which mimics their behaviour. On the other hand, selection systems may be, for all intents and purposes, purely random. If this is the case, then not only have I wasted a good deal of my time, there is no way that we could profit from using a selection system of any kind.
