Random Test Quiniela

HURST IN THE 1X2 QUINIELA

I did a randomness test in the pool using the Hurst exponent, the theory says:

H = Hurst

H = 0.5 A process that falls within this equivalence class is a random and uncorrelated process, where the future is not influenced by what happens in the present. For example, when you flip a coin and have 2 options (heads or tails).

H <0.5 an anti-persistent or random process, in which there is a tendency of the values ​​that the process takes to compensate each other. The intensity of this anti-persistent behavior will depend on how close the value of H is to zero. Due to their behavior, the time series of this type of process can be more volatile than a random series. ex. Lotto.

H> 0.5 A persistent or fractal process, in which the values ​​taken by the process tend to reinforce the current trend, that is, if the trend of the time series has been positive in the last period observed, it is easier than this The trend continues to be positive than negative in the following period. The intensity of persistent behavior increases when H approaches one, and it is this long-term memory effect that causes the appearance of trends and cycles in the process. The greater the probability that the next member exhibits the current trend.

For this test I converted the history of the Spain 1, X or 2 league from 14 matches to 42 numbers using the history of 2181 pools of PacoHH until day 34 of 2006.

1 X 2
1 2 3
4 5 6
7 8 9
10 11 12
13 14 15
16 17 18
19 20 21
22 23 24
25 26 27
28 29 30
31 32 33
34 35 36
37 38 39
40 41 42

To obtain the Hurst exponent, use the Fractan 4.4 program.


Result:

The Quiniela 1x2 Hurst exponent,

H = 0.7062 +/- 0.2093


H> 0.5 There is a tendency in the pool, which persists in time and there is a structure in the system. The pools are fractal series that follow a skewed random walk where today's winning results may continue to affect future results for many periods.

The presence of persistence in the pool means that football matches have a behavior of reinforcing past trends.

The fractal dimension of the pool is 2-H = 1.2938 +/- 0.2093

A time series will be more irregular (random) if its fractal dimension approaches 2.

The standard deviation.

"The standard deviation measures the probability that an observation is at a certain distance from the average, the greater this number, the greater the dispersion." Great dispersion means that the asset (investing in pools) is risky.

However, the standard deviation as a dispersion measure is only valid if the system is completely random. If the observations are correlated (As in the case of the pool), then the utility of the standard deviation as a measure of dispersion is considerably weakened. "

The standard deviation of the history of the pool you use is 12.1271.

Kurtosis negative history (platykurtic) -1.2012

Skewness of the history 0.0007


GIVE IT TO THE RANDOM

To continue with the experiment, generate in excel 2182 pools at random, that is, each of the 14 parties has the same probability of sign 1, X or 2.

If the results of the games of the pool were random then the Hurst exponent after 2182 pools would be around:

H = 0.3044 = / - 0.1125

Fractal dimension 2-H = 1.6956 +/- 0.1125

The standard deviation of the 2182 random pools is 12,124, the skewness is 0.0011 and the negative kurtosis -1.1987, these 3 tests have similar results to the history, so we do not differentiate the samples.


It can be concluded by the Hurst exponent that the 1x2 Spain Quiniela does not behave as if it were random (H <0.5).